Fuzzy Set Theory and Its Applications. Second, Revised Edition. H.-J. Zimmermann. Kluwer Academic Publishers Boston / Dordrecht/ London
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1 Fuzzy Set Theory and Its Applications Second, Revised Edition H.-J. Zimmermann KM ff Kluwer Academic Publishers Boston / Dordrecht/ London
2 Contents List of Figures List of Tables Foreword Preface Preface for the Revised Edition ix xiii xv xvii xix 1 Introduction to Fuzzy Sets Crispness, Vagueness, Fuzziness, Uncertainty Fuzzy Set Theory 5 Part One: Fuzzy Mathematics 9 2 Fuzzy Sets Basic Definitions Basic Definitions Basic Set-Theoretic Operations for Fuzzy Sets 16 3 Extensions Types of Fuzzy Sets Further Operations on Fuzzy Sets Algebraic Operations Set-Theoretic Operations Criteria for Selecting Appropriate Aggregation Operators 39 4 Fuzzy Measures and Measures of Fuzziness Fuzzy Measures Measures of Fuzziness 47 5 The Extension Principle and Applications The Extension Principle Operations for Type 2 Fuzzy Sets Algebraic Operations with Fuzzy Numbers 57 v
3 VI CONTENTS Part Two: Special Extended Operations Extended Operations for LR-Representation of Fuzzy Sets Fuzzy Relations and Fuzzy Graphs Fuzzy Relations on Sets and Fuzzy Sets Compositions of Fuzzy Relations Properties of the Min-Max Composition Fuzzy Graphs Special Fuzzy Relations Fuzzy Analysis Fuzzy Functions on Fuzzy Sets Extrema of Fuzzy Functions Integration of Fuzzy Functions Integration of a Fuzzy Function over a Crisp Interval Integration of a (Crisp) Real-Valued Function over a Fuzzy Interval Fuzzy Differentiation Possibility Theory, Probability Theory, and Fuzzy Set Theory Possibility Theory Fuzzy Sets and Possibility Distributions Possibility and Necessity Measures Probability of Fuzzy Events Probability of a Fuzzy Event as a Scalar Probability of a Fuzzy Event as a Fuzzy Set Possibility vs. Probability Applications of Fuzzy Set Theory Fuzzy Logic and Approximate Reasoning Linguistic Variables Fuzzy Logic Classical Logics Revisited Truth Tables and Linguistic Approximation Approximate Reasoning Fuzzy Languages Support Logic Programming Support Hörn Clause Logic Representation Approximate Reasoning in SLOP Expert Systems and Fuzzy Control Fuzzy Sets and Expert Systems Introduction to Expert Systems Uncertainty Modeling in Expert Systems Applications Fuzzy Control
4 CONTENTS Introduction to Fuzzy Control Process of Fuzzy Control Applications of Fuzzy Control Pattern Recognition Models for Pattern Recognition The Data Structure or Pattern Space Feature Space and Feature Selection Classification and Classification Space Fuzzy Clustering Clustering Methods Cluster Validity Decision Making in Fuzzy Environments Fuzzy Decisions Fuzzy Linear Programming Symmetrie Fuzzy LP Fuzzy LP with Crisp Objective Function Fuzzy Dynamic Programming Fuzzy Multi Criteria Analysis Multi Objective Decision Making Multi Attributive Decision Making Fuzzy Set Models in Operations Research Introduction Fuzzy Set Models in Logistics Fuzzy Approach to the Transportation Problem Fuzzy Linear Programming in Logistics Fuzzy Set Models in Production Control and Scheduling A Fuzzy Set Decision Model as Optimization Criterion Job-Shop Scheduling with Expert Systems A Method to Control Flexible Manufacturing Systems Aggregate Production and Inventory Planning Fuzzy Mathematical Programming for Maintenance Scheduling Scheduling Courses, Instructors, and Ciassrooms Fuzzy Set Models in Inventory Control A Discrete Location Model Empirical Research in Fuzzy Set Theory Formal Theories vs. Factual Theories vs. Decision Technologies Models in Operations Research and Management Science Testing Factual Models Empirical Research on Membership Functions Type A-Membership Model Type B-Membership Model Vll
5 Vlll CONTENTS 14.3 Empirical Research on Aggregators Conclusions Future Perspectives 369 Bibliography 373 Index 393
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