Fuzzy Domination and its Applications: New Concepts and Results

Abstract

Fuzzy domination is a generalization of domination in graphs, where the degree to which a vertex dominates another vertex is not binary, but rather can be any value in the interval [0, 1]. This allows for a more nuanced representation of domination, as the degree of domination can be used to represent the strength or confidence of the domination relationship. This paper presents new concepts and results in fuzzy domination, including fuzzy domination with multiple objectives, fuzzy domination with uncertain weights, and a new approximation algorithm for fuzzy domination problems. The findings of this research indicate that fuzzy dominance may be an effective strategy for addressing a wide range of challenges that are encountered in the actual world.