Fuzzy Optimization, Decision-making and Operations Research: Theory and Applications

✍ Scribed by Chiranjibe Jana (editor), Madhumangal Pal (editor), Ghulam Muhiuddin (editor), Peide Liu (editor)

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 753
• Category: Library

✦ Synopsis

After developing fuzzy set theory, many contributors focused their research on the extension of fuzzy sets and their computational methodologies, strengthening modern science and technology. In some real-life phenomena, the conventional methods and traditional fuzzy sets cannot be explained, whereas the extension of fuzzy sets and effective new computing methods can explain it adequately.

This edited book presents a new view of fuzzy set-measurement methods entitled "Fuzzy Optimization, Decision Making and Operations Research: Theory and Applications", which deals with different perspectives and areas of research. All chapters are divided into three parts: fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

The goal of this book is to provide a relevant methodological framework covering the core fields of fuzzy decision-making method, fuzzy optimization method, fuzzy graphics method, fuzzy operations research, fuzzy optimization using graph theory, fuzzy support systems and its real and industrial applications.

For many people, fuzzy words' industrial engineering and scientific meanings are still an advanced system for improving modern science and technology. Although fuzzy logic can be applied to many different areas, people do not know how different fuzzy approaches can be applied to various products currently on the market. It is written for professionals who wish to share their expertise, improve their findings, and provide relevant information in the fields of fuzzy methods and their application in decision-making, optimization theory, graph theory and operations research.

This book is aimed at experts and practitioners in the fields of fuzzy optimization, fuzzy decision-making, and fuzzy operation research.

