NEUTROSOPHY, NEUTROSOPHIC LOGIC, NEUTROSOPHIC SET,

NEUTROSOPHIC PROBABILITY AND STATISTICS

(philosophy, math, science)


Short Definitions of Neutrosophics:   

    1. Neutrosophic Logic is a general framework for unification of many existing logics, such as fuzzy logic (especially intuitionistic fuzzy logic), paraconsistent logic, intuitionistic logic, etc.  The main idea of NL is to characterize each logical statement in a 3D Neutrosophic Space, where each dimension of the space represents respectively the truth (T), the falsehood (F), and the indeterminacy (I) of the statement under consideration, where T, I, F are standard or non-standard real subsets of ]-0, 1+[ with not necessarily any connection between them.

For software engineering proposals the classical unit interval [0, 1] is used.

For single valued neutrosophic logic, the sum of the components is:

0 t+i+f 3 when all three components are independent;

0 t+i+f 2 when two components are dependent, while the third one is independent from them;

0 t+i+f 1 when all three components are dependent.

When three or two of the components T, I, F are independent, one leaves room for incomplete information (sum < 1), paraconsistent and contradictory information (sum > 1), or complete information (sum = 1). 

If all three components T, I, F are dependent, then similarly one leaves room for incomplete information (sum < 1), or complete information (sum = 1). 

In general, the sum of two components x and y that vary in the unitary interval [0, 1] is: 0 ≤ x+y ≤ 2 – d°(x,y), where d°(x,y) is the degree of dependence between x and y, while –d°(x,y) is the degree of independence between x and y.

In a general Refined Neutrosophic Logic, T can be split into subcomponents T1, T2, ..., Tp, and I into I1, I2, ..., Ir, and F into F1, F2, ...,Fs, where p+r+s = n ≥ 1.  Even more: T, I, and/or F (or any of their subcomponents Tj ,Ik, and/or Fl) can be countable or uncountable infinite sets.

As a particular case, one can split the Indeterminate I into Contradiction (true and false), and Uncertainty (true or false), and we get an extension of Belnap's four-valued logic.

Even more, one can split I into Contradiction, Uncertainty, and Unknown, and we get a five-valued logic.

See this most general published case here.

As an example: a statement can be between [0.4, 0.6] true, {0.1} or between (0.15,0.25) indeterminate, and either 0.4 or 0.6 false.

                    The distinctions between Neutrosophic Logic/Set and Intuitionistic Fuzzy Logic/Set are here.

    2. Neutrosophic Set.  Let U be a universe of discourse, and M a set included in U.  An element x from U is noted with respect to the set M as x(T, I, F) and belongs to M in the following way:  it is t% true in the set, i% indeterminate (unknown if it is) in the set, and f% false, where t varies in T, i varies in I, f varies in F.

Statically T, I, F are subsets, but dynamically T, I, F are functions/operators depending on many known or unknown parameters.

Neutrosophic Set generalizes the fuzzy set (especially intuitionistic fuzzy set), paraconsistent set, intuitionistic set, etc.

     3. Neutrosophic Probability is a generalization of the classical probability and imprecise probability in which the chance that an event A occurs is t% true - where t varies in the subset T, i% indeterminate - where i varies in the subset I, and f% false - where f varies in the subset F. 

In classical probability n_sup <= 1, while in neutrosophic probability n_sup <= 3+.

In imprecise probability: the probability of an event is a subset T in [0, 1], not a number p in [0, 1], what’s left is supposed to be the opposite, subset F (also from the unit interval [0, 1]); there is no indeterminate subset I in imprecise probability.

                    A book on Introduction to Neutrosophic Probability is here.

    4. Neutrosophic Statistics is the analysis of events described by the neutrosophic probability.

The function that models the neutrosophic probability of a random variable x is called neutrosophic distribution: NP(x) = ( T(x), I(x), F(x) ), where T(x) represents the probability that value x occurs, F(x) represents the probability that value x does not occur, and I(x) represents the indeterminate / unknown probability of value x.

                    A book on Introduction to Neutrosophic Statistics is here.

    5. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.

This theory considers every notion or idea <A> together with its opposite or negation <antiA> and with their spectrum of neutralities <neutA> in between them (i.e. notions or ideas supporting neither <A> nor <antiA>). The <neutA> and <antiA> ideas together are referred to as <nonA>. Neutrosophy is a generalization of Hegel's dialectics (the last one is based on <A> and <antiA> only).

According to this theory every idea <A> tends to be neutralized and balanced by <antiA> and <nonA> ideas - as a state of equilibrium.

In a classical way <A>, <neutA>, <antiA> are disjoint two by two.

But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that <A>, <neutA>, <antiA> (and <nonA> of course) have common parts two by two, or even all three of them as well.

The Lupasco-Nicolescu’s Law of Included Middle [<A>, <nonA>, and a third value <T> which resolves their contradiction at another level of reality] is generalized to the Law of Included Multiple-Middle [<A>, <antiA>, and <neutA>, where <neutA> is split into a multitude of neutralities between <A> and <antiA>, such as <neut1A>, <neut2A>, etc.]. The <neutA> value (i.e. neutrality or indeterminacy related to <A>) actually comprises the included middle value. Also the Principle of Dynamic Opposition [opposition between <A> and <antiA>] is extended to the Principle of Dynamic Neutrosophic Opposition [which means oppositions among <A>, <antiA>, and <neutA>]. This book is here.

Neutrosophy is the base of neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics that are used in engineering applications (especially for software and information fusion), medicine, military, airspace, cybernetics, physics.

The neutrosophics were introduced by Florentin Smarandache in 1995.

                    An article on Neutrosophy, A New Branch of Phylosophy is here.

 The most important books and papers in the development of neutrosophcis

     

 

1995-1998 - introduction of neutrosophic set/logic/probability/statistics;

                     generalization of dialectics to neutrosophy;

http://fs.gallup.unm.edu/eBook-neutrosophics5.pdf (5th edition)

 

2003 – introduction of neutrosophic numbers (a+bI, where I = indeterminacy)

2003 – introduction of I-neutrosophic algebraic structures

2003 – introduction to neutrosophic cognitive maps

http://fs.gallup.unm.edu/NCMs.pdf

 

2005 - introduction of interval neutrosophic set/logic

http://fs.gallup.unm.edu/INSL.pdf

 

2006 - introduction of the degree of dependence and degree of independence

           between the neutrosophic components

http://fs.gallup.unm.edu/eBook-neutrosophics5.pdf (5th edition)

 

2009 – introduction of N-norm and N-conorm

http://fs.gallup.unm.edu/N-normN-conorm.pdf

 

2013 - development of neutrosophic probability
           (chance that an event occurs, indeterminate chance of occurrence,

           chance that the event does not occur)

http://fs.gallup.unm.edu/NeutrosophicMeasureIntegralProbability.pdf

 

2013 - refinement of components (T1, T2, ...; I1, I2, ...; F1, F2, ...)

http://fs.gallup.unm.edu/n-ValuedNeutrosophicLogic.pdf

 

2014 – introduction of the law of included multiple middle

(<A>; <neut1A>, <neut2A>, …; <antiA>)

http://fs.gallup.unm.edu/LawIncludedMultiple-Middle.pdf

 

2014 - development of neutrosophic statistics (indeterminacy is introduced into classical statistics with respect to the sample/population, or with respect to the individuals that only partially belong to a sample/population)

http://fs.gallup.unm.edu/NeutrosophicStatistics.pdf

 

2015 - introduction of neutrosophic precalculus and neutrosophic calculus

http://fs.gallup.unm.edu/NeutrosophicPrecalculusCalculus.pdf

 

2015 – refined neutrosophic numbers (a+ b1I1 + b2I2 + … + bnIn)

2015 – neutrosophic graphs

2015 - Thesis-Antithesis-Neutrothesis, and Neutrosynthesis, Neutrosophic Axiomatic System, neutrosophic dynamic systems, symbolic neutrosophic logic, (t, i, f)-Neutrosophic Structures, I-Neutrosophic Structures,  Refined Literal Indeterminacy, Multiplication Law of Subindeterminacies:  http://fs.gallup.unm.edu/SymbolicNeutrosophicTheory.pdf

