Decision-Making with Neutrosophic Set: Theory and Applications in Knowledge Management

Description

This book introduces readers to the concept of the neutrosophic set which can deal with dynamic and complex decision-making problems. With the complexity of the socio-economic environment, today’s decision-making is one of the most notable ventures, whose mission is to decide the best alternative under numerous known or unknown criteria. This book provides a large amount of theoretical and practical information about the latest research in the field, allowing readers to gain an extensive understanding of both the fundamentals and applications of neutrosophic sets to solve different kinds of decision-making problems and mathematical programming such as medical diagnosis, pattern recognition, construction problems, technology selection etc. Contents Preface Section I: Mathematical Aspects of Neutrosophic Set Chapter 1 Neutrosophic Set Theory and Engineering Applications: A Study Abstract 1. Introduction 1.1. Types of Neutrosophic Set Interval Valued Neutrosophic Set Fuzzy Neutrosophic Set Intuitionistic Neutrosophic Set Single Valued Neutrosophic Set Bipolar Neutrosophic Set 1.2. Neutrosophic Set Operations Containment Complement Union Intersection Product Addition Subtraction Equality Inclusion Division 2. Terminologies 3. Neutrospophic Set Applications in Civil Engineering Property-1 Applicability Description Usefulness Property-2 Applicability Description Usefulness Property-3 Applicability Description Usefulness Illustration of Interval Value Based Analysis of Efficiency Achieved by the Neutrosophic Based Civil Engineering 4. Neutrospophic Set Applications in Aeroscape Engineering Property-1 Applicability Description Usefulness Property-2 Applicability Description Usefulness Property-3 Applicability Description Usefulness Illustration of Interval Value Based Analysis of Efficiency Achieved by the Neutrosophic Based Aerospace Engineering 5. Neutrospophic Set Applications in Mechanical Engineering Property-1 Applicability Description Usefulness Property-2 Applicability Description Usefulness Property-3 Applicability Description Usefulness Illustration of Interval Value Based Analysis of Efficiency Achieved by the Neutrosophic Based Mechanical Engineering Conclusion References Chapter 2 A New Type of Quasi Open Functions in Neutrosophic Topological Environment Chapter 3 Accordance with Neutrosophic Logic? A Multimoora Approach for Countries Worldwide 1. The Credit Rating of Firms Companies Do they Work Scientifically? 2. Choice of Objectives (Criteria) Characterizing the Economies of the Countries 3. A Choice of a Method for the Multi-Objective Optimization of the Rating of Countries 3.1. Neutrosophic False 3.2. Neutrosphic True 3.3. Multi-Objective Optimization by Ratio Analysis (MOORA) 3.3.1. The First Part of MOORA: The Ratio Analysis 3.3.2. The Second Part of MOORA with the Reference Point 3.4. MULTIMOORA 3.5. The Theory of Ordinal Dominance 3.5.1. Axioms on Ordinal and Cardinal Scales 3.5.2. Dominance, being Dominated, Transitiveness and Equability Dominance Transitiveness Overall Dominance of One Alternative on Another Equability 4. Indeterminacy towards Neutrosophic Philosophy 4.1. The Liquidity of a Country being its Capacity to pay Debts on Time Due 4.1.1. No Public Debt in Other Currencies 2. Difference between External and Internal Public Debt 3. The Reserves of the Central Bank 4. The Money Machine 4.2. The Solvency of a Country 5. Points Still to be Discussed 5.1. The Importance of Each Objective or Criterion 5.1.1. Multiplication with a Coefficient of Importance (False after Neutrosphic Logic) 5.1.2. Adding a Number to an Objective (False after Neutrosphic Logic) 5.1.3. Multiplying an Objective with an Exponent 5.1.4. Dividing an Objective in Different Sub-Objectives (True after Neutrosphic Logic) 5.2. All Stakeholders 5.3. The Choice of Objectives (Criteria) 5.4. The Choice of Solutions 6. Final Classification of the Countries by MULTIMOORA and Ordinal Dominance 6.1. Previous Studies 6.2. Comparison with Standard & Poor’s Rates 2020 6.2. Missing Countries 6.3. Luxemburg: Another Exception 6.4. Another Hot Issue: Ireland 6.5. The United Kingdom 6.6. The United States 7. Economic Capability per Country: A Method of Forecasting? 