Neutrosophic Publications

- Call for Papers on special issue “Neutrosophic Decision Making in Healthcare - New Directions, Challenges and Applications” at the journal Informatics in Medicine Unlocked (Elsevier, Cite Score: 1.13) https://www.journals.elsevier.com/informatics-in-medicine-unlocked/call-for-papers/neutrosophic-decision-making-in-healthcare

- Call for Papers on special issue “Applications of Neutrosophic Theory in Industry – Challenges and Future Trends” at Computers in Industry (Elsevier, SCIE, IF: 2.850) journal: https://www.journals.elsevier.com/computers-in-industry/call-for-papers/special-issue-applications-neutrosophic-theory-industry . Go to https://www.evise.com/profile/api/navigate/COMIND, Start New Submission, Issue: select VSI:Neutrosophic_Industry

- Call for Papers on special issue “Neutrosophic Fusion of Data and Information- New Directions, Challenges and Applications” at the journal Measurement (Elsevier, IF 2.218), https://www.journals.elsevier.com/measurement/call-for-papers/neutrosophic-fusion-of-data-and-information

- Call for Papers on special issue "Neutrosophic Fusion of Sensors, Data, and Information", at the International Journal of Distributed Sensor Networks (IF = 1.787), http://journals.sagepub.com/page/dsn/collections/special-issues/neutrosophic-fusion

- Call for Papers on special issue "Neutrosophic Operational Research – Challenges and Future Trends" at the journal Operational Research Perspectives journal (Elsevier, Scopus) ]: https://www.journals.elsevier.com/operations-research-perspectives/call-for-papers/neutrosophic-operational-research-challenges

- - Call for Papers on special issue on “Neutrosophic Topology” at Axioms (Scopus, ESCI, SCI) journal, Basel, Switzerland, http://www.mdpi.com/journal/axioms/special_issues/neutrosophic_topology

- Call for Papers on special issue "Neutrosophic Sets and Systems in Data Science" at the journal Cognitive Systems Research international journal (Elsevier, in SCOPUS and ISI-Thomson with IF 1.425, Sci-Exp), https://www.journals.elsevier.com/cognitive-systems-research/call-for-papers/neutrosophic-sets-and-systems-in-data-science

- Call for Papers on Neutrosophic Cognitive Psychology [ see: http://fs.unm.edu/NeutropsychicPersonality-ed2.pdf ] at “New Ideas in Psychology” international journal (Elsevier, IF: 1.367), https://www.journals.elsevier.com/new-ideas-in-psychology/call-for-papers/research-frontiers-in-cognitive-psychology-for-consumer

- Call for Papers on special issue "Applications of Neutrosophic Multicriteria Decision Making to Complex Engineering Problems", at Complex & Intelligent Systems journal, Springer. Go to: http://www.editorialmanager.com/cais/default.aspx , Select “Submit a manuscript”, “Select Article Type”, and choose “SI: Neutrosophic MCDM”. Prepare the manuscripts according to the online submission page https://link.springer.com/journal/40747

- Call for Papers on special issue on "Neutrosophic Statistics" at Statistics international journal (SCI), Basel, Switzerland
http://www.mdpi.com/journal/stats/special_issues/neutro_stat

- Call for Papers on special issue "Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets" at the journal Symmetry (Basel, Zwitzerland, in Scopus, IF: 1.256): http://www.mdpi.com/journal/symmetry/special_issues/Algebraic_Structure_Neutrosophic_Triplet_Neutrosophic_Duplet_Neutrosophic_Multiset

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).

See this paper on Independent/Dependent Neutrosophic Components.

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 1-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, ..., T_p, and I into I₁, I₂, ..., I_r, and F into F₁, F₂, ...,F_s, where p+r+s = n ≥ 1. Even more: T, I, and/or F (or any of their subcomponents T_j, I_k, and/or F_l) can be countable or uncountable infinite sets:
n-ValuedNeutrosophicLogic-PiP.pdf .

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 Neutrosophic Set was extended [Smarandache, 2007] to Neutrosophic Overset (when some Neutrosophic component is > 1), since we observed that, for example, an employee working overtime deserves a degree of membership > 1, with respect to an employee that only works regular full-time and whose degree of membership = 1;

and to Neutrosophic Underset (when some Neutrosophic component is < 0), since, for example, an employee making more damage than benefit to his company deserves a degree of membership < 0, with respect to an employee that produces benefit to the company and has the degree of membership > 0;

and to and to Neutrosophic Offset (when some Neutrosophic components are off the interval [0, 1], i.e. some Neutrosophic component > 1 and some Neutrosophic component < 0).

Then, similarly, the Neutrosophic Logic/Measure/Probability/Statistics etc. were extended to respectively Neutrosophic Over-/Under-/Off- Logic, Measure, Probability, Statistics etc.