BOOKS ON NEUTROSOPHICS

bullet Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability new  
bullet Introduction to Neutrosophic Statistics new  
bullet Neutrosophic Precalculus and Neutrosophic Calculus very new  
bullet Symbolic Neutrosophic Theory very new  
bullet Law of Included Multiple-Middle & Principle of Dynamic Neutrosophic Opposition  
bullet Neutrosophic Graphs: A New Dimension to Graph Theory  
bullet Soft Neutrosophic Algebraic Structures and Their Generalization (Vol. 1, Vol. 2)  
bullet New Research on Neutrosophic Algebraic Structures  
bullet Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models  
bullet New Techniques to Analyse the Prediction of Fuzzy Models  
bullet Algebraic Structures on Fuzzy Unit Square and Neutrosophic Unit square  
bullet Algebraic Structures on Real and Neutrosophic Semi Open Squares  
bullet Finite Neutrosophic Complex Numbers  
bullet Neutrosophic Interval Bialgebraic Structures  
bullet Neutrosophic Bilinear Algebras and Their Generalizations Interval Groupoids  
bullet Neutrality and Many-Valued Logics
bullet Neutrosophy in Arabic Philosophy
bullet الفلسفة العربية من منظور نيوتروسوفيالفلسفة العربية من منظور نيوتروسوفي ( صــــــــلاح   عثمـــــانصــــــــلاح   عثمـــــان ,  فلورنتن سمارانداكهفلورنتن سمارانداكه ) [Arabic]
bullet Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps
bullet Fuzzy Relational Maps and Neutrosophic Relational Maps
bullet Analysis of Social Aspects of Migrant Labourers Living with HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps
bullet Smarandache Neutrosophic Algebraic Structures
bullet Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models
bullet Fuzzy Neutrosophic Models for Social Scientists
bullet Neutrosophic Rings
bullet Infinite Quaternion Pseudo Rings Using [0, n)  
bullet Interval Groupoids
bullet Neutrosophic Crisp Set Theory
bullet A Unifying Field in Logics: Neutrosophic Logic.  Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics (fifth edition)
bullet Сущность нейтрософии; Смарадаке Ф.(перевод Д. Рабунского)[Russian]
bullet 逻辑学的统一:中智逻辑  中智学,中智集合论,中智概率论 (Chinese) [1, 2]
bullet 中道辩证法与唯道主义自然哲学[Chinese Neutrosophy and Taoist Natural Philosophy](Chinese)
bullet Neutrosophic Interpretation of Tao Te Ching (道德经的中智学解读和扩充 ?正反及中智道德经) [English-Chinese]
bullet Neutrosophic Interpretation of The Analects of Confucius 弗羅仁汀·司馬仁達齊,傅昱華 論語的中智學解讀和擴充 —正反及中智論語 English-Chinese Bilingual(英汉双语 )  
bullet Neutrosofia ca reflectarea a realităţii neconvenţionale [Romanian]  
bullet Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics
bullet Proceedings of the Introduction to Neutrosophic Physics: Unmatter & Unparticle International Conference
bullet Introduction to Neutrosophic Logic
bullet Interval Neutrosophic Sets and Logic: Theory and Applications in Computing
bullet Neutrosophic Dialogues
bullet Neutrosophic Emergences and Incidences in Communication and Information
bullet Communication Neutrosophic Routes
bullet Topical Communication Uncertainties
bullet Introduction to Bimatrices
bullet Applications of Bimatrices to some Fuzzy and Neutrosophic Models
bullet Fuzzy Interval Matrices and Neutrosophic Interval Matrices and their Applications
bullet Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists
bullet Special Fuzzy Matrices for Social Scientists
bullet Methods in Industrial Biotechnology for Chemical Engineers
bullet Introduction to Linear Bialgebra
bullet Euclid Squares on Infinite Planes
bullet Uncertainty Communication Solution in Neutrosophic Key
bullet Fuzzy and Neutrosophic Analysis of Women with HIV/AIDS
bullet Fuzzy and Neutrosophic Analysis of Periyar's Views on Untouchability
bullet Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures
bullet Neutrosophic Super Matrices and Quasi Super Matrices
bullet Vedic Mathematics - 'Vedic' or 'Mathematics': A Fuzzy & Neutrosophic Analysis
bullet Proceedings of the First International Conference on Smarandache Multispace & Multistructure
bullet Nidus Idearum de Neutrosophia (blog)
bullet Neutrosophic Logic, Wave Mechanics, and Other Stories (Selected Works 2005-2008)
bullet Neutrosophic Physics: More Problems, More Solutions (Collected Papers)
bullet Unmatter Plasma, Relativistic Oblique-Length Contraction Factor, Neutrosophic Diagram and Neutrosophic Degree of Paradoxicity new
bullet Neutrosophic Theory and its Applications, Vol. 1

 

Ph. D. Dissertations on Neutrosophic Logic/Set/Probability/Statistics and their Applications:

bullet Eng. Stefan Adrian Dumitru, Contributii in dezvoltarea sistemelor de control neuronal al miscarii robotilor mobili autonomi, adviser Dr. Luige Vlădăreanu, Institute of Solid Mechanics, Romanian Academy, Bucharest, 25 September, 2014.
bullet Eng. Dănuț Adrian Bucur, Contribuţii în controlul mișcării sistemelor de prehensiune pentru roboți și mâini umanoide inteligente, adviser Dr. Luige Vlădăreanu, Institute of Solid Mechanics, Romanian Academy, Bucharest, 25 September, 201 4.
bullet Eng. Daniel Octavian Melinte, Cercetari teoretice si experimentale privind controlul sistemelor mecanice de pozitionare cu precizie ridicata, advisers Dr. Luige Vlădăreanu & Dr. Florentin Smarandache, Institute of Solid Mechanics, Romanian Academy, Bucharest, September 2014 .
bullet Eng. Ionel Alexandru Gal, Contributions to the Development of Hybrid Force-Position Control Strategies for Mobile Robots Control, advisers Dr. Luige Vlădăreanu & Dr. Florentin Smarandache, Institute of Solid Mechanics, Romanian Academy, Bucharest, October 14, 2013.
bullet Smita Rajpal, Intelligent Searching Techniques to Answer Queries in RDBMS, Ph D Dissertation in progress, under the supervision of Prof. M. N. Doja, Department of Computer Engineering Faculty of Engineering, Jamia Millia Islamia, New Delhi, India, 2011.
bullet Josué Antonio Nescolarde Selva, A Systematic Vision of Belief Systems and Ideologies, under the supervision of Dr. Josep Llus Usó I Domènech, Dr. Francesco Eves Macià, Universidad de Alicante, Spain, 2010.
bullet Ming Zhang, Novel Approaches to Image Segmentation Based on Neutrosophic Logic, Ph D Dissertation, Utah State University, Logan, Utah, USA, All Graduate Theses and Dissertations, Paper 795, http://digitalcommons.usu.edu/etd/795, 12-1-201, 2010.
bullet Haibin Wang, Study on Interval Neutrosophic Set and Logic, Georgia State University, Atlanta, USA, 2005.
bullet Sukanto Bhattacharya, Utility, Rationality and Beyond - From Finance to Informational Finance [using Neutrosophic Probability], Bond University, Queensland, Australia, 2004.

International Conferences on Neutrosophics:

International Conference on Information Fusion, Tutorial on Foundations of Neutrosophic Set and Logic and Their Applications to Information Fusion, by F. Smarandache, 7th July 2014, Salamanca, Spain.

International Conference on Applications of Plausible, Paradoxical, and Neutrosophic Reasoning for Information Fusion, Cairns, Queensland, Australia, 8-11 July 2003.

First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and Statistics, University of New Mexico, Gallup Campus, 1-3 December 2001.  

Seminars

Foundations of Neutrosophic Logic and Set Theory and their Applications in Science. Neutrosophic Statistics and Neutrosophic Probability. n-Valued Refined Neutrosophic Logic, by F. Smarandache, Universidad Complutense de Madrid, Facultad de Ciencia Matemáticas, Departamento de Geometría y Topología, Instituto Matemático Interdisciplinar (IMI), Madrid, Spain, 9th July 2014.

Tutorial

Tutorial on the Foundations of Neutrosophic Logic and Set and their Applications in Science

Articles on Neutrosophics:

bullet Interval Neutrosophic Sets and its Application in Multi-criteria Decision Making Problems, by Zhang Hongyu, Jian Qiang Wang, and Xiao-hong Chen, The Scientific World Journal, 2013.
bullet Neutrosophic information in the framework of multi-valued representation, by Vasile Patrascu, CAIM, Romanian Society of Applied and Industrial Mathematics et al., 19-22 September 2013, Bucharest, Romania.
bullet N-norm and N-conorm in Neutrosophic Logic and Set, and the Neutrosophic Topologies (2005), in Critical Review, Creighton University, Vol. III, 73-83, 2009.
bullet n-ary Fuzzy Logic and Neutrosophic Logic Operators, by F. Smarandache, V. Christianto, in arXiv.org, and in <Studies in Logic Grammar and Rhetoric>, Belarus, 17 (30), 1-16, 2009.
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Neutrosophic Logic and Set, and Paradoxes chapters by F. Smarandache, V. Christianto, F. Liu, Haibin Wang, Yanqing Zhang, Rajshekhar Sunderraman, André Rogatko, Andrew Schumann, in Multispace & Multistructure. Neutrosophic Transdisciplinarity, NESP, Finland, pp. 395-548 and respectively 604-631, 2010.

