Picture Fuzzy Logic and Its Applications in Decision Making Problems

Chiranjibe Jana · Madhumangal Pal · Valentina Emilia Balas · Ronald R. Yager

Nov 2023 · Elsevier

Ebook

320

Pages

Eligible

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About this ebook

Picture Fuzzy Logic and Its Applications in Decision Making Problems provides methodological frameworks and the latest empirical research findings in the field of picture fuzzy operators, and their applications in scientific research and real-world engineering problems. Although fuzzy logic can be applied in a number of different areas, many researchers and developers are not yet familiar with how picture fuzzy operators can be applied to a variety of advanced decision-making problems. Picture fuzzy set is a more powerful tool than fuzzy set or intuitionistic fuzzy set to tackle uncertainty in a variety real-world modeling applications. Picture fuzzy set is actually the generalization of intuitionistic fuzzy set, and intuitionistic fuzzy set is the generalization of fuzzy set. In this book, the picture fuzzy sets are investigated, and different types of operators are defined to solve a number of important decision making and optimization problems. The hybrid operator on picture fuzzy set based on the combination of picture fuzzy weighted averaging operators and picture fuzzy weighted geometric operators is developed and named Hybrid Picture Fuzzy Weighted Averaging Geometric (H-PFWAG) operator. Another operator is developed for interval-valued picture fuzzy environment, which is named Hybrid Interval-Valued Picture Fuzzy Weighted Averaging Geometric (H-IVPFWAG) operator. These two operators are then demonstrated as solutions to Multiple-Attribute Decision-Making (MADM) problems. The picture fuzzy soft weighted aggregation operators (averaging and geometric) are defined, and these are applied to develop a multi-criteria group decision making system. The Dombi operator in the picture fuzzy environment is then defined and applied to solve MADM problems. Based on the Dombi operator, several other operators are defined. These are the picture fuzzy Dombi aggregation operators, including picture fuzzy Dombi weighted averaging operator, picture fuzzy Dombi order weighted averaging operator, picture fuzzy Dombi hybrid averaging operator, picture fuzzy Dombi weighted geometric operator, picture fuzzy Dombi order weighted geometric operator, and picture fuzzy Dombi hybrid geometric operator. Each of these operators are used to solve MADM problems. An extension picture fuzzy set known as m-polar picture fuzzy set is proposed and investigated along with many properties of m-polar picture fuzzy Dombi weighted averaging and geometric operators; each of these operators are applied to MADM problems. Another extension of the picture fuzzy set is the interval-valued picture fuzzy uncertain linguistic environment. In this set, interval-valued picture fuzzy uncertain linguistic weighted averaging and geometric operators are developed, and interval-valued picture fuzzy uncertain linguistic Dombi weighted aggregation operators are utilized in the MADM process. In the complex picture fuzzy environment, the authors demonstrate some complex picture fuzzy weighted aggregation operators to be used in solving MADM problems. Another approach called MABAC with picture fuzzy numbers is studied and developed as a multi-attribute group decision making model. Furthermore, the picture fuzzy linear programming problem (PFLPP) is initiated, in which the parameters are picture fuzzy numbers (PFNs). The picture fuzzy optimization method is applied for solving the PFLPP. This concept is used to solve the picture fuzzy multi-objective programming problem (PFMOLPP) under the picture fuzzy environment.

Provides in-depth explanations of picture fuzzy logic and its application to computational modeling problems
Helps readers understand the difference between various fuzzy logic methods
Provides concepts used to develop and solve problems within the picture fuzzy environment

About the author

Dr. Chiranjibe Jana is a researcher in the Department of Applied Mathematics with Oceanology and Computer Programming at Vidyasagar University, India. Dr. Jana’s research interests include fuzzy logic, fuzzy set, aggregation operators, BCK-algebra, topological space, fuzzy number, soft set, and congruence relation. He has published on a wide range of these research topics in journals such as International Journal of Intelligent Systems, Computational and Applied Mathematics, Expert Systems, Granular Computing, IEEE Access, and Journal of Ambient Intelligence and Humanized Computing.

Dr. Madhumangal Pal is a Full Professor in the Department of Applied Mathematics with Oceanology and Computer Programming at Vidyasagar University, India. Dr. Pal’s research interests include fuzzy logic, fuzzy number, fuzzy set operations, fuzzy classification, fuzzy subalgebra, aggregation operators, BCK-algebra, and congruence relation. He is the author of A Study on Fuzzy Graphs and Their Applications, Lambert Academic Publishing; Convergence and Inverse of Intuitionistic Fuzzy Matrices, Lambert Academic Publishing; An Optimal Algorithm to Find Minimum K-hop Dominating Set, Lambert Academic Publishing; and Modern Trends in Fuzzy Graph Theory, Springer.

Valentina E. Balas is a Professor in the Department of Automatics and Applied Software at the Faculty of Engineering, “Aurel Vlaicu University of Arad, Romania. She holds a PhD Cum Laude, in Applied Electronics and Telecommunications from Polytechnic University of Timisoara. Dr. Balas is the author of more than 350 research papers. Her research interests are in intelligent systems, fuzzy control, soft computing, smart sensors, information fusion, modeling, and simulation. She is a member of the editorial boards of several national and international journals and evaluator expert for national, international projects, and PhD thesis. Dr. Balas is the Director of Intelligent Systems Research Centre and Director of the Department of International Relations, Programs, and Projects in Aurel Vlaicu University of Arad. She is the recipient of the "Tudor Tanasescu" Prize from the Romanian Academy for contributions in the field of soft computing methods (2019).

Dr. Ronald R. Yager is a researcher in computational intelligence and decision making under uncertainty and fuzzy logic. He is currently Director of the Machine Intelligence Institute and Professor of Information Systems at Iona College. He has been an active IEEE Fellow since 1997 for his contributions to the development of the theory of fuzzy logic. He is the Editor and Chief of the International Journal of Intelligent Systems, which serves as a forum for individuals interested in tapping into the vast theories based on intelligent systems construction. He has also been invited to serve on the Editorial Boards and Executive Advisory Boards for a number of International Journals, including IEEE Intelligent Systems, IEEE Transactions on Fuzzy Systems, and the Fuzzy Sets and Systems Journal.

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