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Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing

Book Description

Successful development of effective computational systems is a challenge for IT developers across sectors due to uncertainty issues that are inherently present within computational problems. Soft computing proposes one such solution to the problem of uncertainty through the application of generalized set structures including fuzzy sets, rough sets, and multisets. The Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing presents double blind peer-reviewed and original research on soft computing applications for solving problems of uncertainty within the computing environment. Emphasizing essential concepts on generalized and hybrid set structures that can be applied across industries for complex problem solving, this timely resource is essential to engineers across disciplines, researchers, computer scientists, and graduate-level students.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Book Series
    1. Mission
    2. Coverage
  5. Editorial Advisory Board
  6. List of Reviewers
  7. Preface
  8. Acknowledgment
  9. Chapter 1: On Theory of Multisets and Applications
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. DEFINITIONS AND NOTATIONS
    4. 3. UNCERTAINTY BASED MULTISETS
    5. 4. APPLICATIONS OF MULTISETS
    6. 5. SOME PROBLEMS FOR FURTHER STUDY
    7. 6. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  10. Chapter 2: Fuzzy Multisets and Fuzzy Computing
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. MULTI-FUZZY SETS AND THEIR PROPERTIES
    5. FUZZY P SYSTEMS
    6. THE FUZZY CHEMICAL ABSTRACT MACHINE
    7. FUZZY PETRI NETS
    8. FUTURE RESEARCH DIRECTIONS
    9. CONCLUSION
    10. ACKNOWLEDGMENT
    11. REFERENCES
  11. Chapter 3: Introduction to Intuitionistic Fuzzy Multisets and Its Applications
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. BACKGROUND
    4. 3. MEDICAL DIAGNOSIS PROBLEM (Shinoj & John, 2012)
    5. 4. ACCURACY IN COLLABORATIVE ROBOTICS (Shinoj & John, 2013)
    6. 5. FUTURE RESEARCH DIRECTIONS
    7. 6. CONCLUSION
    8. REFERENCES
  12. Chapter 4: Intuitionistic Fuzzy Filters for Noise Removal in Images
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. INTUITIONISTIC FUZZY OPERATORS
    4. 3. IF FILTERS IN IMAGE PROCESSING
    5. 4. PROPOSED ALGORITHM
    6. 5. RESULTS AND DISCUSSION
    7. 6. CONCLUSION
    8. REFERENCES
  13. Chapter 5: Soft Sets and Its Applications
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. LITERATURE SURVEY
    4. 3. DEFINITIONS AND CONCEPTS
    5. 4. APPLICATIONS
    6. 5. CONCLUSION AND RECENT TRENDS
    7. REFERENCES
    8. KEY TERMS AND DEFINITIONS
  14. Chapter 6: Some Hybrid Soft Sets and Their Application in Decision Making
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. CONCLUSION
    5. ACKNOWLEDGMENT
    6. REFERENCES
    7. KEY TERMS AND DEFINITIONS
  15. Chapter 7: Soft Topologies Generated by Soft Set Relations
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. SOFT SET TOPOLOGIES GENERATED USING SOFT SET RELATIONS
    5. 4. CONCLUSION
    6. REFERENCES
    7. KEY TERMS AND DEFINITIONS
  16. Chapter 8: γ-Operation and Some Types of Soft Sets and Soft Continuity of (Supra) Soft Topological Spaces
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. GENERALIZATIONS OF OPEN SOFT SETS OF SOFT TOPOLOGICAL SPACES
    5. 4. SOFT SEMI SEPARATION AXIOMS