7.1. The Necessity to Come to a Structural Credit Rating System for Countries Based on Continuity 7.2. S&P’s and Forecasting Conclusion Acknowledgments Appendix B. Appendix C. Share of Pollution for Lithuanian Counties 2002 References Chapter 4 Evaluation of Online Education Software under Neutrosophic Environment Abstract 1. Introduction 2. Neutrosophic Sets Preliminaries of the Single Valued Neutrosophic Set Definition 1 Definition 2 Definition 3 Definition 4 Definition 5 Definition 6 Definition 7 Definition 8 3. Neutrosophic MULTIMOORA Method 3.1. Neutrosophic MOORA- Ratio Method 3.2. Neutrosophic Moora-Reference Point Method 3.3. Neutrosophic MOORA-Full Multiplicative Form 3.4. Dominance Theory 4. Application Neutrosophic MOORA- Ratio Method Neutrosophic Moora-Reference Point Method Neutrosophic MOORA-Full Multiplicative Form Dominance Theory 5. Sensitivity Analysis 6. Comparative Analysis Algorithm 1. Pseudo Representation of NS-TOPSIS Conclusion References Chapter 5 A New Attribute Sampling Plan for Assuring Weibull Distributed Lifetime using Neutrosophic Statistical Interval Method Abstract 1. Introduction 2. Designing of Sampling Plan under Weibull Distribution Using Neutrosophic Statistics 3. Application of the Proposed Plan 4. Comparative Study Conclusion Acknowledgments References Section II: Decision Making Problems with Neutrosophic Set Chapter 6 On Some Propositions of Boundary in Interval Valued Neutrosophic Bitopological Space Abstract 1. Introduction 2. Basic Operations Definition 2.1. [18] Definition 2.2. [18] Definition 2.3. [18] Definition 2.4. [18] Definition 2.5. [18] Definition 2.6. [22] Definition 2.7. [7] Definition 2.8. [7] 3. Main Results Definition 3.1. Example 3.1. Definition 3.2. Example 3.2. Theorem 3.1. Remark 3.1. Example 3.3. Definition 3.3. Example 3.4. Theorem 3.2. Remark 3.2. Example 3.5. Theorem 3.3. Definition 3.4. Proposition 3.1. Remark 3.3. Example 3.6. Proposition 3.2. Remark 3.4. Example 3.7. Proposition 3.3. Example 3.8. Proposition 3.4. Example 3.9. Remark 3.5. Example 3.10. Proposition 3.6. Remark 3.6. Proposition 3.7. Remark 3.7. Example 3.12. Proposition 3.9. Conclusion Acknowledgments References Chapter 7 An Expected Value-Based Novel Similarity Measure for Multi-Attribute Decision-Making Problems with Single-Valued Trapezoidal Neutrosophic Numbers Abstract 1. Introduction 1.1. Existing Research Gap 1.2. Motivation of the Work 1.3. Structure of the Paper 2. Basic Preliminaries 3. Expected Value of a SVTNN and the Proposed SM Approach 3.1. Expected Value Calculation 3.2. Proposed SM Approach 3.3. Validity and Superiority of the Proposed SM Approach 4. MADM under SVN Environment 4.1. Formulate the Decision Matrix 4.2. Standardize the Decision Matrix 4.3. Determining the Ideal Solution According to the Attribute Type 4.4. Evaluate the Similarity Measure Values 4.5. Ranking of the Alternatives 5. Numerical Illustration 5.1. Comparative Study Conclusion Conflict of Interest Ethical Approval References Chapter 8 TrNN-ARAS Strategy for Multi-Attribute Group Decision-Making (MAGDM) in Trapezoidal Neutrosophic Number Environment with Unknown Weight Abstract 1. Introduction 1.1. Motivation of the Work 1.2. Research Methodology 1.3. Research Contribution 2. Literature Review 3. Preliminaries 4. Entropy Measure for TrNNs 4.1. Determination of the Unknown Weights of the Decision Makers and Weights of the Criteria Using the Proposed Entropy Measure 5. Extended ARAS Strategy for MAGDM in TrNNs Environment 6. Numerical Example 7. Comparative Analysis 8. Advantages of the Proposed Strategy Compare to VIKOR Strategy Conclusion and Future Research Direction References Chapter 9 An Application of Reduced Interval Neutrosophic Soft Matrix in Medical Diagnosis Abstract 1. Introduction 2.Preliminaries 2.1. Definition [41] 2.2. Definition [1] 2.3. Definition [15] 2.4. Definition [2] 2.5. Definition [35] 2.6. Definition [37] 2.7. Example 2.8. Definition [25] 2.9. Definition [16] 2.10. Definition [32] 2.11. Definition [21] 2.12. Example 3. Interval Neutrosophic Soft Matrices 3.1. Definition 3.2. Definition 3.3. Definition 3.4. Definition 3.5. Definition 3.6. Definition 3.7. Definition 3.8. Example 3.9. Definition 3.10. Example 3.11. Definition 3.12. Example 3.13. Definition 3.14. Example 3.15. Definition 4. Decision Making Problem by Using the Interval Neutrosophic Soft Sets for Medical Diagnosis Algorithm Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 5. Application of Interval Neutrosophic Soft Matrices in Medical Diagnosis Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Conclusion Acknowledgments References Chapter 10 Interval-Valued Neutrosophic N Soft Set and Intertemporal Interval-Valued Neutrosophic N Soft Set to Assess the Resilience of the Workers Amidst Covid-19 Section III. Extension of the Neutrosophic Set Chapter 11 2-Additive Choquet Cosine Similarity Measures for Simplified Neutrosophic Sets and Applications to Medical Diagnosis Chapter 12 Multi-Attribute Group Decision-Making Based on Uncertain Linguistic Neutrosophic Sets and Power Hamy Mean Operator Abstract 1. Introduction 2. Preliminaries 2.1. Neutrosophic Sets 2.2. Linguistic Neutrosophic Sets 2.3. The Power Average Operator, Hamy Mean Operator and Power Hamy Mean Operator 3. Uncertain Linguistic Neutrosophic Sets 3.1. Definition of ULNSs and ULNNs 3.2. Operational Rules of ULNNs 3.3. Comparison Method of ULNNs 3.4. Distance Measure between two ULNNs 4. Aggregation operators for ULNNs 4.1. The Uncertain Linguistic Neutrosophic Power Average Operator 4.2. The Uncertain Linguistic Neutrosophic Power Weighted Average Operator 4.3. The Uncertain Linguistic Neutrosophic Power Hamy Mean (ULNPHM) Operator 4.4. The Uncertain Linguistic Neutrosophic Power Weighted Hamy Mean (ULNPWHM) Operator 5. A Novel MAGDM Method Under ULNNs 6. Numerical Examples 6.1. Procedure of Decision Making Based on the ULNNPWHM Operator 6.2. Sensitivity Analysis 6.3. Validity Analysis 6.4. Advantages of Our Proposed Method 6.4.1. The Flexibility of Aggregating DMs’ Hesitant Evaluate Information 6.4.2. The Ability of Reducing the Negative Influence of Unreasonable Information 6.4.3. The Ability of Considering the Interrelationship Among Multiple Attributes Conclusion Appendixes Acknowledgments Conflict of Interests References Chapter 13 An n-Dimensional Neutrosophic Linguistic Approach to Poverty Analysis with an Empirical Study Abstract Abbreviations 1. Introduction 2. Literature Review 3. Methodology 4. Basic Concepts Definition 1. Fuzzy Sets (Zadeh, 1965) Definition 2. Neutrosophic Sets (Smarandache, 2005) Definition 3. Single Valued Neutrosophic Sets (Wang, et al. 2012) Definition 3. Subtraction of Two Neutrosophic Numbers (Smarandache, 2016) Definition 4. Division of Two Neutrosophic Numbers (Smarandache, 2016) Definition 5. Direct Sum Definition 6. Score Function of Neutrosophic Numbers 5. Neutrosophic Approach to Poverty Measurement 5.1. Linguistic Neutrosophic Membership Function of Poverty (LNMFP) 5.2. n-Number of Linguistic Neutrosophic Membership Function of Poverty Algorithm for Measuring the Poverty Levels of Householders or Target People 5.3. Neutrosophic Membership Function for Poverty Indicators 5.3.1. Income 5.3.2. Education 5.3.3. Employment 5.3.4. Assets 5.4. Neutrosophic Aggregation Operators 6. Case Study Conclusion Acknowledgments References Chapter 14 Multi-Granulation Single-Valued Neutrosophic Hesitant Fuzzy Rough Sets Abstract Introduction 2. Preliminaries Definition 1 [24] Definition 2 [41] Definition 3 Definition 4 Definition 5 [41] Proposition 1 3. Single-Valued Neutrosophic Hesitant Fuzzy Rough Sets Definition 6 Example 1 4. MGSVNHFRSs 4.1. OMGSVNHFRSs Definition 7 4.2. PMGSVNHFRSs Definition 8 4.3. The Relation between SVNHFRS, OMGSVNHFRS, and PMGSVNHFRS 5. Comparative Analysis Conclusion References About the Editor About the Contributors Index Blank Page