This book introduces readers to the novel concept of spherical fuzzy sets, showing how these sets can be applied in practice to solve various decision-making problems. It also demonstrates that these sets provide a larger preference volume in 3D space for decision-makers. Written by authoritative researchers, the various chapters cover a large amount of theoretical and practical information, allowing readers to gain an extensive understanding of both the fundamentals and applications of spherical fuzzy sets in intelligent decision-making and mathematical programming.
Author(s): Cengiz Kahraman; Fatma Kutlu Gündoğdu
Series: Studies in Fuzziness and Soft Computing, 392
Publisher: Springer
Year: 2020
Language: English
Pages: 532
City: Cham
Preface
From Ordinary Fuzzy Sets to Spherical Fuzzy Sets
Introduction
Fuzzy Set Theory with Graphical Illustrations
Advanced Fuzzy Extensions
Spherical Fuzzy Sets
Conclusions
References
Contents
Preliminaries of Spherical Fuzzy Set Theory
Properties and Arithmetic Operations of Spherical Fuzzy Sets
1 Introduction
2 Spherical Fuzzy Sets: Preliminaries
3 Interval-Valued Spherical Fuzzy Sets: Preliminaries
4 Conclusions
References
Interval Valued Spherical Fuzzy Aggregation Operators and Their Application in Decision Making Problem
1 Introduction
2 Review of Literature
3 Basic Concepts
3.1 Fuzzy Set (Qin and Liu 2014)
3.2 Type-2 Fuzzy Set (Qin and Liu 2014)
3.3 Interval Valued Type-2 Fuzzy Set (Qin and Liu 2014)
3.4 Intuitionistic Fuzzy Set (Garg 2018)
3.5 Interval Valued Intuitionistic Fuzzy Set (Garg 2018)
3.6 Pythagorean Fuzzy Set (Ashraf et al. 2019a, b)
3.7 Interval Valued Pythagorean Fuzzy Set (Peng 2018a, b)
3.8 Picture Fuzzy Set (Ashraf et al. 2019a, b)
4 Proposed Concepts
4.1 Interval Valued Spherical Fuzzy Set
4.2 Operational Laws
4.3 Proposed Score Function for Interval Valued Spherical Fuzzy Numbers
5 Aggregation Operators for Interval Valued Spherical Fuzzy Numbers
5.1 Interval Valued Spherical Fuzzy Weighted Arithmetic Operator
5.2 Interval Valued Spherical Fuzzy Weighted Geometric Operator
6 Application of Proposed Operators
6.1 Proposed Methodology
6.2 Application of Proposed Aggregation Operator in Decision Making
7 Comparative Analysis
8 Conclusion
References
Spherical Fuzzy Numbers and Multi-criteria Decision-Making
1 Introduction
2 Preliminary
3 Spherical Fuzzy Numbers
3.1 Spherical Trapezoidal Fuzzy Numbers
3.2 Spherical Triangular Fuzzy Numbers
4 SF-Multi-criteria Group Decision-Making Method
4.1 STF-Multi-criteria Group Decision-Making Method
4.2 STrF-Multi-criteria Group Decision-Making Method
5 Conclusion
References
The Generalized Dice Similarity Measures for Spherical Fuzzy Sets and Their Applications
1 Introduction
2 Preliminaries
3 Some Dice Similarity Measure for Spherical Fuzzy Sets
3.1 Dice Similarity Measure for Spherical Fuzzy Sets
3.2 Another Form of the Dice Similarity Measure for Spherical Fuzzy Sets
3.3 The Generalized Dice Similarity Measure for Spherical Fuzzy Sets
4 Generalized Dice Similarity Measures for MADM with SFNs
5 Numerical Example and Comparative Analysis
5.1 Numerical Example
5.2 Comparative Analysis
6 Conclusion
References
Spherical Fuzzy Bonferroni Mean Aggregation Operators and Their Applications to Multiple-Attribute Decision Making
1 Introduction
2 Preliminaries
2.1 Spherical Fuzzy Sets
2.2 Bonferroni Mean
3 Spherical Fuzzy Bonferroni Mean Aggregation Operators
3.1 Spherical Fuzzy Bonferroni Mean Operator (SFBM)
3.2 Spherical Fuzzy Normalized Weighted Bonferroni Mean Operator (SFNWBM)
4 Descriptive Analyses
4.1 Illustrative Example
5 Conclusion
References
Spherical Fuzzy Soft Sets
1 Introduction
2 Background
3 Spherical Fuzzy Soft Sets
4 Application of the Spherical Fuzzy Soft Set Model Based on Adjustable Soft Discernibility Matrix
5 Conclusions
References
Decision Making Method Based on Spherical Fuzzy Graphs
1 Introduction
2 Spherical Fuzzy Graphs
3 Applications to Decision Making
3.1 Selection of a Manager
3.2 Selection of a Player
4 Conclusions
References
Spherical Fuzzy Multi-criteria Decision Making
Optimal Site Selection of Electric Vehicle Charging Station by Using Spherical Fuzzy TOPSIS Method
1 Introduction
2 Spherical Fuzzy Sets: Preliminaries
2.1 Spherical Fuzzy TOPSIS Method
3 Application: Site Selection of Electric Vehicle Charge Station
4 Comparative Analyses
5 Conclusions
References
Spherical Fuzzy VIKOR with SWAM and SWGM Operators for MCDM
1 Introduction
2 A Literature Review
3 Fundamentals
3.1 Basic Operators of SFSs
3.2 The VIKOR Method