    6. 5. SUPRA SOFT TOPOLOGICAL SPACES
    7. 6. SUPRA GENERALIZED CLOSED SOFT SETS
    8. 7. DECOMPOSITIONS OF SOME FORMS OF (SUPRA) SOFT CONTINUITY
    9. 8. APPLICATIONS
    10. 9. CONCLUSION
    11. REFERENCES
    12. KEY TERMS AND DEFINITIONS
  17. Chapter 9: Sequences, Nets, and Filters of Fuzzy Soft Multi Sets in Fuzzy Soft Multi Topological Spaces
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. SEQUENCES OF FUZZY SOFT MULTI SETS
    5. 4. NETS IN FUZZY SOFT MULTI TOPOLOGICAL SPACES
    6. 5. FILTERS IN FUZZY SOFT MULTI TOPOLOGICAL SPACES:
    7. 6. CONCLUSION
    8. REFERENCES
  18. Chapter 10: Fuzzy Multi-Criteria Assignment Problems Using Two-Dimensional Fuzzy Soft Set Theory
    1. ABSTRACT
    2. 1 INTRODUCTION
    3. 2 BASIC CONCEPTS AND PRELIMINARIES
    4. 3 FUZZY MULTI-CRITERIA ASSIGNMENT PROBLEMS WITH MULTIPLE DECISION MAKERS
    5. 4 THE METHODOLOGY BASED ON TWO-DIMENSIONAL FUZZY SOFT SET FOR SOLVING FUZZY MULTI-CRITERIA ASSIGNMENT PROBLEMS WITH MULTIPLE DECISION MAKERS
    6. 5 ASSIGNMENT PROBLEMS WITH MULTI-CRITERIA AND ONE DECISION MAKER
    7. 6 ASSIGNMENT PROBLEMS WITH MULTI-CRITERIA AND MULTIPLE DECISION MAKERS
    8. 7 APPLICATION OF 2-DFS ALGORITHM FOR SOLVING FUZZY MULTI-CRITERIA ASSIGNMENT PROBLEMS IN MEDICAL SCIENCE
    9. 8 CONCLUSION
    10. REFERENCES
  19. Chapter 11: Generalized Rough Sets
    1. ABSTRACT
    2. 1 INTRODUCTION
    3. 2 PRELIMINARIES
    4. 3 ROUGH SET IN IDEAL TOPOLOGICAL ORDERED SPACES
    5. 4 GENERALIZED ROUGH SETS VIA FILTERS BY USING INCREASING AND DECREASING SETS
    6. 5 GENERALIZED ROUGH SETS VIA FILTER BY USING
    7. CONCLUSION
    8. REFERENCES
  20. Chapter 12: New Approaches of Rough Sets via Ideals
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. ROUGH SETS VIA IDEAL
    5. 4. NEW APPROACHES OF ROUGH APPROXIMATIONS VIA IDEAL
    6. 5. SOME IMPORTANT EXAMPLES
    7. 6. ROUGH MEMBERSHIP FUNCTIONS VIA IDEALS
    8. 7. NEW APPROACH OF ROUGH SET
    9. 8. CONCLUSION
    10. REFERENCES
  21. Chapter 13: Rough Approximations on Hesitant Fuzzy Sets
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. RELATIONS
    5. 4. HESITANT FUZZY ROUGH SETS
    6. 5. CONCLUSION
    7. REFERENCES
    8. KEY TERMS AND DEFINITIONS
  22. Chapter 14: Neutrosophic Soft Sets and Their Properties
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. NEUTROSOPHIC SOFT SETS
    4. 3. DISTRIBUTIVE LAWS FOR NEUTROSOPHIC SOFT SETS
    5. 4. MAPPINGS ON NEUTROSOPHIC SOFT CLASSES
    6. 5. INTUITIONISTIC NEUTROSOPHIC SOFT SET
    7. 6. AN APPLICATION OF INTUITIONISTIC NEUTROSOPHIC SOFT SET IN A DECISION MAKING PROBLEM
    8. 7. CONCLUSION
    9. REFERENCES
    10. KEY TERMS AND DEFINITIONS
  23. Chapter 15: Creating Generalized and Hybrid Set and Library with Neutrosophy and Quad-Stage Method
    1. ABSTRACT
    2. INTRODUCTION
    3. CONCLUSION
    4. REFERENCES
  24. Chapter 16: Refined Neutrosophic Sets and Refined Neutrosophic Soft Sets
    1. ABSTRACT
    2. 1. BACKGROUND
    3. 2. PRELIMINARIES
    4. 3. REFINED THEORY WITH NEUTROSOPHIC AND SOFT SETS
    5. 4. APPLICATIONS
    6. 5. FUTURE RESEARCH DIRECTIONS
    7. 6. CONCLUSION
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  25. Chapter 17: Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3 INTERVAL NEUTROSOPHIC TRAPEZOID LINGUISTIC SETS
    5. 4. INTERVAL NEUTROSOPHIC TRAPEZOID LINGUISTIC AGGREGATION OPERATORS
    6. 5. DECISION MAKING METHOD BY INTRLWAA AND INTRLWGA OPERATORS.
    7. 6. ILLUSTRATIVE EXAMPLE
    8. 7. CONCLUSION
    9. REFERENCES
  26. Chapter 18: Triangular and Trapezoidal Fuzzy Assessment Models
    1. ABSTRACT
    2. INTRODUCTION
    3. MAIN FOCUS OF THE CHAPTER
    4. APPLICATIONS
    5. FUTURE RESEARCH DIRECTIONS
    6. CONCLUSION
    7. REFERENCES
    8. KEY TERMS AND DEFINITIONS
  27. Chapter 19: Uncertainty Analysis Using Fuzzy Random Set Theory
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. UNCERTAINTY ANALYSIS
    4. 3. MATHEMATICAL BACKGROUND OF FUZZY RANDOM SET
    5. 4. FUZZY RANDOM VARIABLE MODEL
    6. 5. PROBLEM STATEMENT
    7. 6. FUZZY RANDOM CONTAMINANT MIGRATION MODEL
    8. 7. CONCLUSION
    9. REFERENCES
  28. Chapter 20: Generalized Fuzzy Closed Sets in Smooth Bitopological Spaces
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. PRELIMINARIES
    4. 3. -(𝛕, 𝛕) -GENERALIZED FUZZY CLOSED SETS
    5. 4. () --CONTINUOUS AND () --IRRESOLUTE MAPPINGS
    6. 5. -𝛕-GENERALIZED FUZZY CLOSED SETS
    7. 6. A NEW APPROACH OF GENERALIZED SUPRA FUZZY CLOSURE OPERATOR
    8. 7. SOME TYPES OF GENERALIZED FP*-MAPPINGS
    9. REFERENCES
  29. Chapter 21: Interval Wavelet Method for Solving Imprecisely Defined Diffusion Equations
    1. ABSTRACT
    2. 1. INTRODUCTION
    3. 2. THEORY OF WAVELET
    4. 3. INTERVAL WAVELET METHOD (IWM)
    5. 4. CASE STUDY
    6. 5. CONCLUSION
    7. REFERENCES
    8. KEY TERMS AND DEFINITIONS
  30. Chapter 22: Wavelet-Based Recognition of Handwritten Characters Using Artificial Neural Network
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. METHODOLOGY OF THE PROPOSED HCR SYSTEM
    5. PREPROCESSING AND FEATURE EXTRACTION
    6. CLASSIFICATION AND RECOGNITION
    7. EXPERIMENTAL RESULTS
    8. CONCLUSION
    9. REFERENCES
  31. Chapter 23: Introducing “NR-Statistics”
    1. ABSTRACT
    2. INTRODUCTION
    3. PRELIMINARIES
    4. MULTISET METRIC SPACE AND POPULATION SPACE IN NR-STATISTICS
    5. FURTHER CHARACTERIZATIONS OF ‘POPULATION’ IN NR-STATISTICS
    6. METRIC MEAN (MM) AND FEW OTHER NEW KIND OF MEASURES FOR MEAN IN NR-STATISTICS
    7. NUCLEUS OF A POPULATION (R or NR)
    8. SCATTER OF A POPULATION (R OR NR)
    9. PLOT FUNCTION, m-MAPPING AND m-MAPPING
    10. LM, LV, LSD, AND RM, RV, RSD IN ALGEBRAIC STATISTICS
    11. INTRODUCING ‘BIG DATA STATISTICS’
    12. CONCLUSION
    13. FUTURE RESEARCH DIRECTIONS
    14. REFERENCES
    15. KEY TERMS AND DEFINITIONS
  32. Chapter 24: Application of Artificial Intelligence to Gearbox Fault Diagnosis
    1. ABSTRACT
    2. INTRODUCTION
    3. BACKGROUND
    4. APPLICATION OF AI TO GFD
    5. FUTURE RESEARCH DIRECTIONS
    6. CONCLUSION
    7. ACKNOWLEDGMENT
    8. REFERENCES
    9. KEY TERMS AND DEFINITIONS
  33. Compilation of References
  34. About the Contributors