Neutrosophic Operational Research: Methods and Applications

Description

This book addresses new concepts, methods, algorithms, modeling, and applications of green supply chain, inventory control problems, assignment problems, transportation problem, linear problems and new information related to optimization for the topic from the theoretical and applied viewpoints of neutrosophic sets and logic. The book is an innovatory of new tools and procedures, such as: Neutrosophic Statistical Tests and Dependent State Samplings, Neutrosophic Probabilistic Expert Systems, Neutrosophic HyperSoft Set, Quadripartitioned Neutrosophic Cross-Entropy, Octagonal and Spherical and Cubic Neutrosophic Numbers used in machine learning. It highlights the process of neutrosofication {which means to split the universe into three parts, two opposite ones (Truth and Falsehood), and an Indeterminate or neutral one (I) in between them}. It explains Three-Ways Decision, how the universe set is split into three different distinct areas, in regard to the decision process, representing: Acceptance, Noncommitment, and Rejection, respectively. The Three-Way Decision is used in the Neutrosophic Linguistic Rough Set, which has never been done before. Contents Neutrosophical Plant Hybridization in Decision-Making Problems 1 Introduction 2 Preliminaries 3 Neutrosophic Methodologies in Multi-criteria Decision-Making Problems 4 The Summary of Process 5 Numerical Examples in Multi-criteria Decision-Making Problem 6 Results and Discussion 7 Limitations and Advantages 8 Future and Summary of Work References Multicriteria Decision-Making Based on Quadripartitioned Neutrosophic Cross-Entropy 1 Introduction 2 Preliminaries 3 Cross-Entropy of QSVNS 4 Multicriteria Decision-Making Method Based on the Cross-Entropy of QSVNSs 4.1 Practical Example 5 Cross-Entropy for IQNS 6 Multicriteria Decision-Making Method Based on the Cross-Entropy of IQNSs 6.1 Practical Example 7 Conclusion References New Entropy, Similarity Measures of Interval-Valued Neutrosophic Sets, and Application in Supplier Selection 1 Introduction 2 Preliminaries 3 Entropy on the Interval-Valued Neutrosophic Set 4 Similarity Measure of IVNS Set Based on Entropy 5 Applications in Supplier Selection 6 Conclusion References Control Chart for Monitoring Variation Using Multiple Dependent State Sampling Under Neutrosophic Statistics 1 Introduction 2 Designing of the Proposed Chart 3 The Performance of the Proposed Chart 4 The Comparison of the Proposed Chart with the Existing MDS Sampling Chart 4.1 Simulation Data 5 Real-Word Example 6 Concluding Remarks References Three-Way Decisions with Single-Valued Neutrosophic Uncertain Linguistic Decision-Theoretic Rough Sets Based on Generalized Maclaurin Symmetric Mean Operators 1 Introduction 2 Preliminaries 2.1 Review of the Three-Way Decisions Based on D-TRSs 3 A Novel D-TRS Model Based on Single-Valued Neutrosophic Uncertain Linguistic Variables 4 Some Single-Valued Neutrosophic Uncertain Linguistic Generalized Maclaurin Symmetric Mean Operators 5 Three-Way Decisions Based on the S-VULVs 6 Conclusion References Novel Distance Measures Over SVTN-Numbers and Their Application to Multi-Criteria Decision Making Problems 1 Introduction 2 Preliminary 3 Distance Measures Over the SVTN-Numbers 4 Multi-Criteria Decision Making Based on Normal SVTN-Numbers 5 An Illustrative Example 6 Conclusion References The Determinant and Adjoint of an Interval-Valued NeutrosophicMatrix 1 Introduction 2 Preliminaries 2.1 Neutrosophic Sets 2.2 Interval-Valued Neutrosophic Sets 2.3 Interval-Valued Neutrosophic Matrices 3 Determinant of the Square IVN-Matrix 4 Adjoint of a Square IVN-Matrix 5 Conclusions References Neutrosophic Normal Probability Distribution—A Spineof Parametric Neutrosophic Statistical Tests: Propertiesand Applications 1 Introduction 2 Neutrosophic Normal Probability Distribution 2.1 Neutrosophic Normal Probability Distribution with Indeterminate Mean 2.2 Neutrosophic Normal Probability Distribution with Indeterminate Variance 