Distances and Similarities in Intuitionistic Fuzzy Sets

by Eulalia Szmidt

Author	: Eulalia Szmidt
Publisher	: Springer
Total Pages	: 151
Release	: 2013-07-23
Genre	: Technology & Engineering
ISBN	: 3319016407

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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.

Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Physica
Total Pages	: 336
Release	: 2013-03-20
Genre	: Mathematics
ISBN	: 3790818704

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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.

Interval-Valued Intuitionistic Fuzzy Sets

by Krassimir T. Atanassov

Author	: Krassimir T. Atanassov
Publisher	: Springer Nature
Total Pages	: 205
Release	: 2019-09-21
Genre	: Technology & Engineering
ISBN	: 3030320901

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The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail. The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.

Pythagorean Fuzzy Sets

by Harish Garg

Author	: Harish Garg
Publisher	: Springer Nature
Total Pages	: 443
Release	: 2021-07-22
Genre	: Mathematics
ISBN	: 9811619891

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This book presents a collection of recent research on topics related to Pythagorean fuzzy set, dealing with dynamic and complex decision-making problems. It discusses a wide range of theoretical and practical information to the latest research on Pythagorean fuzzy sets, allowing readers to gain an extensive understanding of both fundamentals and applications. It aims at solving various decision-making problems such as medical diagnosis, pattern recognition, construction problems, technology selection, and more, under the Pythagorean fuzzy environment, making it of much value to students, researchers, and professionals associated with the field.

Intelligent and Fuzzy Techniques: Smart and Innovative Solutions

by Cengiz Kahraman

Author	: Cengiz Kahraman
Publisher	: Springer Nature
Total Pages	: 1701
Release	: 2020-07-10
Genre	: Technology & Engineering
ISBN	: 3030511561

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This book gathers the most recent developments in fuzzy & intelligence systems and real complex systems presented at INFUS 2020, held in Istanbul on July 21–23, 2020. The INFUS conferences are a well-established international research forum to advance the foundations and applications of intelligent and fuzzy systems, computational intelligence, and soft computing, highlighting studies on fuzzy & intelligence systems and real complex systems at universities and international research institutions. Covering a range of topics, including the theory and applications of fuzzy set extensions such as intuitionistic fuzzy sets, hesitant fuzzy sets, spherical fuzzy sets, and fuzzy decision-making; machine learning; risk assessment; heuristics; and clustering, the book is a valuable resource for academics, M.Sc. and Ph.D. students, as well as managers and engineers in industry and the service sectors.

Computational Intelligence in Decision and Control

by Da Ruan

Author	: Da Ruan
Publisher	: World Scientific
Total Pages	: 1201
Release	: 2008
Genre	: Computers
ISBN	: 9812799478

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FLINS, originally an acronym for Fuzzy Logic and Intelligent Technologies in Nuclear Science, is now extended to Computational Intelligence for applied research. The contributions to the eighth edition in the series of FLINS conferences cover state-of-the-art research, development, and technology for computational intelligence systems in general, and for intelligent decision and control in particular.

Hesitant Fuzzy Sets Theory

by Zeshui Xu

Author	: Zeshui Xu
Publisher	: Springer
Total Pages	: 474
Release	: 2014-01-30
Genre	: Technology & Engineering
ISBN	: 3319047116

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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.

Entropy, Measures of Distance and Similarity of Q-Neutrosophic Soft Sets and Some Applications

by Majdoleen Abu Qamar

Author	: Majdoleen Abu Qamar
Publisher	: Infinite Study
Total Pages	: 16
Release	:
Genre	: Mathematics
ISBN	:

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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.

Decision Making with Spherical Fuzzy Sets

by Cengiz Kahraman

Author	: Cengiz Kahraman
Publisher	: Springer Nature
Total Pages	: 551
Release	: 2020-05-27
Genre	: Technology & Engineering
ISBN	: 3030454614

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This book introduces readers to the novel concept of spherical fuzzy sets, showing how these sets can be applied in practice to solve various decision-making problems. It also demonstrates that these sets provide a larger preference volume in 3D space for decision-makers. Written by authoritative researchers, the various chapters cover a large amount of theoretical and practical information, allowing readers to gain an extensive understanding of both the fundamentals and applications of spherical fuzzy sets in intelligent decision-making and mathematical programming.