Abstract
Fuzzy decision method deals with the ambiguous decision problems applying fuzzy sets theory. It is an important issue for fuzzy decision making to define the preference relation between outcomes represented by fuzzy sets.
In this paper, based on the model concept such as possibility and necessity, fuzzy preference relation between elements is extended to six relations between fuzzy sets. The preference relation extended by Orlovsky and Baldwin and Guild is a special case of these relations. The proposed relations are corresponding to the rankings of fuzzy numbers proposed by Dubois and Prade when the fuzzy preference relation is the large and small relation. The properties of these six preference relations are investigated. These relations preserve the properties between possibility and necessity, which is satisfied in modal logic, for the fuzzy sets whose membership functions attain 1. Since the preference relations extended in this paper are all based on the modal concept, it is possible to obtain the decision procedures reflecting the various modalities of decision maker.
