Interval-valued pre-(quasi-)grouping functions and its application in constructing interval-valued directional monotonic fuzzy implications

How to expand the variable domain and monotonicity of aggregation functions to generate new aggregation functions is an important research content in aggregation functions. In this work, the concept of interval-valued pre-(quasi-)grouping functions is given by relaxing the interval monotonicity ofinterval-valued (quasi-)grouping functions to interval directional monotonicity. Then, some basic properties of interval-valued pre-(quasi-)grouping functions and the relationship between interval-valued pre-(quasi-)grouping functions and pre-(quasi-)grouping functions are presented. Accordingly, several construction methods of interval-valued pre-(quasi-)grouping functions are proposed. Finally, the concept of (IG,IN) -interval-valued directional monotonic fuzzy implications and QL -interval-valued directional monotonic operations are introduced on the basis of interval-valued pre-(quasi-)grouping functions IG , interval-valued overlap functions IO and interval-valued fuzzy negations IN. In addition, related studies were conducted on the basic properties of (IG,IN) -interval-valued directional monotonic fuzzy implications and QL -interval-valued directional monotonic operations.