The Research Of Fuzzy Rank Function

Fuzzy matroids was based on the theory of crisp matroids, At present, the basic Frame of fuzzy matroids has been set up. The study includes fuzzy bases, fuzzy circuits, fuzzy rank function, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatrods, quasi-fuzzy graph matroid, fuzzy graphic matroids, fuzzy dual matroid and so on. Basing on the existing theory of crisp matroids and fuzzy matroids, the paper studies mainly fuzzy rank function and fuzzy submodularity function, The main contributions of the paper are as follows:(1) define the fuzzy submodularity function according to submodularity function, at the same time investigate many properties of the fuzzy submodularity function and relation of the fuzzy submodularity function and fuzzy rank function;(2) Deeply discussing the fuzzy rank function of strict-good-base fuzzy matroid from its definition, obtain some important properties of the fuzzy rank function;(3) Deeply study the fuzzy rank function through utilizing fuzzy submodularity function, and extend theorem 2.2 in the seventh paper of the reference to obtain a wider sufficient condition for certifying fuzzy rank function.these are all important subjects in the research fields of fuzzy matroids, they will enrich the theory of fuzzy matroids and provide supports for the further researches.