On transformations from semi-three-way decision spaces to three-way decision spaces based on triangular norms and triangular conorms

Abstract Recently, three-way decisions on three-way decision spaces based on partially ordered sets have been proposed by the axiomatic definitions. And, in the theory of three-way decision spaces, the decision evaluation function (which is defined by the so-called minimum element axiom, monotonicity axiom and complement axiom) is a vital notion and plays pretty important role in practical decision-making problems. However, there are many meaningful handy functions which can not become decision evaluation functions because they only satisfy minimum element axiom and monotonicity axiom in general. Therefore, there arises one discussion in which the author introduced the concept of semi-decision evaluation function without complement axiom lately. And three-way decisions based on semi-three-way decision spaces are proposed. This paper continues this research topic and gives several transformation methods from semi-three-way decision spaces to three-way decision spaces based on triangular norms and triangular conorms. Based on them, decision-makers can obtain more useful decision evaluation functions thereby having more choices in realistic decision-making problems. In addition, as an application, we analyse a reality example of an evaluation problem of credit card applicants by using the results obtained in this paper.