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Fuzzy Sets, Fuzzy Logic and Their Applications • Michael Gr Fuzzy Sets, Fuzzy Logic and Their Applications • Michael Gr. Voskoglou • Michael Gr. Fuzzy Sets, Fuzzy Logic and Their Applications Edited by Michael Gr. Voskoglou Printed Edition of the Special Issue Published in Mathematics www.mdpi.com/journal/mathematics Fuzzy Sets, Fuzzy Logic and Their Applications Fuzzy Sets, Fuzzy Logic and Their Applications Special Issue Editor Michael Gr. Voskoglou MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editor Michael Gr. Voskoglou Graduate Technological Educational Institute of Western Greece Greece Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Mathematics (ISSN 2227-7390) (available at: https://www.mdpi.com/journal/mathematics/special issues/Fuzzy Sets). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03928-520-4 (Pbk) ISBN 978-3-03928-521-1 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Fuzzy Sets, Fuzzy Logic and Their Applications” .................... ix Yu-Cheng Wang and Tin-Chih Toly Chen A Partial-Consensus Posterior-Aggregation FAHP Method—Supplier Selection Problem as an Example Reprinted from: Mathematics 2019, 7, 179, doi:10.3390/math7020179 ................. 1 Lingqiang Li p-Topologicalness—A Relative Topologicalness in -Convergence Spaces Reprinted from: Mathematics 2019, 7, 228, doi:10.3390/math7030228 ................. 17 Michael Gr. Voskoglou Methods for Assessing Human–Machine Performance under Fuzzy Conditions Reprinted from: Mathematics 2019, 7, 230, doi:10.3390/math7030230 ................. 35 Huarong Zhang and Minxia Luo The “Generator” of Int-Soft Filters on Residuated Lattices Reprinted from: Mathematics 2019, 7, 236, doi:10.3390/math7030236 ................. 57 Chiranjibe Jana and Madhumangal Pal On (α,β)-US Sets in BCK/BCI-Algebras Reprinted from: Mathematics 2019, 7, 252, doi:10.3390/math7030252 ................. 67 Qiu Jin, Lingqiang Li and Guangming Lang Reprinted from: Mathematics 2019, 7, 370, doi:10.3390/math7040370 ................. 85 Hui-Chin Tang and Shen-Tai Yang Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets Reprinted from: Mathematics 2019, 7, 437, doi:10.3390/math7050437 ................. 99 Cen Zuo, Anita Pal and Arindam Dey New Concepts of Picture Fuzzy Graphs with Application Reprinted from: Mathematics 2019, 7, 470, doi:10.3390/math7050470 .................109 Songsong Dai, Lvqing Bi and Bo Hu Distance Measures between the Interval-Valued Complex Fuzzy Sets Reprinted from: Mathematics 2019, 7, 549, doi:10.3390/math7060549 .................127 Adil Baykaso˘glu and Ilker˙ G¨olcuk ¨ An Interactive Data-Driven (Dynamic) Multiple Attribute Decision Making Model via Interval Type-2 Fuzzy Functions Reprinted from: Mathematics 2019, 7, 584, doi:10.3390/math7070584 .................139 Qiu Jin, Lingqiang Li and Jing Jiang Fuzzy Counterparts of Fischer Diagonal Condition in -Convergence Spaces Reprinted from: Mathematics 2019, 7, 685, doi:10.3390/math7080685 .................171 v Zhenyu Xiu and Qinghua Li Degrees of L-Continuity for Mappings between L-Topological Spaces Reprinted from: Mathematics 2019, 7, 1013, doi:10.3390/math7111013 ................189 Hamed Nozari, Esmaeil Najafi, Mohammad Fallah and Farhad Hosseinzadeh Lotfi Quantitative Analysis of Key Performance Indicators of Green Supply Chain in FMCG Industries Using Non-Linear Fuzzy Method Reprinted from: Mathematics 2019, 7, 1020, doi:10.3390/math7111020 ................205 Jeong-Gon Lee, Kul Hur Bipolar Fuzzy Relations Reprinted from: Mathematics 2019, 7, 1044, doi:10.3390/math7111044 ................225 Marc Sanchez-Roger, Mar´ıa Dolores Oliver-Alfonso and Carlos Sanch´ıs-Pedregosa Fuzzy Logic and Its Uses in Finance: A Systematic Review Exploring Its Potential to Deal with Banking Crises Reprinted from: Mathematics 2019, 7, 1091, doi:10.3390/math7111091 ................243 Guangwang Su, Taixiang Sun On ω-Limit Sets of Zadeh’s Extension of Nonautonomous Discrete Systems on an Interval Reprinted from: Mathematics 2019, 7, 1116, doi:10.3390/math7111116 ................265 Tin-Chih Toly Chen, Yu-Cheng Wang, Yu-Cheng Lin, Hsin-Chieh Wu and Hai-Fen Lin A Fuzzy Collaborative Approach for Evaluating the Suitability of a Smart Health Practice Reprinted from: Mathematics 2019, 7, 1180, doi:10.3390/math7121180 ................273 