A Goal Programming Method for Ranking Alternatives Based on Fuzzy Preference Relation

Fuzzy sets theory might provide the flexibility needed to represent the uncertainty resulting from the lack of knowledge [1-3]. The fuzzy preference relation is a kind of representation of the information about provided by the decision maker [4-6]. It is an important research topic how to choose an optimal alternative or rank alternatives from a finite set of alternatives according to the fuzzy preference relation. The purpose of this paper is to study a decision making problem, where the preference information about the alternatives provided by the decision makers is of a fuzzy preference relations. This paper proposes a new method for ranking alternatives. Firstly, the fuzzy preference relation and its meaning are introduced. Secondly, a linear goal programming model is constructed based on the fuzzy preference relation provided by the decision maker, and by solving the model the ranking values of the alternatives can be obtained. It may be observed that the method is clearly useful for solving problems of ranking alternatives by using the fuzzy preference relation and it is also a supplement or extension of the existing methods [7]. The proposed method requires the preference information of a single decision maker. It can also be extended to support the situation where the preference information is given by multiple decision makers. The paper is set out as follows. The fuzzy preference relation its meaning are introduced in Section 2. How to choose an optimal alternative or rank alternatives based on the fuzzy preference relation is discussed in Section 3, where we present a linear goal programming model to compute the overall values of alternatives. Then, and for the sake of illustrating the method proposed in this paper, Section 4 is devoted to develop a numerical example. In Section 5 some conclusions are pointed out.