✦ Table of Contents

Preface
Contents
Contributors
1 Fundamentals of Fuzzy Optimization and Decision-Making Problems
1 Optimization Problems
2 Development of Optimization Problems
3 Classical Optimization Techniques
3.1 Multi-Objective Programming Problems
4 Modern Optimization Techniques
4.1 Neural Network
4.2 Genetic Algorithm
4.3 Ant Colony Optimization
4.4 Particle Swarm Optimization
5 Fuzzy Optimization
6 Formulation of Fuzzy Mathematical Programming Problem
6.1 Feasible Solutions of Optimization Problem
7 Decision-Making Problem
8 t-Norms and t-Conorms-Based Operators
8.1 Dombi Operations
8.2 Hamacher Operations
8.3 Einstein Operators
8.4 Power Averaging (PA) Operator
8.5 Prioritized Average (PA) Operator
8.6 Bonferroni Mean (BM) Operator
8.7 Maclaurin Symmetric Mean (MSM) Operator
8.8 Frank Aggregation Operator
8.9 Heronian Mean (HM) Operator
9 Aggregation Operators
9.1 Aggregation Operators for Numerical Data
References
2 What Is the Most Adequate Fuzzy Methodology?
1 Outline
2 What Is Fuzzy Methodology: A Brief Reminder
3 How to Decide Which Fuzzy Methodology Is the Most Adequate
4 Toward the Most Adequate Fuzzy Methodology
References
3 How Measurement-Related Ideas Can Help Us Use Expert Knowledge When Making Decisions: Three Case Studies
1 Introduction
1.1 Using Expert Knowledge Is Important, But How?
1.2 How Can Experts Help?
1.3 Why Is This Useful?
1.4 But How Exactly Can We Use Expert Knowledge to Supplement Measurement Results?
1.5 Three Case Studies
2 First Case Study: Measurement-Type Calibration'' of Expert Estimates Improves Their Accuracy and Their Usability: Pavement Engineering 2.1 Experts Are Often Used for Estimation 2.2 Expert Estimates Are Often Very Imprecise 2.3 It Is Difficult to Find Good Experts: Example from Pavement Engineering 2.4 Calibration 2.5 Idea: Let Us Calibrate Experts 2.6 Such Calibration Is Indeed Helpful 2.7 We Applied Our Idea to Pavement Engineering 2.8 As a Result, More Experts Are Selected 2.9 For Most Originally Selected Experts, Re-scaling Leads to More Accurate Estimates 3 Second Case Study: Relationship Between Measurement Results and Expert Estimates of Cumulative Quantities, on the Example of Pavement Roughness 3.1 Cumulative Quantities 3.2 Formulation of the Problem 3.3 Case Study: Estimating Pavement Roughness 3.4 Empirical Relation Between Measurement Results and Expert Estimates 3.5 What We Do in This Section 3.6 Main Idea 3.7 Motivation for Invariance 3.8 Conclusions of This Section 4 Third Case Study: Normalization-Invariant Fuzzy Logic Operations Explain Empirical Success of Student Distributions in Describing Measurement Uncertainty 4.1 Traditional Engineering Approach to Measurement Uncertainty 4.2 Need for Heavy-Tailed Distributions 4.3 What We Do 4.4 Need for Normalization 4.5 How to Combine Degrees 4.6 Deriving Student Distribution 5 Conclusions and Future Work 5.1 Why Do We Need to Use Expert Knowledge 5.2 Challenges Related to the Use of Expert Knowledge 5.3 Measurement-Related Ideas Can Help 5.4 Future Work 6 Auxiliary Results for Sect.2 6.1 First Auxiliary Result: Why 50%? 6.2 Why 88% References 4 On Fusion of Soft and Hard Computing: Traditional (Hard Computing'') Optimal Rescaling Techniques SimplifyFuzzy Control
1 Introduction
1.1 Fuzzy Control: One of the Most Successful Soft Computing Techniques
1.2 Tuning Is Necessary
1.3 Usually, Soft Computing Techniques Are Used For Tuning, But This May Not Be the Best Idea
1.4 Natural Idea: Let's Use Hard Computing for Tuning
2 Rescaling: An Important Particular Case of Tuning
2.1 Rescaling: Physical Motivations
2.2 The Main Problem: Informally
2.3 What We Are Planning to Do
3 Toward the Use of Hard Computing: Motivations of the Proposed Formal Description of the Problem
3.1 Why Is This Problem Difficult?
3.2 Some Rescalings Preserve Equal Spacing
3.3 We Must Choose a Family of Scaling Functions, Not a Single Function
3.4 Which Family Is the Best?
3.5 The Criterion for Choosing the Best Family Must Be Consistent
3.6 The Criterion Must Be Final
3.7 The Criterion Must Be Reasonably Invariant
4 Definitions and the Main Result
5 Proof of the Main Result
6 Conclusions
References
5 A Novel Fully Interval-Valued Intuitionistic Fuzzy Multi-objective Indefinite Quadratic Transportation Problem with an Application to Cost and Wastage Management in the Food Industry
1 Introduction
2 Literature Review
3 Preliminary
4 Fully Interval-Valued Intuitionistic Fuzzy Multi-objective Indefinite Quadratic Transportation Problem (FIVIFMOIQTP)
