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Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices

Book Description

The use of fuzzy logic has become prominent in a variety of fields and applications. By implementing these logic sets, problems and uncertainties are more effectively resolved. Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices is a pivotal reference source for the latest scholarly perspectives on the interdisciplinary use of fuzzy logic theory, focusing on the application of sets and matrices. Highlighting theoretical framework and empirical research findings, this book is ideally designed for academics, practitioners, upper-level students, and professionals interested in an innovative overview of fuzzy logic sets and matrices.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Book Series
    1. Mission
    2. Coverage
  5. Preface
  6. Acknowledgment
  7. Chapter 1: Fuzzy Sets, Intuitionistic Fuzzy Sets
    1. ABSTRACT
    2. INTRODUCTION
    3. SOME DEFINITIONS AND PROPERTIES
    4. SEPARATION OF GENERALIZED INTERVAL-VALUED INTUITIONISTIC FUZZY SETS
    5. SOME OPERATORS OF GENERALIZED INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND ITS PROPERTIES
    6. CONCLUSION
    7. REFERENCES
  8. Chapter 2: Neutrosophic Sets and Logic
    1. ABSTRACT
    2. INTRODUCTION
    3. NEUTROSOPHIC SET, SIMILARITY MEASURES, NEUTROSOPHIC NORMS
    4. CRISP NEUTROSOPHIC SET, NEUTROSOPHIC CRISP NEIGHBORHOOD SYSTEMS, NEUTROSOPHIC CRISP LOCAL FUNCTIONS
    5. INTERVAL VALUED NEUTROSOPHIC SETS
    6. APPLICATIONS OF NEUTROSOPHIC SETS
    7. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  9. Chapter 3: Interval-Valued Intuitionistic Fuzzy Partition Matrices
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. DIFFERENT KINDS OF INTERVAL-VALUED INTUITIONISTIC FUZZY SUBMATRIX AND PARTION MATRIX
    5. INTERVAL-VALUED INTUITIONISTIC FUZZY BLOCK MATRIX
    6. OPERATIONS ON INTERVAL-VALUED INTUITIONISTIC FUZZY BLOCK MATRIX
    7. SOME ALGEBRAIC OPERATIONS OF INTUITIONISTIC FUZZY MATRICES
    8. CONCLUSION
    9. REFERENCES
  10. Chapter 4: P-F Fuzzy Rings and Normal Fuzzy Ring
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. T-PURE FUZZY IDEALS
    4. 3. P-F FUZZY RINGS
    5. 4. NORMAL FUZZY RINGS
    6. REFERENCES
  11. Chapter 5: Intutionistic Fuzzy Difference Equation
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. DIFFERENCE EQUATION AND INTUITIONISTIC FUZZY DIFFERENCE EQUATION
    5. SOLUTION OF INTUITIONISTIC FUZZY DIFFERENCE EQUATION
    6. NUMERICAL EXAMPLE
    7. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  12. Chapter 6: Semiring of Generalized Interval-Valued Intuitionistic Fuzzy Matrices
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. SOME OPERATIONS OF GIVIFMS
    5. DIFFERENT TYPES OF GIVIFMS
    6. POSET OF FUZZY SETS AND GIVIFMS
    7. SOME ALGEBRIC OPERATIONS ON GIVIFMS
    8. SOME PROPERTIES OF GIVIFMS
    9. CONCLUSION
    10. REFERENCES
  13. Chapter 7: Classification Techniques in Data Mining
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. MAIN FOCUS OF THE CHAPTER
    5. MATHEMATICAL PROGRAMMING METHODS
    6. CONCLUSION
    7. REFERENCES
  14. Chapter 8: Multiobjective Optimization of Solar-Powered Irrigation System with Fuzzy Type-2 Noise Modelling
    1. ABSTRACT
    2. INTRODUCTION
    3. OVERVIEW OF TYPE-2 FUZZY LOGIC
    4. TYPE-2 FUZZY LOGIC FOR NOISE MODELLING
    5. SOLAR-POWERED IRRIGATION SYSTEM
    6. BACTERIA FORAGING ALGORITHM
    7. SIGMA DIVERSITY METRIC
    8. COMPUTATIONAL OUTCOME AND ANALYSIS
    9. CONCLUSION
    10. FUTURE RESEARCH DIRECTIONS
    11. ACKNOWLEDGMENT
    12. REFERENCES
    13. ADDITIONAL READING
    14. KEY TERMS AND DEFINITIONS
  15. Chapter 9: Non-Linear Intuitionistic Fuzzy Number and Its Application in Partial Differential Equation
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. NON LINEAR INTUITIONISTIC FUZZY NUMBER
    5. INTUITIONISTIC DIFFERENCE AND INTUITIONISTIC PARTIAL DERIVATIVE
    6. PARTIAL DIFFERENTIAL EQUATION IN INTUITIONISTIC FUZZY ENVIRONMENT
    7. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  16. Chapter 10: Use of Fuzzy Set Theory in DNA Sequence Comparison and Amino Acid Classification
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. MAIN FOCUS OF THE CHAPTER
    5. SOLUTIONS AND RECOMMENDATIONS
    6. FUTURE RESEARCH DIRECTIONS
    7. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  17. Chapter 11: On Bipolar Fuzzy B-Subalgebras of B-Algebras
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. MAIN RESULTS
    5. CONCLUSION
    6. REFERENCES
  18. Chapter 12: Decision Making by Using Intuitionistic Fuzzy Rough Set
    1. ABSTRACT
    2. INTRODUCTION
    3. FOUNDATIONS OF ROUGH COMPUTING
    4. ROUGH SET BASED ON TWO UNIVERSAL SETS
    5. APPLICATIONS TO MULTI CRITERION DECISION MAKING
    6. CONCLUSION
    7. REFERENCES
  19. Chapter 13: An Efficient Method for Forecasting Using Fuzzy Time Series
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. RESEARCH OBJECTIVE
    4. 3 . FUZZY SETS AND FUZZY TIME SERIES
    5. 4. FREQUENCY BASED RE-PARTITIONING CLUSTERING TECHNIQUE
    6. 5. PROPOSED FUZZY TIME SERIES MODEL
    7. 6. EMPIRICAL ANALYSIS: THE UNIVERSITY ENROLLMENTS FORECASTING
    8. 7. DAILY TEMPERATURE FORECASTING: A CASE STUDY
    9. 8. CONCLUSION AND THE WAY AHEAD
    10. REFERENCES
  20. Chapter 14: A Three-Level Supply Chain Model with Necessity Measure
    1. ABSTRACT
    2. INTRODUCTION
    3. PREREQUISITE MATHEMATICS
    4. ASSUMPTIONS AND NOTATIONS
    5. MATHEMATICAL FORMULATION OF THE SUPPLY CHAIN
    6. INVENTORY MODEL OF RAW MATERIAL IN PRODUCER’S WAREHOUSE
    7. INVENTORY MODEL OF PRODUCER’S FINISHED GOODS
    8. INVENTORY MODEL FOR THE RETAILERS FOR FINISHED GOODS
    9. INTEGRATED MODEL
    10. NUMERICAL EXAMPLE
    11. DISCUSSION
    12. CONCLUSION
    13. REFERENCES
  21. Chapter 15: Modified Iterative Methods for Solving Fully Fuzzy Linear Systems
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. NUMERICAL EXPERIMENTS
    5. CONCLUSION
    6. REFERENCES
  22. Compilation of References
  23. About the Contributors