Bijective soft set decision system based parameters reduction under fuzzy environments

Gong et al. (2010) and Xiao et al. (2010) have proposed the notion of bijective soft set and exclusive disjunctive soft set, respectively, which is a subtype of soft set. On the basis of their work, this paper extends these notions to fuzzy environments, and formulates the concept of bijective fuzzy soft set, which can deal with more uncertain problems. Moreover, this paper proposes two parameters reduction algorithms: one (Algorithm 1) is based on bijective fuzzy soft system, and the other (Algorithm 2) takes weight of an element into consideration. Since the threshold plays an important role in these algorithms, we proposed an algorithm (Algorithm 3) to decide the optimal value of threshold specially. Afterwards, an example analysis of the two parameters reduction algorithms is given and the result shows that the two algorithms lead to the same parameters reduction of a bijective fuzzy soft system. Since Algorithm 2 considers the detail weights of elements, thus it can be used in more uncertain problems, such as time series analysis problems, than Algorithm 1.