The induced basis axioms for a closed G-V fuzzy matroid

Abstract

In this paper, we research a class of axioms in closed G-V fuzzy matroids. The main research method is to transform fuzzy matroids into matroids. First, we study many properties of the basis family of induced matroids, and define a new mapping which can reflect the relationship between bases of induced matroids of a G-V fuzzy matroid. Second, we discuss the new mapping, and reveal the relationship and properties among the fundamental sequence, the induced basis family and the new mapping of a G-V fuzzy matroid. From these relationships and properties, we extract four key attributes: normativity property, inclusion property, exchange property, and right surjection. Finally, we propose and prove “the induced basis axioms for a closed G-V fuzzy matroid” by these key attributes. With the help of these axioms, a closed G-V fuzzy matroid can be uniquely determined by a finite number sequence, a subset family and a mapping on this subset family when they satisfy above four attributes, and vice versa.