2.3 Neutrosophic Normal Probability Distribution with Indeterminate Mean and Variance 3 Quantiles of Neutrosophic Normal Distribution 4 Properties of Neutrosophic Normal Probability Distribution 5 The Entropy of Neutrosophic Normal Distribution 6 Maximum Likelihood Estimates of Neutrosophic Normal Distribution 7 Fisher Information Matrix of Neutrosophic Normal Distribution References New Algorithms for Bipolar Single-Valued Neutrosophic Hamiltonian Cycle 1 Introduction 2 Review of Literature 3 Preliminaries 3.1 Fuzzy Set [1] 3.2 Fuzzy Graph [5] 3.3 Bipolar Fuzzy Set [4] 3.4 Bipolar Fuzzy Graph [8] 3.5 Intuitionistic Fuzzy Set [17] 3.6 Intuitionistic Fuzzy Graph [17] 3.7 Bipolar Intuitionistic Fuzzy Graph [17] 3.8 Single-Valued Neutrosophic Set [3] 3.9 Bipolar Neutrosophic Set [15] 3.10 Bipolar Neutrosophic Graph [14] 3.11 Hamiltonian Path and Hamiltonian Cycle [16] 4 Proposed Algorithms to Find Bipolar Single-Valued Neutrosophic Hamiltonian Cycle (BSVNHC) 4.1 Modified Form of the Score Function of BSVNNs 4.2 Algorithm to Find BSVNHC Using Adjacency Matrix 4.3 Algorithm to Find BSVNHC Using the Lowest Vertex Degree (LVD) 5 Comparative Analysis and Discussion 6 Conclusion References Improved Cosine Similarity Measures of Simplified Neutrosophic Sets for Medical Diagnoses: Suggested Modifications 1 Introduction 2 Drawbacks of Ye's Measures of Similarity 2.1 Drawbacks of Improved Cosine Similarity Measures for Single-Valued Neutrosophic Sets 2.2 Drawbacks of Improved Cosine Similarity Measures for Interval-Valued Neutrosophic Sets 3 Suggested Modifications 3.1 Suggested Cosine Similarity Measures for Single-Valued Neutrosophic Sets 3.2 Suggested Cosine Similarity Measures for Interval-Valued Neutrosophic Sets 4 Conclusions References Fuzzy Multi-Objective Inventory Model for Deteriorating Items, with Shortages Under Space Constraint: Neutrosophic Hesitant Fuzzy Programming Approach 1 Introduction 2 Mathematical Model 2.1 Notations 2.2 Assumptions 2.3 Model Formation 3 Prerequisite Mathematics 4 Fuzzy Model 5 Mathematical Analysis 5.1 Neutrosophic Hesitant Fuzzy Non-Linear Programming (NHFNLP) Technique 5.2 Fuzzy Programming Technique to Solve MOIM 6 Numerical Example 7 Sensitivity Analysis 8 Conclusions References Bulbul Disaster Assessment Using Single-Valued Spherical Hesitant Neutrosophic Dombi Weighted Aggregation Operators 1 Introduction 2 Preliminaries 3 Single-Valued Spherical Hesitant Neutrosophic Numbers 4 Single-Valued Spherical Hesitant Neutrosophic Dombi Weighted Aggregation Operators 5 Multi-attribute Decision-Making Using SVSHNNs 5.1 An Illustrative Example 6 Comparative Study 7 Conclusion References Application of Generalized Aggregate Operators on Neutrosophic Hypersoft Set in Decision-Making 1 Introduction 2 Preliminaries 3 Generalized Aggregate Operators on Neutrosophic Hypersoft Set and Properties 4 Necessity and Possibility Operations 5 Conclusion References Neutrosophic Statistics for Grouped Data: Theory and Applications 1 Introduction 2 Neutrosophic Arithmetic Mean (NAM) 3 Neutrosophic Geometric Mean (NGM) 4 Neutrosophic Harmonic Mean (NHM) 5 Neutrosophic Median (N.Md) 6 Neutrosophic Mode 7 Neutrosophic Quantiles (NQ) 8 Neutrosophic Deciles (ND) 9 Neutrosophic Percentiles (NP) 10 Neutrosophic Range (NR) 11 Neutrosophic Coefficient of Range (NCR) 12 Neutrosophic Quartile Deviation (NQD) 13 Neutrosophic Variance (NV) 14 Neutrosophic Standard deviation (N.S.D) 15 Neutrosophic Coefficient of Variation (N.C.V) 16 Neutrosophic Mean Deviation (N.M.D) 17 Neutrosophic Empirical Relation Between Mean, Median, and Mode 18 Neutrosophic Moments About Mean 19 Neutrosophic Moments About Origin 20 Neutrosophic Skewness 21 Neutrosophic Kurtosis 22 Neutrosophic Moment Ratios References A New Approach to Neutrosophic Soft Mappings and Application in Decision Making 1 Introduction 2 Preliminaries 3 Neutrosophic Soft Mappings 4 An Application in Decision Making 5 Conclusion References Multiple Attribute Decision-Making Based on Uncertain Linguistic Operators in Neutrosophic