The Research Of Algorithm Of Closed Fuzzy Matroids

Fuzzy matroids is a theory which is set up by introducing the notion"fuzzy"into theory of matroid, it has existed nearly 20 years old. At present, the basic frame of fuzzy matroids has been set up.The study includes the fuzzy independent set, fuzzy bases, fuzzy circuits, fuzzy rank, fuzzy hyperplanes, fuzzy closure operator, fuzzy submatroid, quasi-fuzzy graph matroids, fuzzy graphic matroids, fuzzy dual matroid and so on.Based on the existed theory of mareoids and fuzzy matroids, this thesis studies the closed regular fuzzy matroid and its fundamental sequence, the fuzzy base and its algorithm of closed fuzzy matroids, the fuzzy circuit and its algorithm of closed fuzzy matroids and so on. The main contributions of this thesis are as follows:1) The necessary and sufficient condition of closed regular fuzzy matroid and a property of its fuzzy dual matroid are found by studying some properties of closed regular fuzzy matroid.2) By studying some properties of fuzzt bases of closed fuzzy matroid, the necessary and sufficient condition of judging fuzzy bases of closed fuzzy matroids and some corollaries are found. In the end, an algorithm of obtaining a fuzzy base is given.3) By studying some properties of fuzzt circuits of closed fuzzy matroid, some necessary and sufficient conditions of using its fundamental sequence to express fuzzy circuits are found. An algorithm of obtaining a fuzzy circuit is given.4) By studying the fundamental sequence of closed regular fuzzy matroid, some necessary and sufficient conditions of fundamental sequence of closed regular fuzzy matroid are found.The fundamental sequence, fuzzy bases and its algorithm, fuzzy circuits and its algorithm are studied in this thesis are all important topics in the research fields of fuzzy matroids. They enrich the theory of fuzzy matroids and it is very useful for them to push the change of fuzzy matroid from basic research to application research.