Three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces

The concept of bipolar-valued fuzzy set was introduced by Zhang. Can we discuss three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces? In response to this problem, firstly, the paper discusses partially orders on truth values of bipolar-valued fuzzy sets and three-way decision spaces on this basis. Secondly, this paper presents construction method of decision evaluation functions based on bipolar-valued fuzzy sets over three-way decision spaces. Thirdly, this paper makes three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces and uses an example on an evaluation problem of credit card applicants to illustrate some notions of the (semi-, quasi-)three-way decision spaces and benefits of constructing methods from semi-(quasi-)decision evaluation functions to decision evaluation functions. Finally, the conclusions are summed up.