Picture Fuzzy Logic and Its Applications in Decision Making Problems

1st Edition - November 8, 2023
Authors: Chiranjibe Jana, Madhumangal Pal, Valentina Emila Balas, Ronald R. Yager
Language: English
Paperback ISBN:
9 7 8 - 0 - 4 4 3 - 2 2 0 2 4 - 1
eBook ISBN:
9 7 8 - 0 - 4 4 3 - 2 2 0 2 3 - 4

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… Read more

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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. In this book, 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. In addition, 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.

Cover image
Title page
Table of Contents
Copyright
1: Introduction to picture fuzzy sets and operators
Abstract
1.1. Introduction
1.2. Preliminaries
1.3. Relation on picture fuzzy set
1.4. Picture fuzzy graph
1.5. Arithmetics on picture fuzzy set
1.6. Ordering of PFN
1.7. Similarity measures between picture fuzzy sets
1.8. Convex combination of picture fuzzy sets
1.9. Picture fuzzy averaging operators
1.10. Implication operator on picture fuzzy set
1.11. Topological operators on picture fuzzy set
1.12. Dombi operations on PFNs
1.13. Picture fuzzy Dombi aggregation operator
1.14. Conclusion
References
2: Picture fuzzy hybrid weighted operators and their application in the decision-making process
Abstract
2.1. Introduction
2.2. Preliminaries
2.3. Aggregation operators with PFN information
2.4. Interval-valued picture fuzzy approach
2.5. MCDM based on the proposed operators
2.6. Sensitivity analysis for the parameter γ
2.7. Conclusion
References
3: Multicriteria group decision-making process based on a picture fuzzy soft parameterized environment
Abstract
3.1. Introduction
3.2. Basic concept of PFSS and PFSN
3.3. Picture fuzzy soft weighted average operators
3.4. Model for MCGDM method using picture fuzzy soft information
3.5. Case study
3.6. Comparative studies
3.7. Advantages of the approach
3.8. Conclusions
References
4: Picture fuzzy Dombi operators and their applications in multiattribute decision-making processes
Abstract
4.1. Introduction
4.2. Preliminaries
4.3. Picture fuzzy Dombi weighted average operators
4.4. Picture fuzzy Dombi weighted geometric operators
4.5. The MADM model based on PFN
4.6. Numerical results
4.7. Analysis on the effect of parameter ϱ on decision making results
4.8. Comparative analysis
4.9. Conclusions
References
5: Picture fuzzy Dombi prioritized operators and their application in decision-making processes
Abstract
5.1. Introduction
5.2. Preliminaries
5.3. Picture fuzzy Dombi prioritized weighted arithmetic aggregation operators
5.4. Picture fuzzy Dombi prioritized geometric aggregation operators
5.5. Model for MADM using picture fuzzy Dombi operator
5.6. Numerical example and comparative analysis
5.7. Analysis on the effect of parameter ϱ on decision making results
5.8. Comparative analysis
5.9. Conclusions
References
6: Picture fuzzy power Dombi operators and their utilization in decision-making problems
Abstract
6.1. Introduction
6.2. Basic definitions and terminologies
6.3. Picture fuzzy power Dombi averaging operators
6.4. Dombi power geometric AOs with PFNs
6.5. MADM approach for PFNs
6.6. Case study and comparative analysis
6.7. Conclusion
References
7: m-Polar picture fuzzy Dombi operators and their applications in multicriteria decision-making processes
Abstract
7.1. Introduction
7.2. Preliminaries
7.3. Dombi operations on mPFNs
7.4. mPoPFN Dombi arithmetic operators
7.5. mPoPFN Dombi geometric operators
7.6. Model for MADM using mPoPF data
7.7. Numerical example
7.8. Conclusion
References
8: Picture fuzzy MABAC approach and its application in multi-attribute group decision-making processes
Abstract
8.1. Introduction
8.2. Some results of picture fuzzy sets
8.3. Conventional MABAC model
8.4. MABAC model with PFNs
8.5. Case study
8.6. Compare PFNs MABAC approach with some PFNs operators
8.7. Conclusions
References
9: Linear programming problem in a picture fuzzy environment
Abstract
Abbreviations
9.1. Introduction
9.2. Preliminaries
9.3. Some results
9.4. Methodology for solving FPFLPP with LR flat PFNs
9.5. Numerical example of FPFLPP
9.6. Conclusions
References
10: Multiobjective linear programming problem in a picture fuzzy environment
Abstract
Abbreviations
10.1. Introduction
10.2. Preliminaries
10.3. Multiobjective linear programming problem
10.4. Picture fuzzy multiobjective linear programming problem
10.5. Application of PFMOLPP
10.6. Conclusion
References
11: Picture fuzzy goal programming problem
Abstract
Abbreviations
11.1. Introduction
11.2. Preliminaries
11.3. Picture fuzzy goal programming problem
11.4. An application of picture fuzzy goal programming in the recycling process of plastic
11.5. Conclusion
References
12: Picture fuzzy linear assignment problem and its application in multicriteria group decision-making problems
Abstract
Abbreviations
12.1. Introduction
12.2. Preliminaries
12.3. Linear assignment method on picture fuzzy set
12.4. An application to a sponge iron factory location selection
12.5. Conclusions
References
Index

Chiranjibe Jana

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.

Affiliations and expertise

Researcher, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India

Madhumangal Pal

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.

Affiliations and expertise

Full Professor, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India

Valentina Emila Balas

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).

Affiliations and expertise

Professor, Department of Automatics and Applied Software at the Faculty of Engineering, “Aurel Vlaicu” University of Arad, Romania, and Academy of Romanian Scientists

Ronald R. Yager

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.

Affiliations and expertise

Iona College, Machine Intelligence Institute, New York, USA