| The structures and properties of rank functions, close sets and hyperplanes in fuzzy matroids are investigated based on the existed theory. Specifically, the main contributions of this thesis are as follows:1) The sub-modularity of fuzzy rank function is studied. Moreover, a necessary and sufficient condition between fuzzy matroid and rank function is also exploited.2) Several important properties of fuzzy close sets and fuzzy closure operator are derived by analyzing and investigating relativity, closure operators and fuzzy close sets in the fuzzy matroids.3) In close regular fuzzy matroids, a necessary and sufficient condition that a fuzzy set is the fuzzy hyperplane of a fuzzy matroid is exploited with the help of hyperplane axiom in crisp matroid. Finally, an axiom of the fuzzy hyperplanes in close fuzzy matroids is derived.The contents in this thesis are all the important topics in the research fields of fuzzy matroids, and therefore enrich the theory of fuzzy matroids. On the same time, the proposed results and adopted approaches provide a series of valuable sources for the further research. |
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