Sugeno-inspired aggregation functions

Abstract

This paper introduces a novel class of aggregation functions, called Sugeno-inspired aggregation functions, which are conceptually based on the Sugeno integral. The concept of fuzzy measure is rebuilt by incorporating a function designed to evaluate coalitions composed of all elements except one. This approach frames aggregation as a comparison between the value of a given element and the aggregation outcome of the coalition that excludes it. The fundamental properties of this new class of aggregation functions are investigated and their potential applications are explored. The theoretical analysis shows that Sugeno-inspired aggregation functions preserve key features of the original Sugeno integral while eliminating the need to precompute a fuzzy measure, thereby simplifying their use in practical settings. An illustrative example highlight the effectiveness of the proposed aggregation functions in evaluating clustering quality and suggest the potential for novel aggregation approaches to enhance cluster evaluation methodologies.