Picture Fuzzy Logic and Its Applications in Decision Making Problems

Picture Fuzzy Logic and Its Applications in Decision Making Problems, First edition (2024) 294pp. 978-0-443-22024-1 Front Cover Picture Fuzzy Logic and Its Applications in Decision Making Problems Copyright 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 Back Cover 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 problemsHelps readers understand the difference between various fuzzy logic methodsProvides concepts used to develop and solve problems within the picture fuzzy environment