A Study On Family Of Fuzzy Preference Structures

Currently, Fodor's aximatic definition of fuzzy preference structure is the most general among the existing literature. This definition includes three particular cases among which Case II and III have been investigated in detail by some researchers while there is little discussion around Case I. In view of this, we carry out an overall research on some fundamental properties for Case I. Meanwhile, under a general t-norm, we do a comparative study of transitivity-related properties of the three basic relations (large preference, strict preference and indiffierence) in the three families of fuzzy preference structures. The concrete content and main results are summarized as follows:In the framework of Case I, we investigate various properties of fuzzy preference structures. Firstly, we represent strict preference, indifference and incomparability relation by means of large preference relation and discuss some general properties of the family of preference structures. Next,based on two types of t-norms, we estabish links between transitivity of large preference relation and that of strict preference and indifference relation. Then, under the assumption that the involved incomparability is empty, similar property is considered based on general t-norm and an necessary and sufficient condition is presented. Finally, the relationships between negative transitivity, semitransitiv-ity, Ferrers properties of large preference, strict preference and indifference relation are established without incomparability.From the results on fuzzy preference structures presented in this paper and other literature, we know that there are some difference and common points. To obtain a clear picture of the same and different points in the three preference structures, we carry out a complementary research on properties of the remaining two preference structures. Based on all these research, a detailed comparative study is performed from which we know that Lukasiewicz-like transitivity is a common property of the three types of preference structures without incomparability.In a summary, the research in this thesis is indispensable for the investigation of fuzzy preference structure under Fodor's axiomatic definition. Together with the research on Case II and III, it forms an integrable system which lays a theoretic foundation for the practical mod-elling of decision-makers.