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The Fifth Function of University: “Neutrosophic E-function” of Communication-Collaboration-Integration of University in the Information Age, by F. Smarandache, S. Vlăduţescu

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The Neutrosophic Research Method in Scientific and Humanistic Fields, by Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 732-733, 2010.

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Single Valued Neutrosophic Sets, by Haibin Wang, Florentin Smarandache, Yanqing Zhang, Rajshekhar Sunderraman, in Multispace and Multistructure, Vol. 4, 410-413, 2010.

bullet Neutrosophic Soft Set, by Pabitra Kumar Maji, Annals of Fuzzy Mathematics and Informatics, Vol. 5, No. 1, 157-168, January 2013.
bullet A Neutrosophic Soft Set Approach to A Decision Making Problem, by Pabitra Kumar Maji, Annals of Fuzzy Mathematics and Informatics, Vol. 3, No. 2, 313-319, April 2012.
bullet Correlation Coefficients of Neutrosophic Sets by Centroid Method, by I. M. Hanafy, A. A. Salama, K. M. Mahfouz, International Journal of Probability and Statistics 2013, 2(1): 9-12.
bullet Análisis de textos de José Martí utilizando mapas cognitivos neutrosóficos, por Maikel Leyva-Vazquez, Karina Perez-Teruel, F. Smarandache, 2013, http://vixra.org/abs/1303.0216
bullet Correlation of Neutrosophic Data, by I. M. Hanafy, A.A.Salama and K. Mahfouz, International Refereed Journal of Engineering and Science (IRJES), Vol. 1, Issue 2, 39-43, 2012.
bullet Neutrosophic Filters, by A. A. Salama & H. Alagamy, International Journal of Computer Science Engineering and Information Technology Research (IJCSEITR), Vol. 3, Issue 1, Mar 2013, 307-312.
bullet Neutrosophic Masses & Indeterminate Models. Applications to Information Fusion, by Florentin Smarandache, Proceedings of the 15th International Conference on Information Fusion, Singapore, 9-12 July 2012.
bullet A Geometric Interpretation of the Neutrosophic Set – A Generalization of the Intuitionistic Fuzzy Set, 2011 IEEE International Conference on Granular Computing, edited by Tzung-Pei Hong, Yasuo Kudo, Mineichi Kudo, Tsau-Young Lin, Been-Chian Chien, Shyue-Liang Wang, Masahiro Inuiguchi, GuiLong Liu, IEEE Computer Society, National University of Kaohsiung, Taiwan, 602-606, 8-10 November 2011.
bullet Applications of Neutrosophic Logic to Robotics / An Introduction, by Florentin Smarandache, Luige Vladareanu, 2011 IEEE International Conference on Granular Computing, edited by Tzung-Pei Hong, Yasuo Kudo, Mineichi Kudo, Tsau-Young Lin, Been-Chian Chien, Shyue-Liang Wang, Masahiro Inuiguchi, GuiLong Liu, IEEE Computer Society, National University of Kaohsiung, Taiwan, 607-612, 8-10 November 2011.
bullet Color Image Segmentation Based on Neutrosophic Method, by Ling Zhang, Ming Zhang, H. D. Cheng, Optical Engineering, 51(3), 037009, 2012.
bullet Intuitionistic Neutrosophic Soft Set, by Said Broumi, F. Smarandache, Journal of Information and Computing Science, Vol. 8, No. 2, 2013, pp. 130-140.
bullet A Novel Neutrosophic Logic SVM (N-SVM) and its Application to Image Categorization, by Wen Ju and H. D. Cheng, New Mathematics and Natural Computation (World Scientific), Vol. 9, No. 1, 27-42, 2013.
bullet Activism and Nations Building in Pervasive Social Computing Using Neutrosophic Cognitive Maps (NCMs), by A.Victor Devadoss, M. Clement Joe Anand, International Journal of Computing Algorithm, Volume: 02, Pages: 257-262, October 2013.
bullet A Study of Quality in Primary Education Combined Disjoint Block Neutrosophic Cognitive Maps (CDBNCM), by A.Victor Devadoss, M. Clement Joe Anand, A. Joseph Bellarmin, Indo-Bhutan International Conference On Gross National Happiness Vol. 02, Pages: 256-261,October 2013.
bullet Segmentation of Breast Ultrasound Images Based on Neutrosophic Method, by Ming Zhang, Ling Zhang, H. D. Cheng, Optical Engineering, 49(11), 117001-117012, 2010.
bullet A Neutrosophic Approach to Image Segmentation Based on Watershed Approach, by Ming Zhang, Ling Zhang, H. D. Cheng, Signal Processing, 90(5), 1510-1517, 2010.
bullet “On neutrosophic paraconsistent topology”, by F .G. Lupiáñez, Kybernetes 39 (2010), 598-601.
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Strategy on T, I, F Operators. A Kernel Infrastructure in Neutrosophic Logic, by Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 414-419, 2010.

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On Similarity and Entropy of Neutrosophic Sets, by Pinaki Majumdar & S. K. Samanta. M.U.C Women College, Burdwan (W. B.), India, 2013.

bullet An Effective Neutrosophic Set-Based Preprocessing Method for Face Recognition, by Mohammad Reza Faraji and Xiaojun Qi, Utah State University, Logan, 2013.
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Toward Dialectic Matter Element of Extenics Model, by Liu Feng, Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 420-429, 2010.

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Self Knowledge and Knowledge Communication, by Liu Feng and Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 430-435, 2010.

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A Neutrosophic Description Logic, by Haibin Wang, Andre Rogatko, Florentin Smarandache, Rajshekhar Sunderraman,Proceedings of 2006 IEEE International Conference on Granular Computing, edited by Yan-Qing Zhang and Tsau Young Lin, Georgia State University, Atlanta, 305-308, 2006.

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Neutrosophic Relational Data Model, by Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko, in <Critical Review> (Society for Mathematics of Uncertainty, Creighton University), Vol. II, 19-35, 2008.

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Short Definitions of Neutrosophic Notions [in Russian], by F. Smarandache, translated by A. Schumann, Philosophical Lexicon, Minsk-Moscow, Econompress, Belarus-Russia, 2008.

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Neutrosophic Logic Based Semantic Web Services Agent, by Haibin Wang, Yan-Qing Zhang, Rajshekhar Sunderraman, Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 505-519, 2010.

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Neutrosophic Transdisciplinarity (Multi-Space & Multi-Structure), by Florentin Smarandache, presented at Scoala de Vara Internationala, Interdisciplinara si Academica, Romanian Academy, Bucharest, 6-10 July 2009.

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Neutrosophic Logic as a Theory of Everything in Logics, by Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 525-527, 2010.

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Blogs on Applications of Neutrosophics and Multispace in Sciences, by Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 528-548, 2010.

bullet A Neutrosophic Multicriteria Decision Making Method, by Athar Kharal, National University of Science and Technology, Islamabad, Pakistan.
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A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets, by J. Ye, Journal of Intelligent and Fuzzy Systems (2013) doi: 10.3233/IFS-130916.

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Single valued neutrosophic cross-entropy for multicriteria decision making problems, by Jun Ye, Applied Mathematical Modelling (2013) doi: 10.1016/j.apm.2013.07.020.

bullet Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment, by Jun Ye, International Journal of General Systems, Vol. 42, No. 4, 386-394, 2013.
bullet Similarity Measures between Interval Neutrosophic Sets and their Multicriteria Decision Method, by Jun Ye, Shaoxing Univ., China.
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Neutrosophic Degree of a Paradoxicity, by Florentin Smarandache, in Multispace and Multistructure, Vol. 4, 605-607, 2010.

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Neutrosophic Diagram and Classes of Neutrosophic Paradoxes, or To The Outer-Limits of Science, by Florentin Smarandache, Prog. Physics, Vol. 4, 18-23, 2010.

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S-denying a Theory, by Florentin Smarandache,  in Multispace and Multistructure, Vol. 4, 622-629, 2010.

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Five Paradoxes and a General Question on Time Traveling, by Florentin Smarandache, Prog. Physics, Vol. 4, 24, 2010.

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H. D. Cheng, Yanhui Guo and Yingtao Zhang, A Novel Image Segmentation Approach Based on Neutrosophic Set and Improved Fuzzy C-means Algorithm, New Mathematics and Natural Computation, Vol. 7, No. 1 (2011) 155-171.

