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Neutrosophic Set A Generalization Of The Intuitionistic Fuzzy Set
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Book Synopsis Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set by : Florentin Smarandache
Download or read book Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set written by Florentin Smarandache and published by Infinite Study. This book was released on 2010-08-23 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET by : Florentin SMARANDACHE
Download or read book NEUTROSOPHIC SET – A GENERALIZATION OF THE INTUITIONISTIC FUZZY SET written by Florentin SMARANDACHE and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic by : Florentin Smarandache
Download or read book Neutrosophic Logic - A Generalization of the Intuitionistic Fuzzy Logic written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited by : Florentin Smarandache
Download or read book Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited written by Florentin Smarandache and published by Infinite Study. This book was released on 2018-09-03 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 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) by : Florentin Smarandache
Download or read book 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) written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis 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) by : Florentin Smarandache
Download or read book 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) written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Interval Neutrosophic Sets and Logic: Theory and Applications in Computing by : Haibin Wang
Download or read book Interval Neutrosophic Sets and Logic: Theory and Applications in Computing written by Haibin Wang and published by Infinite Study. This book was released on 2005 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intuitionistic Neutrosophic Set by : Monoranjan Bhowmik
Download or read book Intuitionistic Neutrosophic Set written by Monoranjan Bhowmik and published by Infinite Study. This book was released on with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we define intuitionistic neutrosophic set (INSs) and truth-value based INSs. In fact, all INSs are neutrosophic set but all neutrosophic sets are not INSs. We define some new operations on INSs with examples for the implementation of the operations in real life problems. Also, we studied some properties of INSs.
Book Synopsis About Rough Neutrosophic Soft Sets Theory and Study Their Properties by : Somen Debnath
Download or read book About Rough Neutrosophic Soft Sets Theory and Study Their Properties written by Somen Debnath and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Intuitionistic Fuzzy Sets by : Krassimir T. Atanassov
Download or read book Intuitionistic Fuzzy Sets written by Krassimir T. Atanassov and published by Physica. This book was released on 2013-03-20 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines the degree of non-membership) in the definition of these sets and to study the properties of the new objects so defined. I defined ordinary operations as "n", "U", "+" and "." over the new sets, but I had began to look more seriously at them since April 1983, when I defined operators analogous to the modal operators of "necessity" and "possibility". The late George Gargov (7 April 1947 - 9 November 1996) is the "god father" of the sets I introduced - in fact, he has invented the name "intu itionistic fuzzy", motivated by the fact that the law of the excluded middle does not hold for them. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. In this sense, it has also a referential character.
Book Synopsis Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets by : Florentin Smarandache
Download or read book Arithmetic Operations of Neutrosophic Sets, Interval Neutrosophic Sets and Rough Neutrosophic Sets written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.
Book Synopsis Neutrosophy by : Florentin Smarandache
Download or read book Neutrosophy written by Florentin Smarandache and published by . This book was released on 1998 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets by : A. Rezaei
Download or read book A short history of fuzzy, intuitionistic fuzzy, neutrosophic and plithogenic sets written by A. Rezaei and published by Infinite Study. This book was released on 2022-01-01 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Interval , Double-valued Neutrosophic Intuitionistic Fuzzy Graph by : K. Kalaiarasi
Download or read book Interval , Double-valued Neutrosophic Intuitionistic Fuzzy Graph written by K. Kalaiarasi and published by Infinite Study. This book was released on with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Operators on Interval Valued Neutrosophic Sets by : Abhijit Saha
Download or read book New Operators on Interval Valued Neutrosophic Sets written by Abhijit Saha and published by Infinite Study. This book was released on with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed by F. Smarandache to represent imprecise, incomplete and inconsistent information existing in the real world. A neutrosophic set is characterized by a truth-membership function, an indeterminacy membership function, and a falsity-membership function. An interval neutrosophic set is an instance of a neutrosophic set, which can be used in real scientific and engineering applications. In this paper we have defined some new operators on interval valued neutrosophic sets and studied their properties. In addition, we give numerical examples to illustrate the defined operations.
Book Synopsis Plithogeny, Plithogenic Set, Logic, Probability, and Statistics by : Florentin Smarandache
Download or read book Plithogeny, Plithogenic Set, Logic, Probability, and Statistics written by Florentin Smarandache and published by Infinite Study. This book was released on 2017-10-01 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce for the first time the concept of plithogeny in philosophy and, as a derivative, the concepts of plithogenic set / logic / probability / statistics in mathematics and engineering – and the degrees of contradiction (dissimilarity) between the attributes’ values that contribute to a more accurate construction of plithogenic aggregation operators and to the plithogenic relationship of inclusion (partial ordering).
Book Synopsis Neutrosophic Sets and Systems, Vol. 42, 2021 by : Florentin Smarandache
Download or read book Neutrosophic Sets and Systems, Vol. 42, 2021 written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. In this issue: A hybrid Model Using MCDM Methods and Bipolar Neutrosophic Sets for Select Optimal Wind Turbine: Case Study in Egypt, Graphical Representation of Type-2 Neutrosophic sets, PESTEL Analysis to Identify Key Barriers to Smart Cities Development in India.
