The Consistency Between Cross Entropy And Distance Measures In Fuzzy Sets
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The Consistency Between Cross Entropy And Distance Measures In Fuzzy Sets
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Author : Yameng Wang
language : en
Publisher: Infinite Study
Release Date :
The Consistency Between Cross Entropy And Distance Measures In Fuzzy Sets written by Yameng 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 with Mathematics categories.
The processing of uncertain information is increasingly becoming a hot topic in the artificial intelligence field, and the information measures of uncertainty information processing are also becoming of importance. In the process of decision-making, decision-makers make decisions mostly according to information measures such as similarity, distance, entropy, and cross-entropy in order to choose the best one. However, we found that many researchers apply cross-entropy to multi-attribute decision-making according to the minimum principle, which is in accordance with the principle of distance measures.
Distance Measures Between The Interval Valued Complex Fuzzy Sets
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Author : Songsong Dai
language : en
Publisher: Infinite Study
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Distance Measures Between The Interval Valued Complex Fuzzy Sets written by Songsong Dai 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.
Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [0, 1] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.
Entropy Measures Of Distance And Similarity Of Q Neutrosophic Soft Sets And Some Applications
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Author : Majdoleen Abu Qamar
language : en
Publisher: Infinite Study
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Entropy Measures Of Distance And Similarity Of Q Neutrosophic Soft Sets And Some Applications written by Majdoleen Abu Qamar 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 idea of the Q-neutrosophic soft set emerges from the neutrosophic soft set by upgrading the membership functions to a two-dimensional entity which indicate uncertainty, indeterminacy and falsity. Hence, it is able to deal with two-dimensional inconsistent, imprecise, and indeterminate information appearing in real life situations. In this study, the tools that measure the similarity, distance and the degree of fuzziness of Q-neutrosophic soft sets are presented. The definitions of distance, similarity and measures of entropy are introduced. Some formulas for Q-neutrosophic soft entropy were presented. The known Hamming, Euclidean and their normalized distances are generalized to make them well matched with the idea of Q-neutrosophic soft set. The distance measure is subsequently used to define the measure of similarity. Lastly, we expound three applications of the measures of Q-neutrosophic soft sets by applying entropy and the similarity measure to a medical diagnosis and decision making problems.
Handbook Of Research On Advances And Applications Of Fuzzy Sets And Logic
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Author : Broumi, Said
language : en
Publisher: IGI Global
Release Date : 2022-03-04
Handbook Of Research On Advances And Applications Of Fuzzy Sets And Logic written by Broumi, Said and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-04 with Mathematics categories.
Fuzzy logic, which is based on the concept of fuzzy set, has enabled scientists to create models under conditions of imprecision, vagueness, or both at once. As a result, it has now found many important applications in almost all sectors of human activity, becoming a complementary feature and supporter of probability theory, which is suitable for modelling situations of uncertainty derived from randomness. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights into branches of traditional mathematics like algebra, analysis, geometry, topology, and more. With such widespread applications, fuzzy sets and logic are an important area of focus in mathematics. The Handbook of Research on Advances and Applications of Fuzzy Sets and Logic studies recent theoretical advances of fuzzy sets and numbers, fuzzy systems, fuzzy logic and their generalizations, extensions, and more. This book also explores the applications of fuzzy sets and logic applied to science, technology, and everyday life to further provide research on the subject. This book is ideal for mathematicians, physicists, computer specialists, engineers, practitioners, researchers, academicians, and students who are looking to learn more about fuzzy sets, fuzzy logic, and their applications.
New Distance And Similarity Measures Of Single Value Neutrosophic Sets With Application In Multi Criteria Decision Making
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Author : Yameng Wang
language : en
Publisher: Infinite Study
Release Date :
New Distance And Similarity Measures Of Single Value Neutrosophic Sets With Application In Multi Criteria Decision Making written by Yameng 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 with Mathematics categories.
The processing of uncertainty information has gradually became one of the hot issues in arti cial intelligence eld, and the infor- mation measures of uncertainty information processing are of importance. Single value neutrosophic sets (SVNSs) provide us a exible mathematical framework to process uncertainty information. In this paper, we mainly consider the measures of SVNSs. The existing information measures mostly are constructed based on the two typical inclusion relations about single value neutrosopgic sets. However, there exist some practical problems that do not apply to the two typical inclusion relations. Therefore, there exists another inclusion relation which is called the type-3 inclusion relation about SVNSs.
Intuitionistic Fuzzy Sets
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Author : Krassimir T. Atanassov
language : en
Publisher: Physica
Release Date : 2013-03-20
Intuitionistic Fuzzy Sets written by Krassimir T. Atanassov and has been published by Physica this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-20 with Mathematics categories.
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.
Hesitant Fuzzy Sets Theory
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Author : Zeshui Xu
language : en
Publisher: Springer
Release Date : 2014-01-30
Hesitant Fuzzy Sets Theory written by Zeshui Xu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-30 with Technology & Engineering categories.
This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) characterized by uncertain ("hesitant") information. Because of its clarity and self contained explanations, the book can also be adopted as a textbook from graduate and advanced undergraduate students.
Distances And Similarities In Intuitionistic Fuzzy Sets
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Author : Eulalia Szmidt
language : en
Publisher: Springer
Release Date : 2015-08-08
Distances And Similarities In Intuitionistic Fuzzy Sets written by Eulalia Szmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-08 with Technology & Engineering categories.
This book presents the state-of-the-art in theory and practice regarding similarity and distance measures for intuitionistic fuzzy sets. Quantifying similarity and distances is crucial for many applications, e.g. data mining, machine learning, decision making, and control. The work provides readers with a comprehensive set of theoretical concepts and practical tools for both defining and determining similarity between intuitionistic fuzzy sets. It describes an automatic algorithm for deriving intuitionistic fuzzy sets from data, which can aid in the analysis of information in large databases. The book also discusses other important applications, e.g. the use of similarity measures to evaluate the extent of agreement between experts in the context of decision making.
A Novel Similarity Measure For Interval Valued Intuitionistic Fuzzy Sets And Its Applications
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Author : Minxia Luo
language : en
Publisher: Infinite Study
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A Novel Similarity Measure For Interval Valued Intuitionistic Fuzzy Sets And Its Applications written by Minxia Luo 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.
In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.
Multi Criteria Decision Making Approach Using The Fuzzy Measures For Environmental Improvement Under Neutrosophic Environment
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Author : Gang Li
language : en
Publisher: Infinite Study
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Multi Criteria Decision Making Approach Using The Fuzzy Measures For Environmental Improvement Under Neutrosophic Environment written by Gang Li 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 uncertainty, incomplete and inconsistent information can lead to some difficulties of decision making under the single valued neutrosophic set (SVNS) environment. Information measure plays an important role in SVNS theory, which has received more and more attention in recent years. In this study, we develop a multi-attribute decision making (MADM) method based on the single valued neutrosophic information measures.