Rough Evaluation Structure: Application of Rough Set Theory to Generate Simple Rules for Inconsistent Preference Relation

概要

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Since management decision-making becomes complex and preferences of the decision-maker frequently becomes inconsistent, multi-attribute decision-making problems were studied. To represent inconsistent preference relation, the concept of evaluation structure was introduced. We can generate simple rules to represent inconsistent preference relation by the evaluation structures. Further rough set theory for the preference relation was studied and the concept of approximation was introduced. One of our main aims of this paper is to introduce a concept of rough evaluation structure for representing inconsistent preference relation. We apply rough set theory to the evaluation structure, and develop a method for generating simple rules for inconsistent preference relations. In this paper, we introduce concepts of totally ordered information system, similarity class of preference relation, upper and lower approximation of preference relations. We also show the properties of rough evaluation structure and provide a simple example. As an application of rough evaluation structure, we analyze questionnaire survey of customer preferences about audio players.