Ebook: Advances in Fuzzy Sets, Possibility Theory, and Applications

Since its inception by Professor Lotfi Zadeh about 18 years ago, the theory of fuzzy sets has evolved in many directions, and is finding applications in a wide variety of fields in which the phenomena under study are too complex or too ill-defined to be analyzed by conventional techniques. Thus, by providing a basis for a systematic approach to approximate reasoning and inexact inference, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, engineering, law, medicine, decision-analysis, information retrieval, and artificial intelli­ gence. This volume consists of 24 selected papers invited by the editor, Professor Paul P. Wang. These papers cover the theory and applications of fuzzy sets, almost equal in number. We are very fortunate to have Professor A. Kaufmann to contribute an overview paper of the advances in fuzzy sets. One special feature of this volume is the strong participation of Chinese researchers in this area. The fact is that Chinese mathematicians, scientists and engineers have made important contributions to the theory and applications of fuzzy sets through the past decade. However, not until the visit of Professor A. Kaufmann to China in 1974 and again in 1980, did the Western World become fully aware of the important work of Chinese researchers. Now, Professor Paul Wang has initiated the effort to document these important contributions in this volume to expose them to the western researchers.

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Content:
Front Matter....Pages i-xii
Fuzzy Set Theory: Past Present Future....Pages 1-11
Advances in Fuzzy Sets — An Overview....Pages 13-30
A Survey of Some Aspects on the Research Work of Fuzzy Topology in China....Pages 31-36
Some Properties in Fuzzy Convex Sets....Pages 37-47
“Non-Standard” Concepts in Fuzzy Topology....Pages 49-57
The Spaces of Fuzzy Probability and Possibility (I)....Pages 59-70
An Algebraic System Generalizing the Fuzzy Subsets of a Set....Pages 71-80
From the Fuzzy Statistics to the Falling Random Subsets....Pages 81-96
On Fuzzy Relations and Partitions....Pages 97-105
Fuzzy Set Structure with Strong Implication....Pages 107-136
Inference Regions for Fuzzy Propositions....Pages 137-148
Fuzzy Tree Grammar and Fuzzy Forest Grammar....Pages 149-179
Fuzzy Production Rules: A Learning Methodology....Pages 181-198
Decision Support with Fuzzy Production Systems....Pages 199-216
Imprecision in Computer Vision....Pages 217-236
Fuzzy Programming: Why and How? — Some Hints and Examples....Pages 237-251
A Fuzzy, Heuristic, Interactive Approach to the Optimal Network Problem....Pages 253-276
Application of Fuzzy Set Theory to Economics....Pages 277-305
Use of Fuzzy Logic for Implementing Rule-Based Control of Industrial Processes....Pages 307-323
A New Approach to Design of Fuzzy Controller....Pages 325-334
Advanced Results on Applications of Fuzzy Switching Functions to Hazard Detection....Pages 335-349
The Application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security....Pages 351-376
Fuzzy Models of Human Problem Solving....Pages 377-386
A Concept of a Fuzzy Ideal for Multicriteria Conflict Resolution....Pages 387-403
Back Matter....Pages 405-421

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Content:
Front Matter....Pages i-xii
Fuzzy Set Theory: Past Present Future....Pages 1-11
Advances in Fuzzy Sets — An Overview....Pages 13-30
A Survey of Some Aspects on the Research Work of Fuzzy Topology in China....Pages 31-36
Some Properties in Fuzzy Convex Sets....Pages 37-47
“Non-Standard” Concepts in Fuzzy Topology....Pages 49-57
The Spaces of Fuzzy Probability and Possibility (I)....Pages 59-70
An Algebraic System Generalizing the Fuzzy Subsets of a Set....Pages 71-80
From the Fuzzy Statistics to the Falling Random Subsets....Pages 81-96
On Fuzzy Relations and Partitions....Pages 97-105
Fuzzy Set Structure with Strong Implication....Pages 107-136
Inference Regions for Fuzzy Propositions....Pages 137-148
Fuzzy Tree Grammar and Fuzzy Forest Grammar....Pages 149-179
Fuzzy Production Rules: A Learning Methodology....Pages 181-198
Decision Support with Fuzzy Production Systems....Pages 199-216
Imprecision in Computer Vision....Pages 217-236
Fuzzy Programming: Why and How? — Some Hints and Examples....Pages 237-251
A Fuzzy, Heuristic, Interactive Approach to the Optimal Network Problem....Pages 253-276
Application of Fuzzy Set Theory to Economics....Pages 277-305
Use of Fuzzy Logic for Implementing Rule-Based Control of Industrial Processes....Pages 307-323
A New Approach to Design of Fuzzy Controller....Pages 325-334
Advanced Results on Applications of Fuzzy Switching Functions to Hazard Detection....Pages 335-349
The Application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security....Pages 351-376
Fuzzy Models of Human Problem Solving....Pages 377-386
A Concept of a Fuzzy Ideal for Multicriteria Conflict Resolution....Pages 387-403
Back Matter....Pages 405-421
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