Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set
Title | Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Total Pages | 10 |
Release | 2010-08-23 |
Genre | Mathematics |
ISBN |
In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET
Title | NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET PDF eBook |
Author | Florentin SMARANDACHE |
Publisher | Infinite Study |
Total Pages | 10 |
Release | |
Genre | |
ISBN |
In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic
Title | Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Total Pages | 7 |
Release | |
Genre | |
ISBN |
In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.
Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set (Atanassov’s Intuitionistic Fuzzy Set of second type), q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited)
Title | Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set (Atanassov’s Intuitionistic Fuzzy Set of second type), q-Rung Orthopair Fuzzy Set, Spherical Fuzzy Set, and n-HyperSpherical Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited) PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Total Pages | 50 |
Release | |
Genre | Mathematics |
ISBN |
In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of 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 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)
Title | 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) PDF eBook |
Author | Florentin Smarandache |
Publisher | Infinite Study |
Total Pages | 31 |
Release | |
Genre | Mathematics |
ISBN |
In this paper, we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (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 (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.
A Geometric Interpretation of the Neutrosophic Set, A Generalization of the Intuitionistic Fuzzy Set
Title | A Geometric Interpretation of the Neutrosophic Set, A Generalization of the Intuitionistic Fuzzy Set PDF eBook |
Author | Florentin Smarandache |
Publisher | |
Total Pages | 9 |
Release | 2017 |
Genre | |
ISBN |
In this paper we give a geometric interpretation of the Neutrosophic Set using the Neutrosophic Cube. Distinctions between the neutrosophic set and intuitionistic fuzzy set are also presented.
Interval Neutrosophic Sets and Logic: Theory and Applications in Computing
Title | Interval Neutrosophic Sets and Logic: Theory and Applications in Computing PDF eBook |
Author | Haibin Wang |
Publisher | Infinite Study |
Total Pages | 99 |
Release | 2005 |
Genre | Mathematics |
ISBN | 1931233942 |
This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic.