Picture Fuzzy Logic and Its Applications in Decision Making Problems

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Picture Fuzzy Logic and Its Applications in Decision Making Problems
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Contents
1 Introduction to picture fuzzy sets and operators
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
1.13.1 Properties of Dombi aggregation operators
1.14 Conclusion
References
2 Picture fuzzy hybrid weighted operators and their application in the decision-making process
2.1 Introduction
2.2 Preliminaries
2.3 Aggregation operators with PFN information
2.3.1 Hybrid PFN aggregation operators
2.3.2 Hybrid ordered PFN aggregation operators
2.4 Interval-valued picture fuzzy approach
2.5 MCDM based on the proposed operators
2.5.1 Proposed operators-based decision-making approach
Approach 1
Approach 2
2.5.2 Numerical MAGDM model for PFNs
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
3.1 Introduction
3.2 Basic concept of PFSS and PFSN
3.3 Picture fuzzy soft weighted average operators
3.3.1 Operations for PFSNs
3.3.2 Picture fuzzy soft weighted geometric operator
3.4 Model for MCGDM method using picture fuzzy soft information
3.4.1 An approach based on proposed operators
3.5 Case study
3.5.1 Using the PFSWA operator
3.5.2 Using the PFSWG operator
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
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
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
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
6.6.1 Significance of the parameter for decision making
6.6.2 Comparative study
6.7 Conclusion
References
7 m-Polar picture fuzzy Dombi operators and their applications in multicriteria decision-making processes
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
7.7.1 Selection of suitable location for a thermal power station
7.7.2 Analysis on the effect of parameter ρ on decision-making results
7.8 Conclusion
References
8 Picture fuzzy MABAC approach and its application in multi-attribute group decision-making processes
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
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
10.1 Introduction
10.2 Preliminaries
10.3 Multiobjective linear programming problem
10.4 Picture fuzzy multiobjective linear programming problem
Steps to solve PFMOLPP
10.4.1 Linear-type membership functions
10.5 Application of PFMOLPP
10.6 Conclusion
References
11 Picture fuzzy goal programming problem
11.1 Introduction
11.2 Preliminaries
11.3 Picture fuzzy goal programming problem
Linear-type membership functions approach
11.3.1 Generalized picture fuzzy goal programming problem
Exponential-type membership functions approach (ETMFA)
Hyperbolic-type membership functions approach (HTMFA)
11.4 An application of picture fuzzy goal programming in the recycling process of plastic
11.4.1 Modeling in picture fuzzy goal programming problems
11.5 Conclusion
References
12 Picture fuzzy linear assignment problem and its application in multicriteria group decision-making problems
12.1 Introduction
12.2 Preliminaries
12.3 Linear assignment method on picture fuzzy set
12.3.1 Decision environment defined on PFS
12.3.2 Extended linear assignment model
12.3.3 The proposed algorithm
12.4 An application to a sponge iron factory location selection
12.5 Conclusions
References
Index
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