Abstract
Introducing directional monotonicity into aggregation functions is an important research content in the research of aggregation functions. This paper aims to study the properties, constructions and applications of pre-(quasi-)grouping functions. Firstly, the concept of pre-(quasi-)grouping functions is proposed by relaxing the monotonicity of (quasi-)grouping functions to directional monotonicity, and some basic properties are discussed. Subsequently, the relationships between pre-(quasi-)grouping functions and some other pre-aggregation functions are exhibited. Moreover, several construction methods of pre-(quasi-)grouping functions are presented. Finally, based on pre-(quasi-)grouping functions G, fuzzy negations N and overlap functions O, the constructions of (G,N)-directional monotonic fuzzy implications and QL-directional monotonic operations are given, and some important properties and characterizations are investigated.
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