5 Proposed Solution Methodology
6 Numerical Example
7 Discussion
8 Conclusion and Future Work
References
6 Project Management Using Network Analysis in FuzzyEnvironment
1 Introduction
2 Stages of Project Management
2.1 Planning
2.2 Scheduling
2.3 Controlling
3 Advantages of Network Analysis
3.1 Basic Components of a Network and Some Terminologies
3.2 Event or Node
3.3 Activity or Task
3.4 Merge and Burst Events
3.5 Network
3.6 Path
4 Common Errors in a Network
4.1 Looping (Cycling)
4.2 Dangling
4.3 Redundancy
5 Rules to Construct Network
5.1 Numbering the Events
6 Project Management in Uncertain Environment
6.1 Arithmetic of TFNs
6.2 OERI and Acceptance Index
6.3 Deconvolution
7 Critical Path Analysis in Fuzzy Environment
7.1 Notation
7.2 Forward Pass Calculations
7.3 Backward Pass Calculations
7.4 Computation of Floats and Slack Times
8 The Algorithm
9 An Illustrative
10 Conclusion
References
Untitled
7 Generalized Hukuhara Global Subdifferentiability in Interval Optimization Problems
1 Introduction
2 Preludes
2.1 Fundamental Operations and Dominance Relations on Intervals
2.2 Calculus of IVFs
3 gH-global directional derivative for IVFs
4 gH-global subdifferentiability for IVFs
5 Application in Nonsmooth Nonconvex Optimization
6 Conclusion and future directions
References
8 Role of Hexagonal Fuzzy Numbers While Applying the Max-Min Concept to a Transportation Problem
1 Introduction
2 Preliminaries
2.1 Definition: (Fuzzy Set) [13]
2.2 Definition: (Fuzzy Number) [13]
2.3 Definition: Hexagonal Fuzzy Number [6]
2.4 Definition: (Positive and Negative) [6]
2.5 Arithmetic Operation [6]
2.6 Ranking of Hexagonal Fuzzy Number [15, 16]
2.7 Mathematical Analysis of Fuzzy Transportation Problem [7]
3 Max Min Method –Algorithm
4 Numerical Example
4.1 Ranking Method 1
4.2 Ranking Method 2
4.3 Ranking Method 3
4.4 Ranking Method 4
4.5 Ranking Method 5
4.6 Ranking Method 6
5 Conclusion
References
9 Development of an Interval Picture Fuzzy Matrix Game-Based Approach to Combat Cyberthreats in the Healthcare Sector
1 Introduction
1.1 Motivation and Objectives
1.2 Research Gaps
1.3 Contributions
1.4 Literature Review
2 Preliminaries
2.1 Notations
3 Matrix Games with IVPiFN Payoffs
4 Mathematical Model and Solution Approach for IVPiFMG
5 Numerical Illustration
5.1 The Solution Procedure and Result Discussion
5.2 Comparison of the Proposed Approach
6 Conclusion
References
10 Minimization of Span in L(3,1)-Labeling for a Particular Type of Intersection Graphs
1 Introduction
2 Preliminaries and Notations
3 L(3,1)-Labeling of I-Graphs
3.1 Algorithm for L(3,1)-Labeling of I-Graphs
3.2 Illustration of the Algorithm L31
4 Conclusion
References
11 Generalized Neutrosophic Sets and Their Applications for Aggregated Operators Based on Diagnostic Disease Problem
1 Introduction
2 Preliminary
3 Generalized Neutrosophic Sets
3.1 Basic Operations of GNSSs
4 Relations on Generalized Neutrosophic Sets(GNSSs)
4.1 Diagnostic Disease Problem
4.2 Problem: Diabetes in Different Age Sectors
5 Conclusions
References
12 An Application of Neutrosophic Graph in Decision-Making Problem for Alliances of Companies
1 Introduction
1.1 Review of Literature
1.2 Motivation
2 Preliminaries
3 Neutrosophic Graph
4 Balanced Neutrosophic Graph
4.1 An Algorithm
5 Application of Balanced Neutrosophic Graph in Business Alliance
6 Conclusion
References
13 Dombi Hamy Mean Operators Based on Complex Intuitionistic Fuzzy Uncertainty and Their Application in Multi-Attribute Decision-Making
1 Introduction
2 Preliminaries
3 Dombi Hamy Mean Operators for CIF Information
4 Multi-Attribute Decision-Making Problem
4.1 Illustrated Example
4.2 Comparative Analysis
5 Conclusion
References
14 Linear Diophantine Fuzzy Information Aggregation with Multi-criteria Decision-Making
1 Introduction
2 Preliminary
3 Linear Diophantine Fuzzy Aggregation Operators
3.1 LDFWA Operator
3.2 LDFOWA Operator
3.3 LDFWG Operator
3.4 LDFOWG Operator
4 Proposed Methodology Based on Developed AOs
5 MCDM Example
5.1 With LDFWA Operator
5.2 With LDFWG Operator
6 Conclusion
References
15 Hyperbolic Fuzzy TOPSIS Method for Multi-Criteria Decision-Making Problems
1 Significance of the Work
2 Introduction
2.1 Motivation of the Study
2.2 Structure of the Study
3 Preliminaries
4 Hyperbolic Fuzzy Set
4.1 The Idea of HFS
4.2 Basic Definition
4.3 Necessity and Possibility Operators
5 Score Function Based on HFS
5.1 Existing Score Functions
5.2 Novel Score Function Based on HFS
