Affiliations: School of Mathematics, Beijing Institute of Technology, Beijing, P.R. China | Department of Mathematics, Mudanjiang Teachers College, Mudanjiang, Heilongjiang, P.R. China
Note: [] Corresponding author. Fu-Gui Shi, School of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mail: fuguishi@bit.edu.cn
Abstract: In this paper, our aim is to present properties and characterizations of M-fuzzifying matroids. Firstly, we study some properties of M-fuzzifying rank functions. Then we introduce the concepts of M-fuzzy families of dependent sets and M-fuzzifying closure operators by which we can characterize M-fuzzifying matroids. Finally we give applications of fuzzifying matroids in combinatorial optimization.
Keywords: Fuzzy graph, M-fuzzifying matroid, M-fuzzifying rank function, M-fuzzy family of dependent sets, M-fuzzifying closure operator, non-negative gradual number, gradual weight function