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Degree of Negation of an Axiom, by F. Smarandache,to appear in the Journal of Approximate Reasoning, arXiv:0905.0719.

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Remedy for Effective Cure of Diseases using Combined Neutrosophic Relational Maps, by M R Bivin, N.Saivaraju and K S Ravichandran, International Journal of Computer Applications12(12):18?23, January 2011. Published by Foundation of Computer Science.

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Neutrosphic Research Method, by F. Smarandache, in Multispace & Multistructure. Neutrosophic Transdisciplinarity, NESP, Finland, pp. 395-548 and respectively 732-733, 2010.

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A Tool for Qualitative Causal Reasoning On Complex Systems, by Tahar Guerram, Ramdane Maamri, and   Zaidi Sahnoun, IJCSI International Journal of Computer Science Issues, Vol. 7, Issue 6, November 2010.

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A  Study on Suicide problem using Combined Overlap Block Neutrosophic Cognitive Maps, by P. Thiruppathi, N.Saivaraju, K.S. Ravichandran, International Journal of Algorithms, Computing and Mathematics, Vol. 3, Number 4, November 2010.

bullet “On various neutrosophic topologies”, Francisco Gallego Lupiáñez,  “Recent advances in Fuzzy Systems”, WSEAS (Athens , 2009), 59-62.
bullet Interval  neutrosophic sets and  Topology, by F .G. Lupiáñez, Kybernetes 38 (2009), 621-624.
bullet On various  neutrosophic topologies, by F .G. Lupiáñez, Kybernetes 38 (2009), 1009-1013.
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Interval neutrosophic sets and topology, Francisco Gallego Lupiáñez, Kybernetes: The International Journal of Systems & Cybernetics, Volume 38, Numbers 3-4, 2009 , pp. 621-624(4).

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Neutrosophic logics on Non-Archimedean Structures, by Andrew Schumann, Critical Review, Creighton University, USA, Vol. III, 36-58, 2009.

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Positive, Negative and Neutral Law of Universal Gravitation, by Fu Yuhua, Fu Anjie, Zhao Ge, New Science and Technology, 2009 (12), 30-32.

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Intuitionistic Neutrosophic Set, by Monoranjan Bhowmik and Madhumangal Pal, Journal of Information and Computing Science, England, Vol. 4, No. 2, 2009, pp. 142-152.

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Discrimination of Outer Membrane Proteins using Reformulated Support Vector Machine based on Neutrosophic Set, by Wen Ju and H. D. Cheng, Proceedings of the 11th Joint Conference on Information Sciences (2008), Published by Atlantis Press.

bullet

Adaptive fuzzy cognitive maps vs neutrosophic cognitive maps: decision support tool for knowledge based institution, by Goutam Bernajee, Journal of Scientific and Industrial Research, 665-673, Vol. 67, 2008.

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A Method of Imprecise Query Solving, by Smita Rajpal, M.N. Doja, Ranjit Biswas, International Journal of Computer Science and Network Security, Vol. 8  No. 6,  pp. 133-139,  June 2008, http://paper.ijcsns.org/07_book/200806/20080618.pdf

bullet On Neutrosophic Topology, by F .G. Lupiáñez, Kybernetes 37 (2008), 797-800.
bullet Interval  neutrosophic sets and  Topology,  by F .G. Lupiáñez,“Applied and Computational Mathematics”, WSEAS ( Athens , 2008), 110-112.
bullet

A Method of Neutrosophic Logic to Answer Queries in Relational Database, by Smita Rajpal, M.N. Doja and Ranjit Biswas, Journal of Computer Science 4 (4): 309-314, 2008.

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Ensemble Neural Networks Using Interval Neutrosophic Sets and Bagging, by Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong, Third International Conference on Natural Computation (ICNC 2007), Haikou, Hainan, China, August 24-August 27, 2007.

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Lithofacies Classification from Well Log Data using Neural Networks, Interval Neutrosophic Sets and Quantification of Uncertainty, by Pawalai Kraipeerapun, Chun Che Fung, and Kok Wai Wong, World Academy of Science, Engineering and Technology, 23, 2006.

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Redesigning Decision Matrix Method with an indeterminacy-based inference process, by Jose L. Salmeron, Florentin Smarandache, Advances in Fuzzy Sets and Systems, Vol. 1(2), 263-271, 2006.

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Neural network ensembles using interval neutrosophic sets and bagging for mineral prospectivity prediction and quantification of uncertainty, by P. Kraipeerapun, C. C. Fung, W. Brown and K. W. Wong, 2006 IEEE Conference on Cybernetics and Intelligent Systems, 7-9 June 2006, Bangkok, Thailand.

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Processing Uncertainty and Indeterminacy in Information Systems success mapping, by Jose L. Salmeron, Florentin Smarandache, arXiv:cs/0512047v2.

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The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference, by Florentin Smarandache, Jean Dezert; in arXiv:cs/0412091v1. A version of this paper published in Proceedings of 10th International Conference on Fuzzy Theory and Technology (FT&T 2005), Salt Lake City, Utah, USA, July 21-26, 2005.

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Book Review by Milan Mares: W. B. Vasantha Kandasamy and Florentin Smarandache, Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, Kybernetika, Vol. 40 (2004), No. 1, [151]-15.

bullet Set-Theoretic Operators on Degenerated Neutrosophic Set, by H. Wang, Y. Zhang, R. Sunderraman, F. Song, Georgia State UNiversity, Atlanta, 2004.
bullet

Neutrosophy in situation analysis, Anne-Laure Jousselme, Patrick Maupin, Proc. of Fusion 2004 Int. Conf. on Information Fusion, pp. 400-406, Stockholm, Sweden, June 28-July1, 2004 (http://www.fusion2004.org).

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Preamble to Neutrosophic Logic, by C. Lee, Multiple-Valued Logic / An International Journal, Vol. 8, No. 3, 285-296, June 2002.

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Neutrosophy, a New Branch of Philosophy, by Florentin Smarandache, Multiple-Valued Logic / An International Journal, Vol. 8, No. 3, 297-384, June 2002.

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A Unifying Field in Logics: Neutrosophic Field, by Florentin Smarandache, Multiple-Valued Logic / An International Journal, Vol. 8, No. 3, 385-438, June 2002.

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Open Questions to Neutrosophic Inferences, by Jean Dezert, Multiple-Valued Logic / An International Journal, Vol. 8, No. 3, 439-472, June 2002.

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Logic: A Misleading Concept. A Contradiction Study toward Agent's Logic, by Feng Liu, Florentin Smarandache, Proceedings of the First International Conference on Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability and Statistics, University of New Mexico, Gallup Campus, 2001.

bullet

Six Neutral Fundamental Reactions Between Four Fundamental Reactions,  by Fu Yuhua, Fu Anjie, Zhao Ge,
http://wbabin.net/physics/yuhua2.pdf.

bullet

On Rugina's System of Thought, by Florentin Smarandache, International Journal of Social Economics, Vol. 28, No. 8, 623-647, 2001.

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Intentionally and Unintentionally. On Both, A and Non-A, in Neutrosophy, by Feng Liu, Florentin Smarandache, Presented to the First International Conference on Neutrosophy, Neutrosophic Logic, Set, and Probability, University of New Mexico, Gallup, December 1-3, 2001.

bullet

Neutrosophic Transdisciplinarity, by F. Smarandache, 1969.

bullet

Online English Dictionary, Definition of Neutrosophy.

 

 

§  A Geometric Interpretation of the Neutrosophic Set, A Generalization of the Intuitionistic Fuzzy Set, by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 27-35.

§  A Binarization Algorithm for Historical Arabic Manuscript Images using a Neutrosophic Approach, by Khalid M. Amin, Mohamed Abd Elfattah, Aboul Ella Hassanien and Gerald Schaefer. 5 p.

§  A Comparison of Combined Overlap Block Fuzzy Cognitive Maps (COBFCM) and Combined Overlap Block Neutrosophic Cognitive Map (COBNCM) in finding the hidden patterns and indeterminacies in Psychological Causal Models: Case Study of ADHD, by Hojjatollah Farahani, Florentin Smarandache, Lihshing Leigh Wang. In Critical Review, Volume X, 2015, pp. 71-83.

§  Addressing The Dimensions Of Education And Integrated Curriculum Via Generalized Fuzzy Logic, by Tudor Marin, Gheorghe Savoiu. In Euromentor Journal, Volume VI, No. 1/March 2015, pp. 61-73.

§  A Fuzzy Study on the Analysis of Cervical Cancer among women using Combined Disjoint Block Fuzzy Cognitive Maps (CDBFCMs), by T. Bharathi. In International Journal of Research in Science & Technology, Volume 1, November 2014, 5 p.