SVNeutrosophicOverset-JMI.pdf

IV-Neutrosophic-Overset-Underset-Offset.pdf

NSS/DegreesOf-Over-Under-Off-Membership.pdf

NeutrosophicOversetUndersetOffset.pdf

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 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 PUBLICATIONS IN THE DEVELOPMENT OF NeutROSOPHICS
1995-1998 - Smarandache generalizes the dialectics to Neutrosophy; introduces the Neutrosophic set/logic/probability/statistics; introductes the single-valued Neutrosophic set (pp. 7-8); *eBook-Neutrosophics6.pdf (online edition)* 2002 – introduces special types of sets / probabilities / statistics / logics, such as: - intuitionistic set, paraconsistent set, faillibilist set, paradoxist set, pseudo-paradoxist set, tautological set, nihilist set, dialetheist set, trivialist set; - intuitionistic probability and statistics, paraconsistent probability and statistics, faillibilist probability and statistics, paradoxist probability and statistics, pseudo-paradoxist probability and statistics, tautological probability and statistics, nihilist probability and statistics, dialetheist probability and statistics, trivialist probability and statistics; - paradoxist logic (or paradoxism), pseudo-paradoxist logic (or pseudo-paradoxism), tautological logic (or tautologism); DefinitionsDerivedFromNeutrosophics.pdf 2003 - introduction of Neutrosophic numbers (a+bI, where I = indeterminacy) 2003 - introduction of I-Neutrosophic algebraic structures 2003 - introduction to Neutrosophic Cognitive Maps NCMs.pdf 2005 - introduction of Interval Neutrosophic Set/Logic INSL.pdf 2006 - introduction of the Degree of Dependence and Degree of Independence between T, I, and F eBook-Neutrosophics6.pdf (online edition) [p. 92] NSS/DegreeOfDependenceAndIndependence.pdf 2007 - The Neutrosophic Set was extended [Smarandache, 2007] to Neutrosophic Overset (when some Neutrosophic component is > 1), and to Neutrosophic Underset (when some Neutrosophic component is < 0), and to and to Neutrosophic Offset (when some Neutrosophic components are off the interval [0, 1], i.e. some Neutrosophic component > 1 and some Neutrosophic component < 0). Then, similarly, the Neutrosophic Logic/Measure/Probability/Statistics etc. were extended to respectively Neutrosophic Over/Under/Off Logic, Measure, Probability, Statistics etc. SVNeutrosophicOverset-JMI.pdf IV-Neutrosophic-Overset-Underset-Offset.pdf NeutrosophicOversetUndersetOffset.pdf 2007 - introduction of the Neutrosophic Tripolar Set and Neutrosophic Multipolar Set [Smarandache] and consequently - the Neutrosophic Tripolar Graph and Neutrosophic Multipolar Graph eBook-Neutrosophics6.pdf (online edition) [p. 93] IFS-generalized.pdf 2009 - introduction of N-norm and N-conorm 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). NeutrosophicMeasureIntegralProbability.pdf 2013 - Smarandache refined the components (T, I, F) as (T1, T2, ...; I1, I2, ...; F1, F2, ...) n-ValuedNeutrosophicLogic-PiP.pdf 2014 - introduction of the Law of Included Multiple Middle (<A>; <Neut1A>, <Neut2A>, ...; <antiA>) 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) NeutrosophicStatistics.pdf 2015 - introduction of Neutrosophic Precalculus and Neutrosophic Calculus 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, Quadruple Neutrosophic Algebraic Structures, Multiplication Law of Subindeterminacies: SymbolicNeutrosophicTheory.pdf 2015 – Introduction of Neutrosophic Crisp Set <A, B, C> and Topology (Salama & Smarandache) NeutrosophicCrispSetTheory.pdf 2016 - Neutrosophic Multisets (as generalization of classical multisets) NeutrosophicMultisets.htm 2016 - Neutrosophic Triplet structures (introduced by F. Smarandache & M. Ali) NeutrosophicTriplets.htm 2016 - Neutrosophic Duplet structures NeutrosophicDuplets.htm 2017 - introduction by F. Smarandache of Plithogeny (generalization of Dialectics and Neutrosophy), and Plithogenic Set/Logic/Probability/Statistics (generalization of fuzzy, intuitionistic fuzzy, neutrosophic set/logic/probability/statistics) Plithogeny.pdf 2018 - Neutrosophic Psychology (Neutropsyche, Neutropsychic Personality, Eros / Aoristos / Thanatos, Refined Neutrosophic Memory: conscious, aconscious, unconscious, Neutropsychic Crisp Personality, Neutrosophic Body-Soul-Mind Functioning) NeutropsychicPersonality-ed2.pdf 1998 - 2018: Neutrosophic Applications in: Artificial Intelligence, Information Systems, Computer Science, Cybernetics, Theory Methods, Mathematical Algebraic Structures, Applied Mathematics, Automation, Control Systems, Big Data, Engineering, Electrical, Electronic, Philosophy, Social Science, Psychology, Biology, Biomedical, Engineering, Medical Informatics, Operational Research, Management Science, Imaging Science, Photographic Technology, Instruments, Instrumentation, Physics, Optics, Economics, Mechanics, Neurosciences, Radiology Nuclear, Medicine, Medical Imaging, Interdisciplinary Applications, Multidisciplinary Sciences etc. [ Xindong Peng and Jingguo Dai, A bibliometric analysis of neutrosophic set: two decades review from 1998 to 2017, Artificial Intelligence Review, Springer, 18 August 2018; BibliometricNeutrosophy.pdf ].

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

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), Atlantis Press.

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