Environment 1 Introduction 2 Preliminaries 2.1 Some Concept of Interval Neurotrophic Set 2.2 Some Concept of Uncertain Linguistic Variables 3 Interval Neutrosophic Uncertain Linguistic Set (IULN) 4 Interval Neutrosophic Uncertain Linguistic Aggregation Operators 4.1 INULWA Operator 4.2 INULWG Operator 5 Interval Neutrosophic Uncertain Linguistic Dombi Aggregation Operators 5.1 INULDWA Operator 5.2 INULDWG Operator 6 Model for MADM Method with INUL Information 7 Numerical Example 7.1 Application 8 Comparative Study 9 Conclusion 10 Complaince with Ethical Standards References Neutrosophic Probabilistic Expert System for Decision-Making Support in Supply Chain Risk Management 1 Introduction 2 Conceptualization 2.1 SCRM and the SCOR Model 2.2 Neutrosophic AHP-TOPSIS Technique 2.3 Probabilistic Expert Systems 3 Proposed Methodology 3.1 Selection of Risks That May Affect the Supply Chain 3.2 Selection of Strategies for Supply Chain Risk Management 3.3 Selection of Supply Chain Performance Metrics 3.4 Selection of Experts 3.5 Estimation of Weights Using the Neutrosophical AHP Technique 3.6 Estimation of the Probability of Occurrence of Each Risk 3.7 Neutrosophic TOPSIS for the Estimation of Expected Impact for Each Risk 3.8 Neutrosophic TOPSIS for Strategies Selection in Supply Chain Risk Management 3.9 Neutrosophic Probabilistic Expert System Programming 4 Simulation and Results 5 Conclusions References Cloud Computing Technology Selection Using a Novel Neutrosophic Extension of the MULTIMOORA Method Based on the Use of Interval-Valued and Triangular-Valued Neutrosophic Numbers 1 Introduction 2 The Neutrosophic Sets, Concepts, and Operators 2.1 Single-Valued Neutrosophic Sets 2.2 Interval-Valued Neutrosophic Sets 2.3 Triangular Fuzzy Neutrosophic Sets 3 The MULTIMOORA Method 3.1 The Ratio System Approach 3.2 The Reference Point Approach 3.3 The Full Multiplicative Form 3.4 The Final Selection of the Most Appropriate Alternative 4 An Extension of the MULTIMOORA Method Based on Single-Valued Neutrosophic Numbers 4.1 A Single-Valued Neutrosophic Extension of the MULTIMOORA Method 4.1.1 The Ratio System Approach 4.1.2 The Reference Point Approach 4.1.3 The Full Multiplicative Form 4.1.4 The Final Selection of the Most Appropriate Alternative 4.2 An Adoption of the Neutrosophic Extension of the MULTIMOORA Method 5 A Numerical Illustration 5.1 Ranking Alternatives Using the Neutrosophic Extension of the MULTIMOORA Method 5.2 Ranking Alternatives Using the Neutrosophic Extension of the MULTIMOORA Method and Modified Group Decision Matrix 5.3 Ranking Alternatives Using the Neutrosophic Extension of the MULTIMOORA Method and IVNNs 5.4 Ranking Alternatives Using the Neutrosophic Extension of the MULTIMOORA Method and TVNNs 5.5 Final Considerations of the Use of MULTIMORA with Different Approaches 6 Conclusion References Neutrosophic Linear Differential Equation with a New Concept of Neutrosophic Derivative 1 Introduction 1.1 Neutrosophic Set 1.2 Neutrosophic Differential Equation 2 Preliminaries 3 Generalized Neutrosophic Derivative 4 Formulation of the Problem 5 Example 6 Conclusion References Linear and Nonlinear Programming Methods of Two-Person Interval-Valued Neutrosophic Games 1 Introduction 2 Preliminaries 3 Two-Person Interval-Valued Neutrosophic Matrix Game References Neutrosophic Hypersoft Matrix Theory: Its Definition, Operators, and Application in Decision-Making of Personnel Selection Problem 1 Introduction 1.1 Literature Review 1.2 Objective/Motivation of the Study 1.3 Structure of the Article 2 Preliminaries 3 Definition and Aggregate Operators of NHSM 3.1 Definition: NHSM 3.2 Definition: Row NHSM 3.3 Definition: Column NHSM 3.4 Definition: Zero NHSM 3.5 Definition: Universal NHSM 3.6 Definition: Neutrosophic Hypersoft Submatrix (NHSSM) 3.7 Definition: Neutrosophic Hypersoft Equal Matrix (NHSEM) 3.8 Definition: AND Operation 3.9 Definition: OR Operation 3.10 Definition: Product of NHSM 3.11 Definition: Sum of NHSM 4 Neutrosophic Hypersoft Matrix Algorithm (NHSM Algorithm) 4.1 NHSM