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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

In this work, we introduce the concept of interval-valued R-(quasi-)overlap functions and replace increasingness with interval directional increasingness. We analyze the properties of such functions and their relationship with related r-(quasi-)overlap functions. Additionally, we present methods for constructing interval-valued pre-(quasi-)overlap functions from specific binary interval-valued functions, interval multiplicative generator pairs, and interval-valued 0;1-aggregation functions. In the second part, we argue that interval multiplicative generator pairs and additive ones can be converted to each other.