NEUTROSOPHY, NEUTROSOPHIC LOGIC, NEUTROSOPHIC SET,
NEUTROSOPHIC PROBABILITY AND STATISTICS
(philosophy, math,
science)
Short Definitions of Neutrosophics:
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.
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.
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.
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.
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.
The neutrosophics
were introduced by F. Smarandache in 1995.
This theory
considers every notion or idea <A> together with its opposite or negation
<Anti-A> and the spectrum of "neutralities" <Neut-A> (i.e. notions or ideas
located between the two extremes, supporting neither <A> nor <Anti-A>). The <Neut-A>
and <Anti-A> ideas together are referred to as <Non-A>.
According to this
theory every idea <A> tends to be neutralized and balanced by <Anti-A> and
<Non-A> ideas - as a state of equilibrium.
In a classical way
<A>, <Neut-A>, <Anti-A> are disjoint two by two.
But, since in many
cases the borders between notions are vague, imprecise, Sorites, it is
possible that <A>, <Neut-A>, <Anti-A> (and <Non-A> of course) have common parts
two by two as well.
Neutrosophy is the
base of neutrosophic logic, neutrosophic set, neutrosophic probability and
statistics used in engineering applications (especially for software and
information fusion), medicine, military, cybernetics, physics.
EBOOKS ON
NEUTROSOPHICS
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Finite Neutrosophic Complex Numbers
new |
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Neutrosophic
Interval Bialgebraic Structures |
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Neutrosophic Bilinear Algebras and Their Generalizations
Interval
Groupoids |
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Neutrality and
Many-Valued Logics, by A. Schumann, F. Smarandache |
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Neutrosophy
in Arabic Philosophy, by F. Smarandache, Salah Osman |
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(
 
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[Arabic] |
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Fuzzy Cognitive Maps and
Neutrosophic Cognitive Maps, by W. B. Vasantha Kandasamy, F. Smarandache |
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Fuzzy Relational Maps and
Neutrosophic Relational Maps, by W. B. Vasantha Kandasamy, F. Smarandache |
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Analysis of Social
Aspects of Migrant Labourers Living with HIV/AIDS Using Fuzzy Theory and
Neutrosophic Cognitive Maps |
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Smarandache Neutrosophic
Algebraic Structures, by W. B. Vasantha Kandasamy | |
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Basic Neutrosophic Algebraic
Structures and Their Application to Fuzzy and Neutrosophic Models |
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Neutrosophic
Rings |
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Interval
Groupoids | |
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A Unifying
Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set,
Neutrosophic Probability and Statistics (fourth edition) |
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Сущность нейтрософии;
Смарадаке
Ф.(перевод Д. Рабунского)[Russian] | |
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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] | |
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中道辩证法与唯道主义自然哲学[Chinese Neutrosophy and Taoist Natural Philosophy](Chinese) |
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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] |
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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 ) | |
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Proceedings
of the First International Conference on Neutrosophy, Neutrosophic Logic,
Neutrosophic Set, Neutrosophic Probability and Statistics | |
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Proceedings of the Introduction
to Neutrosophic Physics: Unmatter & Unparticle International Conference new |
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Introduction to
Neutrosophic Logic, by C. Ashbacher |
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Interval Neutrosophic Sets and
Logic: Theory and Applications in Computing, by H. Wang, F. Smarandache,
Y-Q. Zhang, R. Sunderraman | |
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Neutrosophic
Dialogues, by F. Smarandache, F. Liu |
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Introduction to
Bimatrices, by W. B. Vasantha Kandasamy, F. Smarandache, K.Ilanthenral |
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Applications of
Bimatrices to some Fuzzy and Neutrosophic Models |
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Fuzzy Interval Matrices and
Neutrosophic Interval Matrices and their Applications |
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Elementary Fuzzy Matrix
Theory and Fuzzy Models for Social Scientists |
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Special Fuzzy
Matrices for Social Scientists |
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Methods in
Industrial Biotechnology for Chemical Engineers |
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Introduction to Linear
Bialgebra |
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Fuzzy and Neutrosophic
Analysis of Women with HIV/AIDS |
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Fuzzy and Neutrosophic
Analysis of Periyar's Views on Untouchability |
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Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic
Structures |
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Vedic Mathematics -
'Vedic' or 'Mathematics': A Fuzzy & Neutrosophic Analysis |
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Neutrosophic Logic,
Wave Mechanics, and Other Stories (Selected Works 2005-2008) |
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Neutrosophic
Physics: More Problems, More Solutions (Collected Papers) |
Ph. D. Dissertations on Neutrosophic
Logic/Set/Probability:
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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. |
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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. |
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Haibin Wang,
Study on Interval Neutrosophic Set and Logic, Georgia State University,
Atlanta, USA, 2005. |
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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. |
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First International
Conference on Neutrosophy, Neutrosophic Logic, Set, Probability and
Statistics, University of New Mexico, Gallup, 1-3 December 2001. |
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Articles on Neutrosophics:
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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. |
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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. |
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F .G. Lupiáñez:
“On neutrosophic
paraconsistent topology”,
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, 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, Arhivele Statului, Filiala Vâlcea, Rm. Vâlcea, 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. |
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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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M R Bivin, N.Saivaraju and K S Ravichandran, Remedy for Effective Cure of
Diseases using Combined Neutrosophic Relational Maps, 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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Tahar