Algorithm 4.2 Problem Description and Formulation 4.3 Calculations Using NHSM Algorithm 4.4 Algorithm Proposed by Saqlain et al. [1] 5 Result Comparison and Discussion 6 Conclusion References TOPSIS Method for Multi-Attribute Group Decision Making Based on Neutrality Aggregation Operator Under Single Valued Neutrosophic Environment: A Case Study of Airline Companies 1 Introduction 2 Basic Concepts 2.1 Neutrosophic Sets 2.2 Neutrality Aggregation 2.3 Promethee Method and GAIA Plane 3 TOPSIS Method for Multiple Attribute Group Decision Making with Neutrality Aggregation Operator Based Single-Neutrosophic Information 4 Numerical Example: Case Study of Airline Companies 4.1 Converting to Neutrosophic Numbers of Users' Rating of the Criteria 4.2 Case Study of Airline Companies 5 Comparative Analysis with Promethee Method 5.1 Base Method: Promethee 6 Conclusion References Aggregate, Arithmetic, and Geometric Operators of Octagonal Neutrosophic Numbers and Its Application in Multi-Criteria Decision-Making Problems 1 Introduction 1.1 Motivation 1.2 The Paper Presentation 2 Preliminaries 2.1 Deductions 3 Calculations 3.1 Sum of ONNs' Sum 3.2 Product of Two ONNs 3.3 Scalar Product of Two ONNs 3.4 Power Rule of ONNs 3.5 Score Function of ONNs 3.6 Accuracy Function of ONNs 3.7 Metric Relations between Two ONNs 4 Weighted Operators 4.1 Weighted Arithmetic Averaging Operator 4.2 Weighted Geometric Averaging Operator (WGAO) 4.3 ONNWAAONNWAA(4937521En23FigaPrint) and ONNWGA(4937521En23FigbPrint) Operators-Based Algorithm 4.4 Case Study 4.4.1 Problem Formulation 4.4.2 Parameters 4.4.3 Assumptions 5 Conclusion References A Study of Neutrosophic Cubic Finite State Machines, Subsystems, and Applications 1 Introduction 2 Preliminaries 3 Neutrosophic Cubic Finite State Machine (NCFSM) 4 Subsystems of Neutrosophic Cubic Finite State Machines 5 Operations on Subsystems of Neutrosophic Cubic FSMs (Finite State Machines) 6 Applications 7 Comparison Analysis 8 Conclusion References Analyzing Shortest Path Problem via Single-Valued Triangular Neutrosophic Numbers: A Case Study 1 Introduction 2 Literature Review 3 Neutrosophic Sets 3.1 Single-Valued Neutrosophic Sets (SVNS) 4 Project Network Terminology 5 Algorithm for Analyzing Single-Valued Triangular Neutrosophic Path Problem 6 Analysis 7 Conclusions References TrNN- EDAS Strategy for MADM with Entropy Weight Under Trapezoidal Neutrosophic Number Environment 1 Introduction 2 Preliminary 3 Calculating Weight Using Entropy Strategy 4 TrNN-EDAS Strategy Under TrNN Environment 5 Numerical Example 6 Comparative Study 7 Conclusion References Neutrosophic Fuzzy Goal Programming Algorithm for Multi-level Multiobjective Linear Programming Problems 1 Introduction 2 Preliminaries 3 Description of ML-MOLPPs 4 Proposed Neutrosophic Fuzzy Goal Programming Techniques 4.1 Characterization of Different Membership Functions Under Neutrosophic Environment 4.2 Neutrosophic Fuzzy Goal Programming Approach 4.3 Neutrosophic Fuzzy Goal Programming Approach for ML-MOLPPs 4.3.1 The First NFGP Algorithm for ML-MOLPPs 4.3.2 The Second NFGP Algorithm for ML-MOLPPs 5 Numerical Illustrations 6 Conclusions Appendix References Multi-Attribute Neutrosophic Decision-Making in Dosimetric Assessment of Radiotherapy Imaging Techniques 1 Introduction 2 Background 3 Decision-Making Procedure Using Subjective and Objective Evaluation in Neutrosophic Environment 3.1 Basic Concepts 3.2 Mathematical Model of Decision Problem 3.2.1 Alternatives and Criteria 3.2.2 Construction of Decision Matrix 3.2.3 Calculation of the Criteria Weights 3.2.4 Classification of Criteria and Ideal Point 3.2.5 Ranking Order of Alternatives 4 Decision-Making Problem in Medical Science 4.1 Data Set 4.1.1 Alternatives (Imaging Techniques) 4.1.2 Criteria (Medical Parameters) 4.1.3 Calculation of Subjective and Objective Weights 4.2 Evaluation 4.2.1 Ideal Point 4.2.2 Test Function of Decision Matrix 5 Results and Discussions 5.1 Comparative Study 5.2 Experts Comments 5.3 Inference and Results 6 Conclusion References Index