On interval-valued pre-(quasi-)overlap functions

In this work, we propose the notion of interval-valued pre-(quasi-)overlap functions, called interval-valued R-(quasi-)overlap functions. The increasingness is replaced with interval directional increasingness. Subsequently, we analyze relative properties of such functions as well as its relationship by related r-(quasi-)overlap functions. Besides, we present several methods for constructing interval-valued pre-(quasi-)overlap functions from certain binary interval-valued functions, interval multiplicative generator pairs and interval-valued 0‾,1‾-aggregation functions. In the second part of it, we argue that interval multiplicative generator pairs and additive ones can be converted to each other.