§  Algebraic Structures Of Neutrosophic Soft Sets, by Asim Hussain, Muhammad Shabir. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 53-61.

§  A multi attribute decision making method based on inclusion measure for interval neutrosophic sets, by Ridvan Sahin, Mesut Karabacak. In International Journal of Engineering and Applied Sciences, Volume 2, February 2015, pp. 13-15.

§  A Multi-criteria neutrosophic group decision making metod based TOPSIS for supplier selection, by Rıdvan şahin, Muhammed Yigider. 11 p.

§  Análisis de textos de José Martí utilizando mapas cognitivos neutrosóficos, by Maikel Leyva-Vazquez, Karina Perez-Teruel, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 463-467.

§  Analysis of Reasons for Stress on College Students using Combined Disjoint Block Fuzzy Cognitive Maps (CDBFCM), by G. Anusha, P. Venkata Ramana. In International Journal For Research In Emerging Science And Technology, Volume 2, February 2015, pp. 16-21.

§  An analitical extended book review. S. Frunza: Advertising constructs reality (2014), by Ștefan Vlăduțescu, Mirela Teodorescu. In International Letters of Social and Humanistic Sciences, 2015, pp. 98-106.

§  An Eidetic Reflex and Moment of Breakthrough in Time and Scientific Creation: 10 Years of Progress in Physics, 100 Years of General Relativity, and the Zelmanov Cosmological Group, by Indranu Suhendro. In Progress in Physics, Vol. 11, 2015, pp. 180-182.

§  A New Approach to Multi-spaces Through the Application of Soft Sets, by Mumtaz Ali, Florentin Smarandache, Said Broumi , and Muhammad Shabir. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 34-39.

§  A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems, by Anjan Mukherjee, Sadhan Sarkar. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 63-68.

§  A New Methodology for Neutrosophic Multi-Attribute Decision-Making with Unknown Weight Information, by Pranab Biswas, Surapati Pramanik, Bibhas C. Giri. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 42-52.

§  An Example of Guiding Scientific Research with Philosophical Principles Based on Uniqueness of Truth and Neutrosophy Deriving Newton's Second Law and the like, by Fu Yuhua. In Critical Review, Volume X, 2015, pp.85-92.

§  An Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variables, by Said Broumi, Jun Ye, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp.22-31.

§  An Original Notion to Find Maximal Solution in the Fuzzy Neutrosophic Relation Equations (FNRE) with Geometric Programming (GP), by Huda E. Khalid. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 3-7.

§  A Note on Square Neutrosophic Fuzzy Matrices, by Mamouni Dhar, Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 37-41.

§  Another Form of Correlation Coefficient between Single Valued Neutrosophic Sets and Its Multiple Attribute Decision-Making Method, by Jun Ye. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 8-12.

§  An outranking approach for multi-criteria decision-making problemswith simplified neutrosophic sets, by Juan-Juan Peng, Jian-qiang Wang, Hong-yu Zhang, Xiao-hong Chen. In Applied Soft Computing, 2014, pp. 336–346.

§  A Novel Image Segmentation Algorithm Based on Neutrosophic Filtering and Level Set, by Yanhui Guo, Abdulkadir Sengur. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 46-49.

§  A novel image thresholding algorithm based on Neutrosophic similarity score, by Yanhui Guo, Abdulkadir Sengur, Jun Ye. In Measurement, 2014, pp. 175–186.

§  A novel method for single-valued neutrosophic multi-criteria decision making with incomplete weight information, by Zhiming Zhang, Chong Wu. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 35-49.

§  Applications of Neutrosophic Logic to Robotics, by Florentin Smarandache, Luige Vladareanu. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 61-66.

§  Art and being in neutrosophic communication, by Elena Rodica Opran, Dan Valeriu Voinea, Mirela Teodorescu. In International Letters of Social and Humanistic Sciences, 2015, pp. 16-27.

§  A Study On Neutrosophic Cognitive Maps (NCM) And Its Applications, by C. Ramkumar, R. Ravanan, A. Lourdusamy, S. Narayanamoorthy. In International Journal of Mathematical Archive, 6(3), 2015, pp. 209-211.

§  A Study on Problems of Hijras in West Bengal Based on Neutrosophic Cognitive Maps, by Kalyan Mondal, Surapati Pramanik. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 21-26.

§  A Unifying Field in Logics. Book Review, by Adrian Nicolescu, Mirela Teodorescu. In International Letters of Social and Humanistic Sciences, 2015, pp.  48-59.

§  Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets & Possible Application to GIS Topology, by A. A. Salama. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 18-22.

§  Communication vs. Information, an Axiomatic Neutrosophic Solution, by Florentin Smarandache, Stefan Vladuțescu. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 38-45.

§  Comparative Study of Intuitionistic and Generalized Neutrosophic Soft Sets, by Debabrata Mandal. In International Journal of Mathematical, Computational, Natural and Physical Engineering, Vol. 9, No. 2, 2015, pp.111-114.

§  Connections between Extension Logic and Refined Neutrosophic Logic, by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 47-54.

§  Correlation Coefficient of Interval Neutrosophic Set, by Said Broumi, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers,Volume 1, EuropaNova, Bruxelles, 2014, pp.  67-73.

§  Correlation Measure For Neutrosophic Refined Sets And Its Application In Medical Diagnosis, by Said Broumi, Irfan Deli. In Palestine Journal of Mathematics, Vol. 3, 2014, pp. 11–19.

§  Cosine Similarity Measure of Interval Valued Neutrosophic Sets, by Said Broumi,  Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 15-20.

§  Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers, by Pranab Biswas, Surapati Pramanik, Bibhas C. Giri. In Neutrosophic Sets and Systems, Vol. 8, 2014, pp. 46-55.

§  Cosine Similarity Measure Of Rough Neutrosophic Sets And Its Application In Medical Diagnosis, by Surapati Pramanik, Kalyan Mondal. In Global Journal Of Advanced Research, Vol. 2, pp. 315-328.

§  Cotangent Similarity Measure Of Rough Neutrosophic Sets And Its Application To Medical Diagnosis, by Surapati Pramanik, Kalyan Mondal. In Journal Of New Theory, 2015, pp. 90-102.

§  Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-stage Method, by Fu Yuhua. 13 p.

§  Dialectics and the Dao: On Both, A and Non-A in Neutrosophy and Chinese Philosophy, by Feng Liu, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 440-444.

§  Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis, by Shan Ye, Jun Ye. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 48-53.

§  Entropy Based Grey Relational Analysis Method for Multi-Attribute Decision Making under Single Valued Neutrosophic Assessments, by Pranab Biswas, Surapati Pramanik, Bibhas C. Giri. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 102-110.

§  Examples of Neutrosophic Probability in Physics, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 32-34.

§  Expanding Newton Mechanics with Neutrosophy and Quadstage Method. New Newton Mechanics Taking Law of Conservation of Energy as Unique Source Law, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 3-13.

§  Expanding Uncertainty Principle to Certainty-Uncertainty Principles with Neutrosophy and Quad-stage Method, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 10-13.

§  Filters via Neutrosophic Crisp Sets, by A. A. Salama, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 34-37.

§  Generalization of Neutrosophic Rings and Neutrosophic Fields, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Luige Vladareanu. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 9-14.

§  Generalization of Soft Neutrosophic Rings and Soft NeutrosophicFields, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Luige Vladareanu. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 34-40.

§  Generalized Neutrosophic Set and Generalized Neutrosophic Topological Spaces, by A. A. Salama, S. A. Alblowi. In Computer Science and Engineering, 2012, pp.  129-132

§  G-Neutrosophic Space, by Mumtaz Ali, Florentin Smarandache, Munazza Naz, Muhammad Shabir. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 116-126.

§  Hypercomplex Neutrosophic Similarity Measure & Its Application In Multi-Criteria Dicision Making Problem, by Kanika Mandal, Kajla Basu. 15 p.

§  Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses, by Jun Ye. In Artificial Intelligence in Medicine, 2015, pp. 171–179.

§  Improved Weighted Correlation Coefficient based on Integrated Weight for Interval Neutrosophic Sets and its Application in Multi-criteria Decision Making Problems, by Hong-yu Zhang, Pu Ji, Jian-qiang Wang, Xiao-hong Chen. 34 p.

§  Interval Neutrosophic Logic, by Haibin Wang, Florentin Smarandache, Yan-Qing Zhang, Rajshekhar Sunderraman. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 142-160.

§  Interval Neutrosophic Rough Set, by Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 23-31.

