The Fuzzy Rough Set Model For Ordered Decision Making

Rough set theory was introduced by Pawlak in 1982. It is a new mathematical tool to deal with vagueness and uncertainty. It has been widely used in the area of machine learning, decision analysis, process control, pattern recognition, data mining, etc. Fuzzy set theory was introduced by L.A.Zadeh in 1965. Artificial Intelligence, fuzzy reasoning as its core technology, has achieved remarkale results and economic benefits in many fields.Fuzzy set theory and rough set theory are an extension of the classical set in dealing with inaccuracy. They all can be used to describe inaccuracy. Indeed, fuzzy set theory is an optimal tool in knowledge engineering to deal with the vagueness implict in human language. Rough set theory, on the other hand, is mainly concerned with the coarsenes with which a set or concept can be defined.Ordered decision making, which has ordered structure in condition attributes and decision attribute, is widespreadly in practical application. Preference analysis is a class of important tasks in multi-criteria decision making. The classical rough set theory was generalized to deal with preference analysis with dominance relation. Fuzzy preference relation can not only reflect the ordered structure, but also reflect the dominance degree between samples.In this paper, we focus on the fuzzy rough set model for ordered decision making. Crisp preference relation rough set model and fuzzy preference relation rough set model for ordered decision making were introduced to this paper .Then we integrate fuzzy preference relation with fuzzy covering rough set model and construct a fuzzy covering preference rough set model for ordered decision making. Based on a fuzzy covering of a universe of discourse, upper and lower fuzzy preference approximation operators was constructed .The relations between the proposed model and the crisp preference rough set model are discussed. Finally, the proposed model is used to analyze fuzzy preference data. It shows the effectiveness of the proposed model.