New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications

Dear Colleagues,

The fields of neutrosophic set, logic, measure, probability, and statistics have been developed and explored very much in the last few years due to their multiple practical applications.

The neutrosophic components truth (T), indeterminacy (I), and falsehood (F) are symmetric in form, since T is symmetric to its opposite F with respect to I, which acts as an axis of symmetry:  T----------I----------F

This Special Issue invites state-of-the-art papers on new topics related of neutrosophic theories and applications, such as

- Studies of corner cases of neutrosophic sets/probabilities/statistics/logics, such as

• neutrosophic intuitionistic sets (which are different from intuitionistic fuzzy sets), neutrosophic paraconsistent sets, neutrosophic faillibilist sets, neutrosophic paradoxist sets, neutrosophic, pseudo-paradoxist sets, neutrosophic tautological sets, neutrosophic nihilist sets, neutrosophic dialetheist sets, and neutrosophic trivialist sets;
• neutrosophic intuitionistic probability and statistics, neutrosophic paraconsistent probability and statistics, neutrosophic faillibilist probability and statistics, neutrosophic paradoxist probability and statistics, neutrosophic pseudo-paradoxist probability and statistics, neutrosophic tautological probability and statistics, neutrosophic nihilist probability and statistics, neutrosophic dialetheist probability and statistics, and neutrosophic trivialist probability and statistics;
• neutrosophic paradoxist logic (or paradoxism), neutrosophic pseudo-paradoxist logic (or neutrosophic pseudo-paradoxism), and neutrosophic tautological logic (or neutrosophic tautologism):

https://arxiv.org/ftp/math/papers/0301/0301340.pdf

http://fs.unm.edu/DefinitionsDerivedFromNeutrosophics.pdf

• Refined Neutrosophic Set components (T, I, and F) of many neutrosophic sub-components:

(T₁, T₂, ...; I₁, I₂, ...; F₁, F₂, ...);

https://arxiv.org/ftp/arxiv/papers/1407/1407.1041.pdf

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

• Degrees of Dependence and Independence between Neutrosophic Components

T, I, and 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). 

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, and 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, and 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), in which 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.

https://doi.org/10.5281/zenodo.571359

http://fs.unm.edu/NSS/DegreeOfDependenceAndIndependence.pdf

- Neutrosophic Overset (when some neutrosophic component is > 1), since he 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 causing 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 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, neutrosophic logic/measure/probability/statistics, etc., were extended to, respectively, Neutrosophic Over-/Under-/Off- Logic, Measure, Probability, and Statistics, etc.

https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf

http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf

http://fs.unm.edu/SVNeutrosophicOverset-JMI.pdf

http://fs.unm.edu/IV-Neutrosophic-Overset-Underset-Offset.pdf 

• Neutrosophic Tripolar Set and Neutrosophic Multipolar Set

and, consequently, the Neutrosophic Tripolar Graph and Neutrosophic Multipolar Graph

http://fs.unm.edu/eBook-Neutrosophics6.pdf (p. 93)

http://fs.unm.edu/IFS-generalized.pdf

- N-norm and N-conorm

https://arxiv.org/ftp/arxiv/papers/0901/0901.1289.pdf

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

- Neutrosophic Measure and Neutrosophic Probability 
          (chance that an event occurs, indeterminate chance of occurrence,
           chance that the event does not occur)

https://arxiv.org/ftp/arxiv/papers/1311/1311.7139.pdf

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

• Law of Included Multiple-Middle (as middle part of Neutrosophy)

(<A>;  <neut1A>, <neut2A>, …;  <antiA>)

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

- 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, or with respect to the neutrosophic probability distributions)

https://arxiv.org/ftp/arxiv/papers/1406/1406.2000.pdf

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

- Neutrosophic Precalculus and Neutrosophic Calculus

https://arxiv.org/ftp/arxiv/papers/1509/1509.07723.pdf

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

– Refined Neutrosophic Numbers (a+ b₁I₁ + b₂I₂ + … + b_nI_n), in which I₁, I₂, …, I_n are subindeterminacies of indeterminacy I;

(t,i,f)-neutrosophic graphs;

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:

https://arxiv.org/ftp/arxiv/papers/1512/1512.00047.pdf   

http://fs.unm.edu/SymbolicNeutrosophicTheory.pdf

- Theory of Neutrosophic Evolution: Degrees of Evolution, Indeterminacy or Neutrality, and Involution

 http://fs.unm.edu/neutrosophic-evolution-PP-49-13.pdf

- Plithogeny as Generalization of Dialectics and Neutrosophy;

Plithogenic Set/Logic/Probability/Statistics (as generalization of fuzzy, intuitionistic fuzzy, neutrosophic set/logic/probability/statistics)

https://arxiv.org/ftp/arxiv/papers/1808/1808.03948.pdf

http://fs.unm.edu/Plithogeny.pdf

- Neutrosophic Psychology (neutropsyche, refined neutrosophic memory: conscious, aconscious, unconscious, neutropsychic personality, Eros/Aoristos/Thanatos, neutropsychic crisp personality)

http://fs.unm.edu/NeutropsychicPersonality-ed3.pdf

- 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, engineering, operational research, management science, imaging science, photographic technology, instruments, instrumentation, physics, optics, economics, mechanics, neurosciences, radiology nuclear, interdisciplinary applications, multidisciplinary sciences, etc.

[See: 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;

http://fs.unm.edu/BibliometricNeutrosophy.pdf]

Prof. Dr. Florentin Smarandache
Guest Editor

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