5.3 Drawbacks of the Existing Score Functions
6 Distance Measure Based on HFS
7 Solving MCDM Problem Based on HFS Using TOPSIS
7.1 Description of the MCDM Problem with HFNs
7.2 Algorithm of the Proposed Method
8 Illustrate Examples
9 Conclusion and Future Scope
References
16 Advanced TOPSIS-Based College Selection MCGDM Problem in Trapezoidal Pythagorean Fuzzy Environment
1 Introduction
1.1 Advantages and Limitation of the Proposed Method
2 Some Important Definition and Mathematical Preliminaries
3 Trapezoidal Pythagorean Fuzzy Sets
4 Aggregation Operator
4.1 Property of TrPyFWA
5 TOPSIS Strategy for MCGDM Based on TrPyFN
6 Illustrative Example
6.1 Sensitivity Analysis
6.2 Comparison Analysis
7 Conclusion
References
17 Identification and Classification of Prioritized Aczel-Alsina Aggregation Operators Based on Complex Intuitionistic Fuzzy Information and Their Applications in Decision-Making Problem
1 Introduction
2 Preliminaries
3 Prioritized Aczel-Alsina Aggregation Operators for CIFSs
4 MADM Methods for CIFNs
4.1 Numerical Example
5 Comparative Analysis
6 Conclusion
References
18 Intuitionistic Fuzzy Approach for Predicting Maternal Outcomes
1 Introduction
2 Review of Related Works
3 Methodology
3.1 Intuitionistic Fuzzy Sets and Their Distance Measures
IFSs Methods Developed by Szmidt and Kacprzyk
New Method of Intuitionistic Fuzzy Distance Measure
4 Numerical Experiment and Discussion
4.1 Data Source/Descriptions
5 Conclusion
References
19 Study of Fuzzy Fractional Caputo Order Approach to Diabetes Model
1 Introduction
2 Pre-requisite Concepts
3 Model Formulation
4 Model Analysis
4.1 Existence of Equilibrium Point of the System (19Equ419.4)
4.2 Stability Analysis of the System (19Equ419.4)
4.3 Existence of Equilibrium Point of the System (19Equ519.5)
4.4 Stability Analysis of the System (19Equ519.5)
5 Numerical Illustrations
6 Conclusion
References
20 Decision Analysis Framework Based on Information Measures of T-Spherical Fuzzy Sets
1 Introduction
2 Preliminary
2.1 Compared Rules for T-SFNs
3 Certain Information Measures Between T-SFSs
3.1 Distance measures for T-SFSs
3.2 Similarity Measure for T-SFSs
3.3 Entropy for T-SFSs
3.4 Inclusion Measure for T-SFSs
3.5 Information Measure Transformation Connections for T-SFSs
4 Numerical Examples of Information Measures
4.1 Application of Distance Measures to Pattern Recognition
4.2 Application of the Similarity Measure to Recognition of Pattern
5 Comparative Analysis
5.1 Application of the Inclusion Measures to Pattern Recognition
6 Applications of the Inclusion Measures to Bacteria Recognition
7 Conclusions
References
21 New Methods of Computing Correlation Coefficient Based on Pythagorean Fuzzy Information and Their Applications in Disaster Control and Diagnostic Analysis
1 Introduction
2 Preliminaries
2.1 Pythagorean Fuzzy Sets
2.2 Problems with Existing Methods for Computing Correlation Coefficient for Pythagorean Fuzzy Sets
3 New Methods for Computing Correlation Coefficient for Pythagorean Fuzzy Sets
3.1 Computation Example to Show Validity and Superiority
3.2 Theoretical Results
4 Numerical Applications
4.1 Application in Disaster Control
4.2 Application in Medical Diagnosis
5 Conclusion
References
22 Multi-Criteria Group Decision-Making q-Rung Neutrosophic Interval-Valued Soft Set TOPSIS Aggregating Operator for the Selection of Diagnostic Health Imaging
1 Introduction
2 Preliminary
3 MCGDM Based on q-Rung NSIVSS-TOPSIS Aggregating Operator
4 Selection Process Based on Diagnostic Health Imaging
5 Comparison Between the Suggested and the Existing Approach
5.1 Sensitivity Analysis
5.2 Advantages
6 Conclusion
References
23 Cosine Neutrosophic Normal Interval-Valued Aggregation Operators to the Selection of Robotic Engineering
1 Introduction
2 Preliminary
3 Some Basic Operation Based on CTri-NNIVN
4 Distance for CTri-NNIVNs
5 Aggregation Operators for CTri-NNIVNs
5.1 CTri-NNIV Weighted Averaging (CTri-NNIVWA)
5.2 Generalized CTri-NNIVWA (CTri-GNNIVWA)
5.3 Generalized CTri-NNIVWG (CTri-GNNIVWG)
6 MADM Concept Using CTri-NNIV Approach
6.1 Algorithm
6.2 Robotic Engineering Real-Life Example
6.3 Comparison for Proposed Approach with Existing Approach
7 Conclusion
References
24 An Integrated Weighted Distance-Based Approximation Method for Interval-Valued Spherical Fuzzy MAGDM
1 Introduction
2 Preliminaries
2.1 Limitations of the Existing Score Functions
3 Improved Score Function and Distance Measure
3.1 Improved Score Function