Suizhi Luo and Lining Xing Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection Reprinted from: Mathematics 2020, 8, 3, doi:10.3390/math8010003 ..................293 Qianli Zhou, Hongming Mo and Yong Deng A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis Reprinted from: Mathematics 2020, 8, 142, doi:10.3390/math8010142 .................317 Mabruka Ali, Adem Kılı¸cman and Azadeh Zahedi Khameneh Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure Reprinted from: Mathematics 2020, 8, 178, doi:10.3390/math8020178 .................337 vi About the Special Issue Editor Michael Gr. Voskoglou (B.S., M.S., M.Phil. , Ph.D. in Mathematics) is currently an Emeritus Professor of Mathematical Sciences at the Graduate Technological Educational Institute of Western Greece. He was a Visiting Researcher at the Bulgarian Academy of Sciences (1997–2000), a Visiting Professor at the University of Warsaw (2009), of Applied Sciences of Berlin (2010), and at the National Institute of Technology of Durgapur, India (2016). Prof. Voskoglou is the author of 16 books (9 in Greek and 7 in English) and of more than 500 papers published in reputed mathematical journals and proceedings of international conferences of about 30 countries in the five continents (2018 Google Scholar Citations: 2401, H-idex 24). He is also the Editor in Chief of the International Journal of Applications of Fuzzy Sets and Artificial Intelligence (ISSN 2241-1240), reviewer of the AMS and member of the Editorial Board or referee in many mathematical journals. His research interests include algebra, fuzzy sets, Markov chains, artificial intelligence, and mathematics education. vii Preface to ”Fuzzy Sets, Fuzzy Logic and Their Applications” A few decades ago, probability theory used to be the unique tool in the hands of the experts for handling situations of uncertainty appearing in problems of science, technology, and in everyday life. Probability, which is based on the principles of traditional bivalent logic, is sufficient for tackling problems of uncertainty connected to randomness, but not those connected with imprecise or vague information. However, with the development of fuzzy set theory introduced by Zadeh in 1965 and of fuzzy logic which is based on that theory, things have changed. These new mathematical tools gave scientists the ability to model under conditions that are vague or not precisely defined, thus succeeding to mathematically solve problems whose statements are expressed in our natural language. As a result, the spectrum of their applications has rapidly extended, covering all the physical sciences; economics and management; expert systems like financial planners, diagnostic, meteorological, information retrieval, control systems, etc.; industry; robotics; decision making; programming; medicine; biology; humanities; education and almost all the other sectors of te human activity, including human reasoning. The first major commercial application of fuzzy logic was in cement kiln control (Zadeh, 1983), followed by a navigation system for automatic cars, a fuzzy controller for automatic operation of trains, laboratory level controllers, controllers for robot vision, graphics, controllers for automated police sketchers, and many others. Fuzzy mathematics has also significantly developed at the theoretical level, providing important insights even into branches of classical mathematics, like algebra, analysis, and geometry. The present book contains 20 papers collected from amongst 53 manuscripts submitted for the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications” of the MDPI journal Mathematics. These papers appear in the book in the series in which they were accepted, and published in Volumes 7 (2019) and 8 (2020) of the journal and cover a wide range of topics and applications of fuzzy systems and fuzzy logic and their extensions and generalizations. This range includes, among others, management of uncertainty in a fuzzy environment, fuzzy assessment methods of human–machine performance, fuzzy graphs, fuzzy topological and convergence spaces, bipolar fuzzy relations, type-2 fuzzy sets, as well as intuitionistic, interval-valued, complex, picture and Pythagorean fuzzy sets, soft sets, and algebras. The applications presented are oriented to finance, fuzzy
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