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A NOVEL TRIANGULAR INTERVAL TYPE-2 INTUITIONISTIC FUZZY SETS AND THEIR AGGREGATION OPERATORS

Author: HARISH GARG

Publisher: Infinite Study

Published:

Total Pages: 25

ISBN-13:

The objective of this work is to present a triangular interval type2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws.

INTERVAL TYPE-2 FUZZY SETS AND INTERVAL NEUTROSOPHIC SETS IN INTELLIGENT SYSTEMS

Author: M. LATHA MAHESWARI M.

Publisher: Infinite Study

Published:

Total Pages: 407

ISBN-13:

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In this thesis, interval type-2 fuzzy sets (IT2FSs) and interval neutrosophic sets (INSs) have been considered for all the proposed concepts. Fusion of information is an essential task to get the optimized solution for any real world problem. In this task, aggregation operators are playing an important role in all the fields. Since most of the realistic problems have uncertainty in nature, one can use the logic of fuzzy and neutrosophic theory. For the entire proposed concepts interval based logic has been used as it handles more uncertainty.

Fuzzy Set and Its Extension

Author: Tamalika Chaira

Publisher: John Wiley & Sons

Published: 2019-04-23

Total Pages: 304

ISBN-13: 111954419X

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Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy set so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh's extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design.

Uncertainty Data in Interval-Valued Fuzzy Set Theory

Author: Barbara Pękala

Publisher: Springer

Published: 2018-07-12

Total Pages: 0

ISBN-13: 9783319939094

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This book offers an introduction to fuzzy sets theory and their operations, with a special focus on aggregation and negation functions. Particular attention is given to interval-valued fuzzy sets and Atanassov’s intuitionistic fuzzy sets and their use in uncertainty models involving imperfect or unknown information. The theory and application of interval-values fuzzy sets to various decision making problems represent the central core of this book, which describes in detail aggregation operators and their use with imprecise data represented as intervals. Interval-valued fuzzy relations, compatibility measures of interval and the transitivity property are thoroughly covered. With its good balance between theoretical considerations and applications of originally developed algorithms to real-world problem, the book offers a timely, inspiring guide to mathematicians and engineers developing new decision making models or implementing/applying existing ones to a wide range of applications involving imprecise or incomplete data.

Interval-Valued Intuitionistic Fuzzy Sets

Author: Krassimir T. Atanassov

Publisher: Springer Nature

Published: 2019-09-21

Total Pages: 200

ISBN-13: 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.

A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Author: Minxia Luo

Publisher: Infinite Study

Published:

Total Pages: 13

ISBN-13:

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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.

The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method

Author: Majid Khan

Publisher: Infinite Study

Published:

Total Pages: 17

ISBN-13:

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In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Smarandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS).

Proceedings of First International Conference on Mathematical Modeling and Computational Science

Author: Sheng-Lung Peng

Publisher: Springer Nature

Published: 2021-05-04

Total Pages: 675

ISBN-13: 9813343893

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This book presents the most recent scientific and technological advances in the fields of engineering mathematics and computational science, to strengthen the links in the scientific community. It is a collection of high-quality, peer-reviewed research papers presented at the First International Conference on Mathematical Modeling and Computational Science (ICMMCS 2020), held in Pattaya, Thailand, during 14–15 August 2020. The topics covered in the book are mathematical logic and foundations, numerical analysis, neural networks, fuzzy set theory, coding theory, higher algebra, number theory, graph theory and combinatory, computation in complex networks, calculus, differential educations and integration, application of soft computing, knowledge engineering, machine learning, artificial intelligence, big data and data analytics, high-performance computing, network and device security, and Internet of things (IoT).

Pythagorean Fuzzy Sets

Author: Harish Garg

Publisher: Springer Nature

Published: 2021-07-22

Total Pages: 443

ISBN-13: 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.

Extension of the Fuzzy Sugeno Integral Based on Generalized Type-2 Fuzzy Logic

Author: Patricia Melin

Publisher: Springer

Published: 2019-03-28

Total Pages: 65

ISBN-13: 3030164160

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This book presents an extension of the aggregation operator of the generalized interval type-2 Sugeno integral using generalized type-2 fuzzy logic. This extension enables it to handle higher levels of uncertainty when adding any number of sources and types of information in a wide variety of decision-making applications. The authors also demonstrate that the extended aggregation operator offers better performance than other traditional or extended operators. The book is a valuables reference resource for students and researchers working on theory and applications of fuzzy logic in various areas of application where decision making is performed under high levels of uncertainty, such as pattern recognition, time series prediction, intelligent control and manufacturing.