Guerram, Ramdane Maamri, and Zaidi Sahnoun, A Tool for Qualitative
Causal Reasoning On Complex Systems, IJCSI International Journal of
Computer Science Issues, Vol. 7, Issue 6, November 2010. |
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P. Thiruppathi,
N.Saivaraju, K.S. Ravichandran, A Study
on Suicide problem using Combined Overlap Block Neutrosophic Cognitive Maps,
International Journal of Algorithms, Computing and Mathematics, Vol. 3,
Number 4, November 2010. |
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Francisco Gallego
Lupiáñez,
“On various
neutrosophic topologies”, in
“Recent advances in Fuzzy Systems”, WSEAS (Athens , 2009), 59-62. |
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F .G. Lupiáñez:
"Interval
neutrosophic sets and
Topology", Kybernetes
38 (2009), 621-624. |
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F .G. Lupiáñez:
"On various
neutrosophic topologies",
Kybernetes 38
(2009), 1009-1013. |
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Francisco Gallego
Lupiáñez,
Interval neutrosophic sets and topology,
Kybernetes: The
International Journal of Systems & Cybernetics, Volume 38, Numbers
3-4, 2009 , pp. 621-624(4). |
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Andrew Schumann, Neutrosophic logics on Non-Archimedean Structures,
Critical Review,
Creighton University, USA, Vol. III, 36-58, 2009. |
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Fu
Yuhua, Fu Anjie, Zhao Ge. Positive, Negative and Neutral Law of Universal
Gravitation, New Science and Technology, 2009 (12), 30-32. |
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F .G. Lupiáñez: "On
Neutrosophic Topology",
Kybernetes 37
(2008), 797-800. |
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F .G. Lupiáñez:
"Interval
neutrosophic sets and
Topology", in “Applied and Computational
Mathematics”, WSEAS (
Athens , 2008), 110-112. |
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Smita Rajpal,
M.N. Doja and Ranjit Biswas, A Method of Neutrosophic Logia to Answer
Queries in Relational Database, Journal of Computer Science 4 (4):
309-314, 2008. |
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Pawalai Kraipeerapun,
Chun Che Fung,
Kok Wai Wong,
Ensemble Neural Networks Using Interval Neutrosophic Sets and Bagging,
Third International Conference on Natural Computation (ICNC 2007), Haikou,
Hainan, China, August 24-August 27, 2007. |
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Pawalai
Kraipeerapun, Chun Che Fung, and Kok Wai Wong,
Lithofacies Classification
from Well Log Data using Neural
Networks, Interval Neutrosophic Sets and Quantification
of Uncertainty,
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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P.
Kraipeerapun, C. C. Fung,
W. Brown and K.
W.
Wong,
Neural network ensembles using interval neutrosophic sets and bagging for
mineral prospectivity prediction and quantification of uncertainty,
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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Kalin Georgiev, A simplification of the neutrosophic sets. Neutrosophic
logic and intuitionistic fuzzy sets,
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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Milan
Mares, Book Review: W. B. Vasantha Kandasamy and Florentin Smarandache,
Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, Kybernetika, Vol.
40 (2004), No. 1, [151]-15. |
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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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C. Lee, Preamble to Neutrosophic Logic,
Multiple-Valued Logic / An International Journal, Vol. 8, No. 3, 285-296,
June 2002. |
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Florentin Smarandache, Neutrosophy, a New
Branch of Philosophy, Multiple-Valued Logic / An International Journal,
Vol. 8, No. 3, 297-384, June 2002. |
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Florentin Smarandache, A Unifying Field in
Logics: Neutrosophic Field, Multiple-Valued Logic / An International
Journal, Vol. 8, No. 3, 385-438, June 2002. |
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Jean Dezert, Open Questions to Neutrosophic
Inferences, 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,
2001. |
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Fu Yuhua, Fu Anjie, Zhao Ge.
Six Neutral Fundamental Reactions Between Four Fundamental Reactions,
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.
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Seminars on Neutrosophics:
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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.
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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.
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An Introduction to Neutrosophic Logic in Arabic
Philosophy, presented by F. Smarandache & Salah Osman, Minufiya
University, Shebin Elkom, Egypt, 17 December 2007.
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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. |
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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. |
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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. |
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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.
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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.
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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.
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Neutrosophic Subjects for Future Research:
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Neutrosophic topologies, including neutrosophic metric spaces and smooth topological spaces |
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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 |
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Neutrosophic rough sets |
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Neutrosophic relational structures,
including neutrosophic relational equations, neutrosophic similarity
relations, and neutrosophic ordering |
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Neutrosophic
geometry (Smarandache geometries) |
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Neutrosophic probability |
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Neutrosophic logical operations,
including n-norms, n-conorms, neutrosophic implicators, neutrosophic
quantifiers |
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Measures of neutrosophication |
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Deneutrosophication techniques |
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Neutrosophic measures, and neutrosophic
integrals |
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Neutrosophic multivalued mappings |
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Neutrosophic differential calculus |
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Neutrosophic mathematical morphology |
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Neutrosophic algebraic
structures |
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| | Neutrosophic models
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| Neutrosophic matrix,
bimatrix, ..., n-matrix
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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
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| | Neutrosophic fusion rules |
for information fusion
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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. |