On decision evaluation functions in three-way decision spaces derived from overlap and grouping functions

Abstract

Overlap and grouping functions, as two kinds of particular binary aggregation functions, have been continuously discussed in the literature for their vast preponderance in some real applications. Meanwhile, after Hu introduced the notion of three-way decision spaces, the decision evaluation functions in three-way decision spaces constructed from the so-called semi-decision evaluation functions have been investigated consistently. This paper continues to consider this research topic and mainly focuses the decision evaluation functions in three-way decision spaces obtained from overlap and grouping functions. Firstly, based on overlap and grouping functions, we give several methods of constructing semi-decision evaluation functions in semi-three-way decision spaces. Secondly, we show some novel semi-decision evaluation functions which are related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets, respectively. Finally, using overlap and grouping functions, we get some ways to construct decision evaluation functions in three-way decision spaces from semi-decision evaluation functions in semi-three-way decision spaces.