Fuzzifications of matroids relying on overlap functions

Abstract

Matroid theory provides a broad theoretical framework with a wide range of applications. On this basis, fuzzy matroids have also undergone significant development based on lattice theory, fuzzy topology, fuzzy convexity, etc. In this paper, we select an overlap function to model conjunction to provide two fuzzification approaches to matroids. Taking an arbitrary overlap function ⊗, we introduce ⊗-fuzzifying matroids and ⊗-fuzzy matroids and study their relations with classical matroids, respectively. Then we explore the relations between ⊗-fuzzifying matroids and (closed, perfect) ⊗-fuzzy matroids. These findings not only provide a theoretical application of overlap functions but also elucidate the connections between different fuzzifications of matroids.