Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Spherical Fuzzy Set, and q-Rung Orthopair Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited)

Authors : Florentin Smarandache

Pages : 1-31

View : 50 | Download : 11

Publication Date : 2019-12-30

Article Type : Research Paper

Abstract :In this paper, we prove that Neutrosophic Set insert ignore into journalissuearticles values(NS); is an extension of Intuitionistic Fuzzy Set insert ignore into journalissuearticles values(IFS); no matter if the sum of neutrosophic components is <1, or >1, or =1. For the case when the sum of components is 1 insert ignore into journalissuearticles values(as in IFS);, after applying the neutrosophic aggregation operators, one gets a different result than applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembership are taken. NS is also more flexible and effective because it handles, besides independent components, also partially independent and partially dependent components, while IFS cannot deal with these. Since there are many types of indeterminacies in our world, we can construct different approaches to various neutrosophic concepts. Neutrosophic Set insert ignore into journalissuearticles values(NS); is a generalisation of Inconsistent Intuitionistic Fuzzy Set insert ignore into journalissuearticles values(IIFS); -which is equivalent to the Picture Fuzzy Set insert ignore into journalissuearticles values(PFS); and Ternary Fuzzy Set insert ignore into journalissuearticles values(TFS); -, Pythagorean Fuzzy Set insert ignore into journalissuearticles values(PyFS);, Spherical Fuzzy Set insert ignore into journalissuearticles values(SFS);, and q-Rung Orthopair Fuzzy Set insert ignore into journalissuearticles values(q-ROFS);. Moreover, all these sets are more general than Intuitionistic Fuzzy Set. We prove that Atanassov’s Intuitionistic Fuzzy Set of the second type insert ignore into journalissuearticles values(IFS2);, and Spherical Fuzzy Sets insert ignore into journalissuearticles values(SFS); do not have independent components. Furthermore, we show that Spherical Neutrosophic Set insert ignore into journalissuearticles values(SNS); and n-Hyper Spherical Neutrosophic Set insert ignore into journalissuearticles values(n-HSNS); are generalisations of IFS2 and SFS. The main distinction between Neutrosophic Set insert ignore into journalissuearticles values(NS); and all previous set theories are a); the independence of all three neutrosophic components - truth-membership insert ignore into journalissuearticles values( T );, indeterminacy-membership insert ignore into journalissuearticles values( I );, falsehood-nonmembership insert ignore into journalissuearticles values( F ); - concerning each other in NS – while in the previous set theories their components are dependent on each other, and b); the importance of indeterminacy in NS - while in previous set theories indeterminacy is entirely or partially ignored. Also, Regret Theory, Grey System Theory, and Three-Ways Decision are particular cases of Neutrosophication and Neutrosophic Probability. We now extend the Three-Ways Decision to n-Ways Decision.
Keywords : Neutrosophic set, intuitionistic fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, q rung orthopair fuzzy set

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