On discrete quasi-overlap functions

Abstract

In recent years, overlap functions, as a class of bivariate aggregation operators that are widely used in various application problems (see, e.g., in decision-making, image processing, classifications etc.), have been generalized to many forms. In particular, Paiva et al. (R. Paiva, E. Palmeira, R. Santiago, B. Bedregal, Lattice-valued overlap and quasi-overlap functions, Information Sciences 562 (2021) 180–199.) have generalized the overlap functions to the so-called quasi-overlap functions lately. In the meantime, considering aggregation operators on finite chains, especially the commonly bivariate aggregation operators (see, e.g., t-norms, t-conorms, uninorms, t-operators etc.) has become an important research topic in the fields of aggregation operators. In this paper, we take into account this research topic for quasi-overlap functions. First of all, we give the concept of quasi-overlap functions on a finite chain L with n+2 elements and its arbitrary subchains together with three generalized forms of quasi-overlap functions on any subchain of L. And then, we show some examples of quasi-overlap functions on L along with some of its specific subchains and study the idempotent property, Archimedean property and cancellation law of quasi-overlap functions on L. Finally, we obtain two construction methods of quasi-overlap functions on L, one of them is the ordinal sum construction.