On decision evaluation functions in generalized three-way decision spaces

Abstract

Recently, Hu proposed the notion of three-way decision spaces based on partially ordered sets with involutive negations by the axiomatic definition. However, involutive negation is so strong that imposes restrictions on the use of the theory of three-way decision spaces from theoretical point of view. Therefore, this paper attempts to extend the concept of three-way decision spaces from partially ordered sets with involutive negations to partially ordered sets with negations. At first, we generalize three-way decision spaces and three-way decisions based on general partially ordered sets with negations such that the existing three-way decisions are the specific cases of generalized three-way decision spaces discussed in this paper. And then, we give some new decision evaluation functions in generalized three-way decision spaces (e.g., decision evaluation functions based on fuzzy sets, interval-valued fuzzy sets, fuzzy relations, shadowed sets and hesitant fuzzy sets), which enriched the class of decision evaluation functions. In particular, they provide more choices for decision-makers in realistic decision-making problems. Finally, in order to illustrate the practical applications of the results presented in this paper, we analyse a practical example of an evaluation problem of credit card applicants.