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.

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.

In a general Refined Neutrosophic Logic, T can be split into subcomponents T1, T2, ..., Tm, and I into I1, I2, ..., In, and F into F1, F2, ..., Fp.  

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

T, I, F are independent components, leaving room for incomplete information (when their superior sum < 1), paraconsistent and contradictory information (when the superior sum > 1), or complete information (sum of components = 1). 

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 and Intuitionistic Fuzzy Logic 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.

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

    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.

    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.

    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.

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.

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

BOOKS ON NEUTROSOPHICS

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, by A. Schumann, F. Smarandache
bullet Neutrosophy in Arabic Philosophy, by F. Smarandache, Salah Osman
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, by W. B. Vasantha Kandasamy, F. Smarandache
bullet Fuzzy Relational Maps and Neutrosophic Relational Maps, by W. B. Vasantha Kandasamy, F. Smarandache
bullet Analysis of Social Aspects of Migrant Labourers Living with HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps
bullet Smarandache Neutrosophic Algebraic Structures, by W. B. Vasantha Kandasamy
bullet Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models
bullet Fuzzy Neutrosophic Models for Social Scientists new
bullet Neutrosophic Rings
bullet Interval Groupoids
bullet A Unifying Field in Logics: Neutrosophic Logic.  Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics (fourth 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, by C. Ashbacher
bullet Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, by H. Wang, F. Smarandache, Y-Q. Zhang, R. Sunderraman
bullet Neutrosophic Dialogues, by F. Smarandache, F. Liu
bullet Introduction to Bimatrices, by W. B. Vasantha Kandasamy, F. Smarandache, K.Ilanthenral
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 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 Neutrosophic Logic, Wave Mechanics, and Other Stories (Selected Works 2005-2008)
bullet Neutrosophic Physics: More Problems, More Solutions (Collected Papers)

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

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 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 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.  

 

Articles on Neutrosophics:

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, Andr 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 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. new
bullet Anlisis de textos de Jos Mart utilizando mapas cognitivos neutrosficos, por Maikel Leyva-Vazquez, Karina Perez-Teruel, F. Smarandache, 2013, http://vixra.org/abs/1303.0216 nuevo
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.new
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. new
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. new
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. new
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.  new
bullet Color Image Segmentation Based on Neutrosophic Method, by Ling Zhang, Ming Zhang, H. D. Cheng, Optical Engineering, 51(3), 037009, 2012.
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. new
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. Lupiez, 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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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, Andr 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, Arhivele Statului, Filiala Vlcea, Rm. Vlcea, 1969; 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. new
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. new
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 Applications, 12(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 Lupiez,  Recent advances in Fuzzy Systems, WSEAS (Athens , 2009), 59-62.
bullet Interval  neutrosophic sets and  Topology, by F .G. Lupiez, Kybernetes 38 (2009), 621-624.
bullet On various  neutrosophic topologies, by F .G. Lupiez, Kybernetes 38 (2009), 1009-1013.
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Interval neutrosophic sets and topology, Francisco Gallego Lupiez, 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.
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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. Lupiez, Kybernetes 37 (2008), 797-800.
bullet Interval  neutrosophic sets and  Topology,  by F .G. Lupiez,Applied and Computational Mathematics, WSEAS ( Athens , 2008), 110-112.
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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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A simplification of the neutrosophic sets. Neutrosophic logic and intuitionistic fuzzy sets, by Kalin Georgiev, Conference proceedings, Notes on IFS, Volume 11 (2005) Number 2, pages 28?31; Presented at: 9th ICIFS, Sofia, Bulgaria, 7-8 May 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.
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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.
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Six Neutral Fundamental Reactions Between Four Fundamental Reactions,  by Fu Yuhua, Fu Anjie, Zhao Ge,
http://wbabin.net/physics/yuhua2.pdf.
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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.
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Neutrosophic Transdisciplinarity, by F. Smarandache, 1969.
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Online English Dictionary, Definition of Neutrosophy.

 

Seminars on Neutrosophics: 

 

  • 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.
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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.

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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.

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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.

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 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.

 

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