On Fuzzy Implications Derived from General Overlap Functions and Their Relation to Other Classes

There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO,N)-implication functions. We also investigate their properties, the aggregation of (GO,N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.

Automated summary

This paper discusses the techniques for generating fuzzy implication functions using general overlap/grouping functions instead of traditional associative aggregators and fuzzy negations. The use of general overlap functions allows for a more flexible and widely applicable approach to obtaining implication functions.