3.2 Distance Measure
4 Weighted Distance-Based Approximation Method for MAGDM
5 Supplier Selection Problem
5.1 Decision-Making Process
5.2 Comparison Analysis
6 Conclusion
References
25 Investigating Some Parameters of Cubic Fuzzy Graphs and an Application in Decision-Making Problem
1 Introduction
2 Preliminaries
3 The Dominating Set in Cubic Fuzzy Graphs
4 The Vertex Covering in Cubic Fuzzy Graphs
5 Application
6 Conclusions
References
26 Imperfect Production Inventory System Considering Effects of Production Reliability
1 Introduction
2 Research Gaps
3 Novelty and Contribution
4 Inventory Management in Operations Research
5 Basic Concepts and Terminologies
6 Assumption and Notation
6.1 Notations
6.2 Assumptions
7 Model Formulation
8 Numerical Illustration
9 Sensitivity Analysis
10 Managerial Implication
11 Conclusion
Appendix
References
27 A Fuzzy EOQ Model with Exponential Demand and Deterioration with Preservation Technology
1 Introduction
2 Preliminaries
2.1 Fuzzy Set
2.2 Fuzzy Number
2.3 α-cut of a Fuzzy Number
2.4 Trapezoidal Fuzzy Number
2.5 Defuzzification Method
3 Assumptions and Notations
3.1 Notations
3.2 Assumptions
4 Formulation of Mathematical Model
4.1 Crisp Model
4.2 Fuzzy Model
5 Solution Procedure
6 Numerical Examples
6.1 Numerical Example in Crisp Environment
6.2 Numerical Example in Fuzzy Environment
7 Sensitivity Analysis
7.1 Case: I Sensitivity Analysis in Crisp Environment
7.2 Case: II Sensitivity Analysis in Fuzzy Environment
8 Graphical Representations
9 Observations and Managerial Insights
9.1 Observations
9.2 Managerial Insights
9.3 Discussion
10 Conclusion
References
28 An EOQ Model with Price and Stock-Dependent Demand Including Trade Credit Using De-intuitification Technique Under Triangular Intuitionistic Fuzzy Environment
1 Introduction
1.1 Literature Review
1.2 Motivation
1.3 Novelty
1.4 Structure of the Chapter
2 Mathematical Preliminaries
3 De-intuitification of Triangular Intuitionistic Fuzzy Number
3.1 De-intuitification Skill Using Removal Area Method
4 Application of Triangular Intuitionistic Fuzzy Number in EOQ Model
4.1 Notations
4.2 Assumptions
4.3 Prototypical Design of Inventory Model
Case I: Supplier Arrives Before the Completion of Inventory (R =≤ T1)
Case II: Supplier Arrives After the Stocks Ends (t1 =≤ R)
Effect of Triangular Intuitionistic Fuzzy Number in the Proposed Model
5 Numerical Illustration
6 Sensitivity Analysis
6.1 Managerial Insight and Limitation of Work
7 Conclusion
References
29 A Study of an EOQ Model Under Triangular Cloudy Fuzzy Neutrosophic Demand Rate
1 Introduction
2 Basic Concepts
2.1 Triangular Cloudy Fuzzy System
2.2 Score Value of an NS [9]
3 Considerations and Symbols
3.1 Crisp Model Formulation
3.2 Neutrosophic Fuzzy Mathematical Model
4 Numerical Experiment
5 Sensitivity Analysis
6 Graphical Illustration
6.1 Managerial Insights
7 Conclusion
References
30 An Application of Intuitionistic Fuzzy Differential Equation to the Inventory Model
1 Introduction
1.1 Motivation and Objectives
1.2 Research Gaps
1.3 Contribution
1.4 Orientation of the Manuscript
2 Literature Review
2.1 Fuzzy Set Theory
2.2 Fuzzy Differential Equation Approach in Inventory Models
2.3 Inventory Problems in Intuitionistic Fuzzy Environment
3 Preliminaries
4 Notations and Assumptions to Define Proposed EOQ Model
5 Formulation of Mathematical Model
5.1 Crisp Model
5.2 Intuitionistic Fuzzy Differential Equation Approach
5.3 Defuzzification of Total Average Cost and Lot Size
6 Numerical Illustration
6.1 Crisp and Fuzzy Solutions
6.2 Comparison Among Three Cases
6.3 Managerial Insights
7 Conclusion
References
31 Solution of the Second-Order Linear Intuitionistic Fuzzy Difference Equation by Extension Principle Scheme
1 Introduction
1.1 Motivation and Objectives
1.2 Research Gaps
1.3 Contribution
1.4 Organization of This Chapter
2 Literature Review
2.1 Intuitionistic Fuzzy Number and Its Application
2.2 Fuzzy Differential Equation in Intuitionistic Environment
2.3 Fuzzy Difference Equation
3 Preliminaries
4 Second-Order Linear Difference Equation in Intuitionistic Fuzzy Environment
5 Extension Principle on Intuitionistic Fuzzy Second-Order Difference Equation
6 Numerical Illustration
7 Application
8 Conclusion
References
32 The Probabilistic Games and the Shapley Function
1 Introduction
2 Preliminary
3 A Class of Probabilistic Games and Its Shapley Function
4 A Special Collection of Probabilistic Games
4.1 Characterization on G0(PN)
5 Conclusions
References
Index