Fuzzy Mathematical Analysis and Advances in Computational Mathematics (Studies in Fuzziness and Soft Computing, 419)

✍ Scribed by S. R. Kannan (editor), Mark Last (editor), Tzung-Pei Hong (editor), Chun-Hao Chen (editor)

• Publisher: Springer
• Year: 2022
• Tongue: English
• Leaves: 273
• Category: Library

✦ Synopsis

The edited volume includes papers in the fields of fuzzy mathematical analysis and advances in computational mathematics. The fields of fuzzy mathematical analysis and advances in computational mathematics can provide valuable solutions to complex problems. They have been applied in multiple areas such as high dimensional data analysis, medical diagnosis, computer vision, hand-written character recognition, pattern recognition, machine intelligence, weather forecasting, network optimization, VLSI design, etc. The volume covers ongoing research in fuzzy and computational mathematical analysis and brings forward its recent applications to important real-world problems in various fields. The book includes selected high-quality papers from the International Conference on Fuzzy Mathematical Analysis and Advances in Computational Mathematics (FMAACM 2020).

✦ Table of Contents

Preface
Contents
Editors and Contributors
Bipolar Complex Pythagorean Fuzzy Graphs
1 Introduction
2 Preliminaries
3 Bipolar Complex Pythagorean Fuzzy Graphs
4 Regular and Edge Regular Bipolar Complex Pythagorean Fuzzy Graphs
5 Conclusion
References
Modified Operations of Trapezoidal Fuzzy Numbers for Solving Fuzzy Linear Programming Problems
1 Introduction
2 Preliminaries
3 Arithmetic Operations of Trapezoidal Fuzzy Numbers
3.1 Addition
3.2 Subtraction
3.3 Multiplication
3.4 Division
4 Disadvantages of the Operations (Subtraction and Division) of Trapezoidal Fuzzy Numbers
5 Modified Operations of Subtraction and Division of Trapezoidal Fuzzy Numbers
5.1 Subtraction
5.2 Notation
5.3 Division
6 Application of the Modified Operations (for Solving Fully Fuzzy Linear Programming Problem)
7 Conclusion
References
An Innovative Method for Finding Optimal Solution Fully Solved by Using Generalized Quadratic Fuzzy Transportation Problems
1 Introduction
2 Preliminaries
2.1 Formulation of Generalized Quadratic Fuzzy Transportation Method
2.2 Definition: Fuzzy Set
2.3 Definition: Fuzzy Number
2.4 The Requirements Assumption [1]
2.5 The Feasible Solutions Property [1]
2.6 Fuzzy Optimal Solution [1]
2.7 Non-Degenerate BFS [1]
2.8 Rank of the Transportation Problem [1]
2.9 Number of Basic Variables [1]
2.10 Integrality Property of Basic Variables [1]
3 Piecewise Quadratic Fuzzy Numbers
3.1 Definition
3.2 Arithmetic Operations
4 Algorithms for Optimal Method
4.1 Algorithm for Generalized Quadratic Fuzzy Vogel’s Approximation Method
4.2 Algorithm for Generalized Quadratic Fuzzy Modified Distribution Method
5 Numerical Example
6 Results Comparison
7 Conclusion
References
A New Ranking Method for Solving Nanogonal Fuzzy Transportation Problem
1 Introduction
2 Preliminaries
3 Nanogonal Fuzzy Number
3.1 Arithmetic Operations on Nanogonal Fuzzy Number
3.2 Measure of Fuzzy Number
4 Proposed Ranking Method
5 Robust Ranking Method for Nanogonal Fuzzy Number
6 Fuzzy Transportation Problem
7 Numerical Example
7.1 Ranking of Nanogonal Fuzzy Number Using Proposed Method
7.2 Crisp Transportation Problem of the Corresponding Nanogonal Fuzzy Transportation Problem
8 Ranking of Nanogonal Fuzzy Number Using Robust Ranking Method
9 Merit of Proposed Method
10 Conclusion
References
Novel Arithmetic Operations on IVIFNs and Their Properties on Ranking Functions
1 Introduction
2 Preliminaries
3 A New Type of IVIFN
3.1 Operations on New Type of IVIFNs
4 Operations on Ranking Functions
5 Numerical Example
6 Application of the Existing Ranking Function in MCDM Problem
6.1 Algorithm
7 Conclusion and Future Scope
References
Fuzzy Clustering Technique for Segmentation on Skin Cancer Dermoscopic Images
1 Introduction
2 Segmentation
3 Review of FCM
4 Segmentation on Skin Cancer Images
5 Experimental Result
6 Conclusion
References
A Study on Fuzzy Coloring in Quadruple Layered Fuzzy Graph
1 Introduction
2 Definitions
2.1 Quadruple Layered Fuzzy Graph
2.2 Definition
2.3 Definition
3 Fuzzy Vertex Coloring on Quadruple Layered Fuzzy Graph
3.1 Example
