Neutrosophic Set A Generalization Of The Intuitionistic Fuzzy Set
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Neutrosophic Set A Generalization Of The Intuitionistic Fuzzy Set
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2010-08-23
Neutrosophic Set A Generalization Of The Intuitionistic Fuzzy Set written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-23 with Mathematics categories.
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
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Author : Florentin SMARANDACHE
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Set A Generalization Of The Intuitionistic Fuzzy Set written by Florentin SMARANDACHE and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Logic A Generalization Of The Intuitionistic Fuzzy Logic written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
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.
Plithogenic Set An Extension Of Crisp Fuzzy Intuitionistic Fuzzy And Neutrosophic Sets Revisited
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2018-09-03
Plithogenic Set An Extension Of Crisp Fuzzy Intuitionistic Fuzzy And Neutrosophic Sets Revisited written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life.
About Rough Neutrosophic Soft Sets Theory And Study Their Properties
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Author : Somen Debnath
language : en
Publisher: Infinite Study
Release Date :
About Rough Neutrosophic Soft Sets Theory And Study Their Properties written by Somen Debnath and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Earlier fuzzy set, vague set, intuitionistic fuzzy set, L-fuzzy set etc are used as a mathematical tools for solving problems based on uncertainties or ambiguous in nature. But due to more complexity involves in problems exist in nature, traditional tools are unable to handle those in a systematic manner. So we need a tool which is more flexible to handle those problems. Which leads to the invention of soft set which was introduced by Molodtsov in 1999. Soft set (SS) theory is a mathematical tool deals with parametric data which are imprecise in nature. Ithis a generalization of fuzzy set theory. On the other hand Rough set (RS) theory and Neutrosophic set (NS) theory both rising as a powerful tool to handle these uncertain, incomplete, inconsistent and imprecise information in an effective manner. Actually Neutrosophic set is a generalization of intuitionistic fuzzy set. Sometimes it is not possible to handle all sorts of uncertain problems with a single mathematical tool. Fusion of two or more mathematical tools give rise to a new mathematical concept which gives an idea how to solve such type of problems in a more sophisticated ways. Which leads to the introduction of fuzzy soft set, rough soft set, intuitionistic fuzzy soft set, soft rough set etc. Neutrosophic soft set (NSS) was established by combining the concept of Soft set and Neutrosophic set. In this paper, using the concept of Rough set and Neutrosophic soft set a new concept known as Rough neutrosophic soft set (RNSS) is developed. Some properties and operations on them are introduced.
A Short History Of Fuzzy Intuitionistic Fuzzy Neutrosophic And Plithogenic Sets
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Author : A. Rezaei
language : en
Publisher: Infinite Study
Release Date : 2022-01-01
A Short History Of Fuzzy Intuitionistic Fuzzy Neutrosophic And Plithogenic Sets written by A. Rezaei and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets.
Interval Double Valued Neutrosophic Intuitionistic Fuzzy Graph
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Author : K. Kalaiarasi
language : en
Publisher: Infinite Study
Release Date :
Interval Double Valued Neutrosophic Intuitionistic Fuzzy Graph written by K. Kalaiarasi and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The notion of interval, double-valued neutrosophic intuitionistic fuzzy sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued intuitionistic fuzzy sets. We apply the concept of interval, double-valued neutrosophic intuitionistic fuzzy sets an instance of neutrosophic intuitionistic fuzzy sets, to graphs. We introduce certain types of strong interval ,double-valued neutrosophic intuitionistic fuzzy graphs and investigate some of their properties with proofs and examples.
Single Valued Neutrosophic Sets
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Author : Haibin Wang
language : en
Publisher: Infinite Study
Release Date : 2010-01-01
Single Valued Neutrosophic Sets written by Haibin Wang and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the settheoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.
Development Of Hybrids Of Hypersoft Set With Complex Fuzzy Set Complex Intuitionistic Fuzzy Set And Complex Neutrosophic Set
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Author : Atiqe Ur Rahman
language : en
Publisher: Infinite Study
Release Date : 2020-12-01
Development Of Hybrids Of Hypersoft Set With Complex Fuzzy Set Complex Intuitionistic Fuzzy Set And Complex Neutrosophic Set written by Atiqe Ur Rahman and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-01 with Mathematics categories.
The complex fuzzy soft set and its generalized hybrids are such effective structures which not only minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulfill all the parametric requirements of soft sets. This feature makes it a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set as it transforms the single attribute function into a multi-attribute function. This generalization demands an extension of complex fuzzy soft-like structures to hypersoft structure for more precise results. In this study, hybrids of hypersoft set with complex fuzzy set and its generalized structures i.e. complex intuitionistic fuzzy set and complex neutrosophic set, are developed along with illustrative examples to address the demand of literature. Moreover, some of their fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic operations i.e. compliment, union, intersection etc. are discussed.
Rough Neutrosophic Soft Sets
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Author : Somen Debnath
language : en
Publisher: Infinite Study
Release Date :
Rough Neutrosophic Soft Sets written by Somen Debnath and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Soft set(SS) theory is a mathematical tool deals with parametric data which are imprecise in nature.It is a generalization of fuzzy set theory. On the other hand Rough set(RS) theory and Neutrosophic set (NS)theory both rising as powerful tool to handle uncertain, incomplete, inconsistent and imprecise information in an effective manner.Actually Neutrosophic set is a generalization of intuitionistic fuzzy set.Earlier Neutrosophic soft set(NSS) was established by combining the concept of Soft set and Neutrosophic set .In this paper , using the concept of Rough set,Neutrosophic set and soft set a hybrid structure Rough neutrosophic soft sets(RNSS) is developed.Some properties and operations on RNSS are introduced.