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

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