§  Interval Valued Fuzzy Neutrosophic Soft Structure Spaces, by I. Arockiarani,  I.R. Sumathi. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 36-44.

§  Interval Valued Neutrosophic Soft Topological Spaces, by Anjan Mukherjee, Mithun Datta, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 17-26.

§  Introduction to Develop Some Software Programs for Dealing with Neutrosophic Sets, by A. A. Salama, Haitham A. El-Ghareeb, Ayman M. Manie, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 53-54.

§  Introduction to Image Processing via Neutrosophic Techniques, by A. A. Salama, Florentin Smarandache, Mohamed Eisa. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 59-64.

§  Introduction to Neutrosophic BCI/BCK-Algebras, by A.A.A. Agboola, B. Davvaz. Pp.1-14.

§  Introduction to Neutrosophic Nearrings, by A.A.A. Agboola, B. Davvaz. 14 p.

§  Introduction to Neutrosophic Topological Spatial Region, Possible Application to GIS Topological Rules, by A. A. Salama, Said Broumi, S. A. Alblowi. In I.J. Information Engineering and Electronic Business, 2014, pp. 15-21.

§  Intrusion Detection Using Neutrosophic Classifier, by V. Jaiganesh, P. Rutravigneshwaran. In The International Journal of Science & Tech., Vol. 2, 2014, pp. 128-133.

§  Intuitionistic Neutrosophic Set Relations and Some of Its Properties, by Monoranjan Bhowmik, Madhumangal Pal. In Journal of Information and Computing Science, Vol. 5, No. 3, 2010, pp. 183-192.

§  Intuitionistic Neutrosophic Soft Set, by Broumi Said, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 162-171.

§  Intuitionistic Neutrosphic Soft Set over Rings, by Broumi Said, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 172-178.

§  Lower and Upper Soft Interval Valued Neutrosophic Rough Approximations of An IVNSS-Relation, by Broumi Said, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 191-198.

§  Mappings on Neutrosophic Soft Classes, by Shawkat Alkhazaleh, Emad Marei. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 3-8.

§  Medical Diagnosis Using Distance-Based Similarity Measures of Single Valued Neutrosophic Multisets, by Shan Ye, Jing Fu, Jun Ye. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 47-52.

§  Misfire Fault Diagnosis Method of Gasoline Engines Using the Cosine Similarity Measure of Neutrosophic Numbers, by Lingwei Kong, Yuefeng Wu, Jun Ye. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 42-45.

§  More on Intuitionistic Neutrosophic Soft Sets, by Broumi Said, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 179-190.

§  Multi-criteria Group Decision Making Approach for Teacher Recruitment in Higher Education under Simplified Neutrosophic Environment, by Kalyan Mondal, Surapati Pramanik. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 27-33.

§  Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment, by Ridvan Sahin. 9 p.

§  Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment, by Yun Ye. In J. Intell. Syst., 2015, pp. 23–36.

§  Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems, by Juan-Juan Peng. In International Journal of Computational Intelligence Systems, Vol. 8, No. 2, 2015, pp. 345-363.

§  Negating Four Color Theorem with Neutrosophy and Quadstage Method, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 59-62.

§  Neutrosofia, o nouă ramură a filosofiei, by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 472-477.

§  Neutrosophic Axiomatic System, by Florentin Smarandache. In Critical Review, Volume X, 2015, pp. 5-28.

§  Neutrosophic Bi-LA-Semigroup and Neutrosophic N-LASemigroup, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Munazza Naz. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 19-24.

§  Neutrosophic circuits of communication. A review, by Jozef Novak-Marcincin, Adrian Nicolescu, Mirela Teodorescu. In International Letters of Social and Humanistic Sciences, 2015, pp. 174-186.

§  Neutrosophic classifier: An extension of fuzzy classifer, by A.Q. Ansari, Ranjit Biswas, Swati Aggarwal. In Applied Soft Computing, 2013, pp. 563–573.

§  Neutrosophic Closed Set and Neutrosophic Continuous Functions, by A. A. Salama, Florentin Smarandache, Valeri Kromov. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 4-8.

§  Neutrosophic Code, by Mumtaz Ali, Florentin Smarandache, Munazza Naz, Muhammad Shabir. 11 p.

§  Neutrosophic cognitive maps for modeling project portfolio interdependencies, by Ameirys Betancourt-Vázquez, Maikel Leyva-Vázquez, Karina Perez-Teruel. In Critical Review, Volume X, 2015, pp. 40-44.

§  Neutrosophic Correlation and Simple Linear Regression, by A. A. Salama, O. M. Khaled, K. M. Mahfouz. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 3-8.

§  Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals, by A. A. Salama, Said Broumi, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp 199-205.

§  Neutrosophic Crisp Points & Neutrosophic Crisp Ideals, by A. A. Salama. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 50-53.

§   *- Neutrosophic Crisp Set & *- Neutrosophic Crisp relations, by A. A. Salama,  Hewayda Elghawalby. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 12-16.

§  Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, by A. A. Salama, Florentin Smarandache, Valeri Kroumov. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 25-30.

§  Neutrosophic Crisp Set Theory, by A. A. Salama, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 27-35.

§  Neutrosophic Decision Making Model of School Choice, by Kalyan Mondal, Surapati Pramanik. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 62-68.

§  Neutrosophic Examples in Physics, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 26-33.

§  Neutrosophic Filters, by A. A. Salama, H. Alagamy. In International Journal of Computer Science Engineering and Information Technology Research (IJCSEITR), Vol. 3, 2013, pp. 307-312.

§  Neutrosophic Game Theoretic Approach to Indo-Pak Conflict over Jammu-Kashmir, by Surapati Pramanik, Tapan Kumar Roy. In Neutrosophic Sets and Systems, Vol. 2, 2013, pp. 82-100.

§  Neutrosophic Hierarchical Clustering Algoritms, by Ridvan Sahin. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 18-24.

§   Neutrosophic Hypercompositional Structures defined by Binary Relations, by A.A.A. Agboola, S.A. Akinleye. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 29-36.

§  Neutrosophic Hypervector Spaces, by A.A.A. Agboola, S.A. Akinleye. 16 p.

§  Neutrosophic Ideal Theory Neutrosophic Local Function and Generated Neutrosophic Topology, by A. A. Salama, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 213-218.

§  Neutrosophic LA-Semigroup Rings, by Mumtaz Ali, Muhammad Shabir, Florentin Smarandache, Luige Vladareanu. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 81-88.

§  Neutrosophic Lattices, by Vasantha Kandasamy, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 2, 2013, pp. 42-47.

§  Neutrosophic Left Almost Semigroup, by Mumtaz Ali, Muhammad Shabir, Munazza Naz, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 18-28.

§  Neutrosophic Logic Approaches Applied to ”RABOT” Real Time Control, by Alexandru Gal, Luige Vladareanu, Florentin Smarandache, Hongnian Yu, Mincong Deng. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 55-60.

§  Neutrosophic Logic for Mental Model Elicitation and Analysis, by Karina Pérez-Teruel, Maikel Leyva-Vázquez. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 31-33.

§  Neutrosophic Measure and Neutrosophic Integral, by Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 3-7.

§  Neutrosophic Modeling and Control, by Swati Aggarwal, Ranjit Biswas, A.Q. Ansari. Intl. Conf. on Computer & Communication Tech., 2010, pp. 718-723.

§  Neutrosophic Parameterized Soft Relations and Their Applications, by Irfan Deli, Yunus Toktas, Said Broumi. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 25-34.

§  Neutrosophic Parametrized Soft Set Theory and Its Decision Making, by Said Broumi, Irfan Deli, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 403-409.

§  Neutrosophic Principle of Interconvertibility Matter-Energy-Information (NPI_MEI), by Florentin Smarandache, Stefan Vladutescu. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 219-227.

§  Neutrosophic Refined Relations and Their Properties, by Said Broumi, Irfan Deli, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 228-248.

§  Neutrosophic Refined Similarity Measure Based on Cosine Function, by Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 41-47.

§  Neutrosophic Refined Similarity Measure Based On Cotangent Function And Its Application To Multi-Attribute Decision Making, by Kalyan Mondal, Surapati Pramanik. In Global Journal of Advanced Research, Vol-2, 2015, pp. 486 -496.

§  Neutrosophic Relations Database, by A. A. Salama, Mohamed Eisa, M. M. Abdelmoghny. In International Journal of Information Science and Intelligent System, 2014, pp. 1-13.

§  Neutrosophic routes in multiverse of communication, by Daniela Gifu, Mirela Teodorescu. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 81-83.

§  Neutrosophic Set and Neutrosophic Topological Spaces, by A.A.Salama, S.A. Alblowi. In IOSR Journal of Mathematics, 2012, pp. 31-35.

