Ebook: Fuzzy Decision Procedures with Binary Relations: Towards A Unified Theory

In decision theory there are basically two appr~hes to the modeling of individual choice: one is based on an absolute representation of preferences leading to a ntDnerical expression of preference intensity. This is utility theory. Another approach is based on binary relations that encode pairwise preference. While the former has mainly blossomed in the Anglo-Saxon academic world, the latter is mostly advocated in continental Europe, including Russia. The advantage of the utility theory approach is that it integrates uncertainty about the state of nature, that may affect the consequences of decision. Then, the problems of choice and ranking from the knowledge of preferences become trivial once the utility function is known. In the case of the relational approach, the model does not explicitly accounts for uncertainty, hence it looks less sophisticated. On the other hand it is more descriptive than normative in the first stand because it takes the pairwise preference pattern expressed by the decision-maker as it is and tries to make the best out of it. Especially the preference relation is not supposed to have any property. The main problem with the utility theory approach is the gap between what decision-makers are and can express, and what the theory would like them to be and to be capable of expressing. With the relational approach this gap does not exist, but the main difficulty is now to build up convincing choice rules and ranking rules that may help the decision process.

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Content:
Front Matter....Pages i-xxiii
Introduction....Pages 1-6
Common Notations....Pages 7-10
Systematization of Choice Rules with Binary Relations....Pages 11-30
Fuzzy Decision Procedures....Pages 31-36
Contensiveness Criteria....Pages 37-45
Fuzzy Inclusions....Pages 47-102
Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environment....Pages 103-107
Choice with Fuzzy Relations....Pages 109-136
Ranking and C-Spectral Properties of Fuzzy Relations....Pages 137-164
Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systems....Pages 165-181
Contensiveness of Fuzzy Decision Procedures in Restricted Environment....Pages 183-197
Efficiency of Fuzzy Decision Procedures....Pages 199-206
Decision-Making with Special Classes of Fuzzy Binary Relations....Pages 207-215
Applications to Crisp Choice Rules....Pages 217-223
Applications to Decision Support Systems and to Multipurpose Decision-Making....Pages 225-239
Back Matter....Pages 240-255

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Content:
Front Matter....Pages i-xxiii
Introduction....Pages 1-6
Common Notations....Pages 7-10
Systematization of Choice Rules with Binary Relations....Pages 11-30
Fuzzy Decision Procedures....Pages 31-36
Contensiveness Criteria....Pages 37-45
Fuzzy Inclusions....Pages 47-102
Contensiveness of Fuzzy Dichotomous Decision Procedures in Universal Environment....Pages 103-107
Choice with Fuzzy Relations....Pages 109-136
Ranking and C-Spectral Properties of Fuzzy Relations....Pages 137-164
Invariant, Antiinvariant and Eigen Fuzzy Subsets. Mainsprings of Cut Technique in Fuzzy Relational Systems....Pages 165-181
Contensiveness of Fuzzy Decision Procedures in Restricted Environment....Pages 183-197
Efficiency of Fuzzy Decision Procedures....Pages 199-206
Decision-Making with Special Classes of Fuzzy Binary Relations....Pages 207-215
Applications to Crisp Choice Rules....Pages 217-223
Applications to Decision Support Systems and to Multipurpose Decision-Making....Pages 225-239
Back Matter....Pages 240-255
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