4 Fuzzy Edge Coloring of Quadruple Layered Fuzzy graph
5 Conclusion
References
On d2-Coloring of Certain Families of Graphs
1 Introduction
2 Main Results
2.1 d2-Coloring of Star Graph Families
2.2 d2-Coloring of C(Pn),M(Pn) and T(Pn)
2.3 d2-Coloring of C[Cn], M[Cn] and T[Cn]
2.4 Characterization of Cactus Graphs and Block Graphs with χd2(G)=χ(G)
References
Improved Solution to a Decision-Making Problem Involving TraIFNs Data with TOPSIS Method
1 Introduction
2 Preliminaries
3 Ranking of TraIFN by Accuracy Functions
4 Ranking by Improved Accuracy Function for TraIFN
4.1 Significance of the Proposed Method
5 TOPSIS Method Based on the Improved AF for TraIFN
5.1 Numerical Examples
6 Application of the Proposed Improved AF in MCDM Problem Using IM Algorithm for Multi-Criteria TraIFIM
6.1 Numerical Example
7 Conclusion and Future Scope
References
A New Distance and Similarity Measure on Soft Parameter Sets and Their Applications to MCDM Problem
1 Introduction
2 Preliminaries
3 Parameter-Based Distance and Similarity Measures on Soft Set
4 Soft Similarity Symmetric Matrix on Parameter-Based Soft Set
5 Multi-criteria Decision-Making Problem on Soft Similarity Symmetric Matrix
5.1 Multi-criteria Decision-Making Algorithm
5.2 Illustrative Example
6 Conclusion
References
Automated Accurate Sleep Stage Classification System Using Machine Learning Techniques with EEG Signals
1 Introduction
2 Related Work
3 Experimental Data
4 Methodology
4.1 Feature Extraction
5 Experimental Results and Discussion
5.1 Classification Accuracy of Category-I Subject ISRUC-Sleep Database
5.2 Classification Accuracy of Category-II Subject ISRUC-Sleep Database
5.3 Classification Accuracy of Category-III Subject ISRUC-Sleep Database
5.4 Summary of Comparative Analysis Results of ISRUC-Sleep (I/II/III) Data
6 Conclusion
References
On Comparative Study of Clustering Using Finite Mixture of Non-Gaussian Distributions
1 Introduction
2 Initialization Method—Weighted K-means Algorithm (WKM)
3 Model-Based Clustering Using Non-Gaussian Distributions
3.1 Model-Based Clustering Using Lognormal Mixture Models
3.2 Model-Based Clustering Using Geometric Skew Normal Mixture Models
3.3 Model-Based Clustering Using Skew Laplace Mixture Models
3.4 Model-Based Clustering Using Skew Normal Mixture Models
3.5 Model-Based Clustering Using Skew-t Mixture Models
4 Numerical Experiments
4.1 Banknote Dataset
4.2 Diabetes Dataset
5 Conclusion
References
M/G/1 Retrial Queueing System with Working Vacation and Starting Failure
1 Introduction
2 Description of the Model
3 Steady-State Analysis of the System
3.1 The Steady-State Equations
3.2 The Steady-State Solutions
3.3 Results
4 Performance Measures
5 Special Cases
6 Conclusion
References
Analysis of MAP/PH1, PH2/2 Queue with Working Breakdown, Starting Failure, and Bernoulli Vacation
1 Introduction
2 Model Description
3 The Generator Matrix
4 System Analysis
4.1 Stability Condition
4.2 The Invariant Probability Vector
5 Analysis of Busy Period
6 System Measures
7 Particular Case
8 Analysis of Waiting Time Distribution
9 Numerical Analysis
9.1 Example
10 Conclusion
References
Results on Revan and Hyper Revan Indices of Some HEX Derived Networks
1 Introduction
2 Results and Discussion on Revan and Hyper Revan Indices of HEX Derived Networks
3 Conclusion
References
Dufour and Soret Effects on MHD Flow of Cu-Water and Al2O3-Water Nanofluid Flow Over a Permeable Rotating Cone
1 Introduction
2 Mathematical Modeling
3 Method of Solution
4 Results and Discussions
5 Conclusion
References
Adaptive Feedback Cancelation in Hearing Aids Using Least Squares Delay-Based Fuzzy Interactive Controller
1 Introduction
2 Literature Survey
2.1 High-Frequency Gain Control
2.2 Phase Cancelation
2.3 Notch Filtering
3 Adaptive Feedback Cancelation
3.1 Adaptive Filtering
3.2 Adaptive Algorithms
4 Methodology
4.1 FIC Implementation
5 Simulation
5.1 Measuring Convergence Rate
5.2 Measuring SNR
6 Discussion
7 Conclusions
References
Retrieval of Erroneous Information by Adopting a Novel Way Using Fuzzy Logic
1 Introduction
1.1 Preliminaries
2 Some Basic Definitions [15]
2.1 Maximum Likelihood Decoding of Fuzzy Codewords [15]
3 An Algorithm for Finding the Transmitted Codeword to be Retrieved by the Receiver
3.1 Procedure for Message Retrieval
4 Conclusion
References
Author Index