§  Neutrosophic Soft Expert Sets, by Mehmet Sahin, Shawkat Alkhazaleh, Vakkas Ulucay. In Applied Mathematics, 2015, pp. 116-127.

§  Neutrosophic soft matrices and NSM-decision making, by Irfan Deli, Said Broumi. In Journal of Intelligent & Fuzzy Systems, 2015, pp. 2233–2241.

§  Neutrosophic Soft Matrix And Its Application in Solving Group Decision Making Problems from Medical Science, by Tanushree Mitra Basu, Shyamal Kumar Mondal. In Computer Communication & Collaboration, 2015, Vol. 3, pp. 1-31.

§  Neutrosophic Soft Multi-Set Theory and Its Decision Making, by Irfan Deli, Said Broumi, Mumtaz Ali. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 65-76.

§  Neutrosophic soft relations and some properties, by Irfan Deli, Said Broumi. In Ann. Fuzzy Math. Inform., 2014, pp. 2-14.

§  Neutrosophic Soft Semirings, by Debabrata Mandal. In Annals of Fuzzy Mathematics and Informatics, 2014, pp. 2-13.

§  Neutrosophic Soft Sets with Applications in Decision Making, by Faruk Karaaslan. In International Journal of Information Science and Intelligent System, 2015, pp. 1-20.

§  Neutrosophic Vague Set Theory, by Shawkat Alkhazaleh. In Critical Review, Volume X, 2015, pp. 29-39.

§  Neutrosophic Vector Spaces, by A.A.A. Agboola, S.A. Akinleye. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 9-18.

§  Neutrosophy, a possible method of process analysis uncertainties solving, by Daniela Gifu, Mirela Teodorescu. 5 p.

§  New Distance and Similarity Measures of Interval Neutrosophic Sets, by Said Broumi, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 249-255.

§  New Neutrosophic Crisp Topological Concepts, by A. A. Salama, Florentin Smarandache, S. A. Alblowi. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 50-54.

§  New operations On Fuzzy Neutrosophic Mattrices, by I. R. Sumathi, I. Arockiarani. In International Journal of Innovative Research and study, 2014, pp. 119-124.

§  New Operations on Interval Neutrosophic Sets, by Said Broumi, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 256-266.

§  New Operations on Intuitionistic Fuzzy Soft Sets Based on First Zadeh's Logical Operators, by Said Broumi, Pinaki Majumdar, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 267-277.

§  New Operations over Interval Valued Intuitionistic Hesitant Fuzzy Set, by Said Broumi, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp 267-276.

§  New Results of Intuitionistic Fuzzy Soft Set, by Said Broumi, Florentin Smarandache, Mamoni Dhar, Pinaki Majumdar. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 386-391.

§  New Type of Fuzzy Relational Equations and Neutrosophic Relational Equations – To analyse Customers Preference to Street Shops, by Vasantha Kandasamy, Sekar. P. Vidhyalakshmi. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 68-76.

§  npn-Soft sets theory and their applications, by Irfan Deli. In Annals of Fuzzy Mathematics and Informatics, 2015, pp. 3-16.

§  N-Valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis, by Said Broumi, Irfan Deli, Florentin Smarandache. In Critical Review, Volume X, 2015, pp. 45-68.

§  n-Valued Refined Neutrosophic Logic and Its Applications to Physics, by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 36-44.

§  On Fuzzy Soft Matrix Based on Reference Function, by Said Broumi, Florentin Smarandache, Mamoni Dhar. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 392-398.

§  On Neutrosophic Canonical Hypergroups and Neutrosophic Hyperrings, by A.A.A. Agboola, B. Davvaz. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 34-41.

§  On Neutrosophic Ideals of Neutrosophic BCI-Algebras, by A.A.A. Agboola, B. Davvaz. In Critical Review, Volume X, 2015, pp. 93-103.

§  On Neutrosophic Implications, by Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 9-17.

§  On Neutrosophic Sets And Topology, by Francisco Gallego Lupianez. 13 p.

§  On single valued Neutrosophic Relations, by Hai-Long Yang,  Zhi-Lian Guo, Xiuwu Liao. 20 p.

§  Pauli Exclusion Principle and the Law of Included Multiple-Middle, by Fu Yuhua. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 3-5.

§  Pragmatical solving of uncertainties on production flow, by Daniela Gifu, Mirela Teodorescu. 15 p.

§  Quantification of Uncertainty in Mineral Prospectivity Prediction Using Neural Network Ensembles and Interval Neutrosophic Sets, by Pawalai Krai Peerapun, Kok Wai Wong, Chun Che Fung, Warick Brown. 2006 International Joint Conference on Neural Networks, pp. 3034-3039.

§  Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies, by Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 9, 2015, pp. 1-5.

§  Relations on Interval Valued Neutrosophic Soft Sets, by Said Broumi, Irfan Deli, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 290-306.

§  Reliability and Importance Discounting of Neutrosophic Masses, by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 13-26.

§  Replacing the Conjunctive Rule and Disjunctive Rule with Tnorms and T-conorms respectively (Tchamova-Smarandache), by Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 45-46.

§  Review of Recommender Systems Algorithms Utilized in Social Networks based e-Learning Systems & Neutrosophic System, by A. A. Salama, Mohamed Eisa, S.A. Elhafeez, M. M. Lotfy. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 32-40.

§  Rough Neutrosophic Multi-Attribute Decision-Making Based on Rough Accuracy Score Function, by Kalyan Mondal, Surapati Pramanik. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 14-21.

§  Rough Neutrosophic Sets, by Said Broumi, Florentin Smarandache, Mamoni Dhar. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 62-67.

§  Rough sets in Fuzzy Neutrosophic approximation space, by C. Antony Crispin Sweety, I. Arockiarani. 16 p.

§  Several Similarity Measures of Neutrosophic Sets, by Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 54-62.

§  Several Similarity Measures of Interval Valued Neutrosophic Soft Sets and Their Application in Pattern Recognition Problems, by Anjan Mukherjee and Sadhan Sarkar. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 54-60.

§  Similarity measure between possibility neutrosophic soft sets and its applications, by Faruk Karaaslan. 10 p.

§  Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems, by Zhang-peng Tian, Jing Wang, Hong-yu Zhang, Xiao-hong Chen, Jian-qiang Wang. Faculty of Sciences and Mathematics, University of Nis, Serbia, Filomat, 24 p.

§  Single Valued Neutrosophic Similarity Measures for Multiple Attribute Decision-Making, by Jun Ye, Qiansheng Zhang. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 48-54.

§  Single Valued Neutrosophic Information Systems Based on Rough Set Theory, by Said Broumi, Florentin Smarandache. 10 p.

§  Single valued neutrosophic multisets, by Rajashi Chatterjee, P. Majumdar, S. K. Samanta. In Annals of Fuzzy Mathematics and Informatics, 2015, pp. 1-16.

§  Soft Interval –Valued Neutrosophic Rough Sets, by Said Broumi, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 69-80.

§  Soft Neutrosophic Bigroup and Soft Neutrosophic N-Group, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Munazza Naz. In Neutrosophic Sets and Systems, Vol. 2, 2014, pp. 55-79.

§  Soft Neutrosophic Bi-LA-semigroup and Soft Neutrosophic N-LA-seigroup, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir. In Neutrosophic Sets and Systems, Vol. 5, 2014, pp. 45-58.

§  Soft Neutrosophic Group, by Muhammad Shabir, Mumtaz Ali, Munazza Naz, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 1, 2013, pp. 13-25.

§  Soft Neutrosophic Groupoids and Their Generalization, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 61-80.

§  Soft Neutrosophic Left Almost Semigroup, by Florentin Smarandache, Mumtaz Ali, Munazza Naz, and Muhammad Shabir. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 317-326.

§  Soft Neutrosophic Loop, Soft Neutrosophic Biloop and Soft Neutrosophic N-Loop, by Mumtaz Ali, Florentin Smarandache, and Muhammad Shabir. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 327-348.

§  Soft Neutrosophic Loops and Their Generalization, by Mumtaz Ali, Christopher Dyer, Muhammad Shabir, Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 4, 2014, pp. 55-75.

§  Soft Neutrosophic Ring and Soft Neutrosophic Field, by Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, Munazza Naz. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 55-61.

§  Soft neutrosophic semigroups and their generalization, by Mumtaz Ali, Muhammad Shabir, Munazza Naz, Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 349-367.

§  Some single valued neutrosophic correlated aggregation operators and their applications to material selection, by Yanbing Ju, Dawei Ju, Wenkai Zhang, Xia Li. 26 p.

