Affiliation:
1. College of Mathematics and Statistics, Chongqing University, Chongqing, China
2. School of Science, Chongqing University of Posts and Telecommunications, Chongqing, China
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.
Subject
Artificial Intelligence,General Engineering,Statistics and Probability
Reference12 articles.
1. On the abstract properties of linear dependence;Whitney;Amer J Math,1935
2. Fuzzy matroids;Goetschel;Fuzzy Sets And Systems,1988
3. Welsh D.J. , Matroid theory. London: Academic Press Inc. (London) Ltd. 1976.
4. Connectedness of refined Goetschel–Voxman fuzzy matroids;Li;Fuzzy Sets and Systems,2010
5. A new approach to the fuzzification of matroids;Shi;Fuzzy Sets and Systems,2008