4 The Spherical Fuzzy VIKOR
5 An Illustrative Example
5.1 Example
5.2 The Stability of Solution
6 Conclusion
References
Simple Additive Weighting and Weighted Product Methods Using Spherical Fuzzy Sets
1 Introduction
2 Spherical Fuzzy Sets: Preliminaries
3 Simple Additive Weighting and Simple Weighted Product Methods Using Single-Valued Spherical Fuzzy Sets
3.1 Simple Additive Weighting Using Single-Valued Spherical Fuzzy Sets
3.2 Simple Weighted Product Methods Using Single-Valued Spherical Fuzzy Sets
3.3 Simple Additive Weighting Using Interval-Valued Spherical Fuzzy Sets
3.4 Simple Weighted Product Methods Using Interval-Valued Spherical Fuzzy Sets
4 An Illustrative Example: Choosing Insurance Options
5 Conclusions
References
Prioritizing Manufacturing Challenges of a Contract Manufacturing Company for Personal Auto by Using Spherical WASPAS Method
1 Introduction
2 Spherical Fuzzy Sets: Preliminaries
3 Spherical Fuzzy WASPAS Method
4 Application
5 Conclusions
References
Assessment of Livability Indices of Suburban Places of Istanbul by Using Spherical Fuzzy CODAS Method
1 Introduction
2 Literature Review: Livability Index
3 Spherical Fuzzy Sets
3.1 Preliminaries: Spherical Fuzzy Sets
3.2 Extension of CODAS with Spherical Fuzzy Sets
4 Applications to Livability Index
4.1 Application of Spherical Fuzzy CODAS
4.2 Sensitivity Analyses
5 Conclusions
References
Interval-Valued Spherical Fuzzy MULTIMOORA Method and Its Application to Industry 4.0
1 Introduction
2 Literature Review
3 Spherical Fuzzy Sets: Preliminaries
4 Extension of MULTIMOORA with Spherical Fuzzy Sets
4.1 Extension of MULTIMOORA with Single-Valued Spherical Fuzzy Sets
4.2 Extension of MULTIMOORA with Interval-Valued Spherical Fuzzy Sets
5 Application to Industry 4.0
5.1 Single-Valued Spherical Fuzzy MULTIMOORA Application
5.2 Interval-Valued Spherical Fuzzy MULTIMOORA Application
6 Conclusions
References
Global Supplier Selection with Spherical Fuzzy Analytic Hierarchy Process
1 Introduction
2 A Literature Review
3 Fundamentals
3.1 Basic Operators of SFSs
3.2 The AHP
4 The SFAHP Method
4.1 The Spherical Fuzzy Preference Relation
4.2 Consistency Check
4.3 Prioritization Function
4.4 The Proposed SFAHP
5 Examples
6 Conclusion
References
Hospital Performance Assessment Using Interval-Valued Spherical Fuzzy Analytic Hierarchy Process
1 Introduction
2 Literature Review
3 Interval-Valued Spherical Fuzzy Sets: Preliminaries
4 Extension of AHP with Spherical Fuzzy Sets
5 A Case Study: Selecting a High-Qualified Hospital
6 A Comparative Analysis
7 Conclusion
References
Evaluating Geothermal Energy Systems Using Spherical Fuzzy PROMETHEE
1 Introduction
2 Preliminaries
2.1 Basic Operators of SFSs
2.2 The Conventional PROMETHEE
3 The SF-PROMETHEE
3.1 The Spherical Fuzzy Preference Function
3.2 The Proposed SF-PROMETHEE
4 Practical Examples
5 Conclusion and Discussion
References
Delivery Drone Design Using Spherical Fuzzy Quality Function Deployment
1 Introduction
2 Literature Review
3 Spherical Fuzzy Sets: Preliminaries
4 Spherical Fuzzy QFD Method
5 An Application: Product Development Using SFS
6 Conclusions
References
Analysis of Usability Test Parameters Affecting the Mobile Application Designs by Using Spherical Fuzzy Sets
1 Introduction
2 Methods Used in Usability Evaluation
2.1 Expert Analysis
2.2 User Participatory Evaluation
2.3 Hybrid Studies
3 Usability Evaluation Criteria
3.1 Evaluation Criteria Used in Usability Studies
3.2 Usability Criteria to Be Considered in the Proposed Approach
4 Methodology
4.1 Preliminaries of Spherical Fuzzy Sets
4.2 Kano Model
4.3 Proposed Approach
5 A Case Study: Usability of Travel Mobile Application
6 Conclusions
References
Mathematical Programming with Spherical Fuzzy Sets
Spherical Fuzzy Linear Programming Problem
1 Introduction
2 Preliminaries
3 Spherical Fuzzy Linear Programming Problem
4 Spherical Fuzzy Optimization Model
5 Numerical Examples
6 Conclusions
References
Spherical Fuzzy Multiobjective Linear Programming Problem
1 Introduction
2 Basic Definitions
3 Spherical Fuzzy Multiobjective Linear Programming Model
4 Numerical Examples
5 Conclusions
References
Spherical Fuzzy Goal Programming Problem
1 Introduction
2 Preliminaries
3 Spherical Fuzzy Goal Programming Model
4 Numerical Examples
5 Conclusions
References
Spherical Fuzzy Geometric Programming Problem
1 Introduction
2 Spherical Fuzzy Geometric Programming Model
2.1 Geometric Programming Problem
2.2 Multiobjective Geometric Programming Problem
3 Numerical Examples
4 Conclusions
References