§  Some Types of Neutrosophic Crisp Sets and Neutrosophic Crisp Relations, by A. A. Salama, Said Broumi and Florentin Smarandache. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 379-385.

§  Some weighted aggregation operators of trapezoidal Neutrosophic numbers and their multiple attribute decision making method, by Jun Ye. 14 p.

§  Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems, by Irfan Deli, Yusuf Subas. 14 p.

§  The Characteristic Function of a Neutrosophic Set, by A. A. Salama, Florentin Smarandache, S. A. Alblowi. In Neutrosophic Sets and Systems, Vol. 3, 2014, pp. 14-17.

§  The Fifth Function of University:“Neutrosophic E-function” of Communication-Collaboration-Integration of University in the Information Age, by Florentin Smarandache, Stefan Vladutescu. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 445-462.

§  The Neutrosophic Entropy and its Five Components, by Vasile Patrascu. In Neutrosophic Sets and Systems, Vol. 7, 2015, pp. 40-46.

§  Thesis-Antithesis-Neutrothesis, and Neutrosynthesis, by Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 57-58.

§  (T, I, F)-Neutrosophic Structures, by Florentin Smarandache. 7 p.

§  (t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited), by Florentin Smarandache. In Neutrosophic Sets and Systems, Vol. 8, 2015, pp. 3-9.

§  Time-Neutrosophic Soft Set And Its Applications, by Shawkat Alkhazaleh. 21 p.

§  To be and Not to be – An introduction to Neutrosophy: A Novel Decision Paradigm, by Florentin Smarandache, Sukanto Bhattacharya. In Neutrosophic Theory and Its Applications. Collected Papers, Volume 1, EuropaNova, Bruxelles, 2014, pp. 424-439.

§  TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment, by Pranab Biswas, Surapati Pramanik, Bibhas C. Giri. In Neural Comput & Applic., 2015, 11 p.

§  Weighted Neutrosophic Soft Sets, by Pabitra Kumar Maji. In Neutrosophic Sets and Systems, Vol. 6, 2014, pp. 6-11.

§  Weighted Neutrosophic Soft Sets Approach In a  Multicriteria Decision Making Problem, by Pabitra Kumar Maji. In Journal of New Theory, 2015, 12 p.

 

Seminars on Neutrosophics: 

 

  • Foundations of Neutrosophic set and Logic and Their Applications to Information Fusion, by F. Smarandache, Osaka University, Inuiguchi Laboratory, Department of Engineering Science, Osaka, Japan, 10 January 2014..
  • Foundations of Neutrosophic set and Logic and Their Applications to Information Fusion, by F. Smarandache, Okayama University of Science, Kroumov Laboratory, Department of Intelligence Engineering, Okayama, Japan, 17 December 2013.
  • An Introduction to Information Fusion Level 1 and to Neutrosophic Logic/Set with Applications, ENSIETA (National Superior School of Engineers and the Study of Armament), Brest, France, 2 July 2010.
  • An Introduction to Fusion Level 1 and to Neutrosophic Logic/Set with Applications, presented by F. Smarandache at Air Force Research Laboratory, in Rome, NY, USA, July 29, 2009.

  • An Introduction to Neutrosophic Logic in Arabic Philosophy, presented by F. Smarandache & Salah Osman, Minufiya University, Shebin Elkom, Egypt, 17 December 2007.
bullet A Neutrosophic Description Logic, by Haibin Wang, Florentin Smarandache, Andre Rogatko, Rajshekhar Sunderraman, 2006 IEEE International Conference on Granular Computing, Georgia State University, Atlanta, USA, May 11, 2006.
bullet An Introduction to Neutrosophic Logic and Set, by F. Smarandache, Invited Speaker at and sponsored by University Kristen Satya Wacana, Salatiga, Indonesia, May 24, 2006.
bullet An Introduction to Neutrosophic Logic and Set, by F. Smarandache, Invited Speaker at and sponsored by University Sekolah Tinggi Informatika & Komputer Indonesia, Malang, Indonesia, May 19, 2006.
bullet

Neutrosophic Set - A Generalization of the Intuitionistic Fuzzy Set, by F. Smarandache (Chair of the Session on Soft Computing), 2006 IEEE International Conference on Granular Computing, Georgia State University, Atlanta, USA, May 11, 2006.

 

  • Introduction to Neutrosophics and their Applications, by F. Smarandache, Invited speaker at Pushchino Institute of Theoretical and Experimental Biophysics, Pushchino (Moscow region), Russia, August 9, 2005.

bullet

To be and Not to be - An Introduction to Neutrosophy: A Novel Decision Paradigm, by F. Smarandache & S. Bhattacharya, Invited speakers at and sponsored by Jadavpur University, Seminar at the Institute of Business Management, National Council of Education, Kolkata, India, December 23, 2004.  

  • Generalization of the Intuitionistic Fuzzy Set to the Neutrosophic Set, by F. Smarandache & M. Khoshnevisan, 2003 BISC FLINT-CIBI International Workshop on Soft Computing for Internet and Bioinformatics, University of Berkeley, December 15-19, 2003.

  • Neutrosophic Logic Operators, by F. Smarandache, International Congress of Mathematicians, Beijing, China, 20-28 August 2002.

bullet

A Unifying Field in Logics: Neutrosophic Logic. / Neutrosophic Probability, Neutrosophic Set, by F. Smarandache, American Mathematical Society Meeting, University of California at Santa Barbara, USA, March 11, 2000.

 

  • Neutrosophic Probability, Set, and Logic, by F. Smarandache, Second Conference of the Romanian Academy of Scientists, American Branch, New York City, USA, February 2, 1999.

 

NSS Neutrosophic Articles

Neutrosophic Subjects for Future Research:

bullet Neutrosophic topologies, including neutrosophic metric spaces and smooth topological spaces.
bullet Neutrosophic numbers (a+bI, where I = indeterminate and I^2 = I, mI+nI=(m+n)I, 0I = 0, and a, b are real or complex numbers) and arithmetical operations, including ranking procedures for neutrosophic numbers.
bullet Neutrosophic rough sets.
bullet Neutrosophic relational structures, including neutrosophic relational equations, neutrosophic similarity relations, and neutrosophic ordering.
bullet Neutrosophic geometry (Smarandache geometries).
bullet Neutrosophic probability.
bullet Neutrosophic logical operations, including n-norms, n-conorms, neutrosophic implicators, neutrosophic quantifiers.
bullet Measures of neutrosophication.
bullet Deneutrosophication techniques.
bullet Neutrosophic measures, and neutrosophic integrals.
bullet Neutrosophic multivalued mappings.
bullet Neutrosophic differential calculus.
bullet Neutrosophic mathematical morphology.
bullet

Neutrosophic algebraic structures.

bulletNeutrosophic soft algebraic structures.

bulletNeutrosophic triplet structures.

bulletNeutrosophic models.

bulletNeutrosophic matrix, bimatrix, ..., n-matrix. 
  • Neutrosophic graph, which is a graph that has at least one indeterminate edge or one indeterminate node.

  • Neutrosophic tree, which is a tree that has at least one indeterminate edge or one indeterminate node.

bulletNeutrosophic fusion rules for information fusion.
bullet Applications: neutrosophic relational databases, neutrosophic image (thresholding, denoising, segmentation) processing, neutrosophic linguistic variables, neutrosophic decision making and preference structures, neutrosophic expert systems, neutrosophic reliability theory, neutrosophic soft computing techniques in e-commerce and e-learning, image segmentation, etc.

A Neutrosophic Recommender System for Medical Diagnosis Based on Algebraic Neutrosophic Measures http://se.mathworks.com/matlabcentral/fileexchange/55239-a-neutrosophic-recommender-system-for-medical-diagnosis-based-on-algebraic-neutrosophic-measures

Webinar called A Perspective Shift from Fuzzy Logic to Neutrosophic Logic, by Dr. Swati Aggarwal, winner of the 2015 IEEE CIS Webinar Competition for Students and Professionals - Real World Applications and Emerging Topics in Computational Intelligenceat https://youtu.be/WryVUv5Bq98

Submit papers for the special session FUZZ-IEEE-35 Moving Towards Neutrosophic Logic, organized by Swati Aggarwal ( swati1178@gmail.com ), at the IEEE World Congress on Computational Intelligence, Vancouver, Canada, 25-29 July 2016,  http://www.wcci2016.org/spsessions.php

Neutrosophic Sets and Systems (international journal): 2013 (Vol. 1); 2014 (Vol. 2; Vol. 3; Vol. 4; Vol. 5; Vol. 6); 2015 (Vol. 7; Vol. 8; Vol. 9; Vol. 10); 2016 (Vol. 11) new journal

Neutrosophic Science International Association

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