Picture Fuzzy Logic and Its Applications in Decision Making Problems

✍ Scribed by Chiranjibe Jana, Madhumangal Pal, Valentina Balas, Ronald R. Yager

• Publisher: Elsevier Science & Technology
• Year: 2023
• Tongue: English
• Leaves: 296
• Category: Library

✦ Synopsis

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...

✦ Table of Contents

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