The Base-graph Of Closed Regular Fuzzy Matroids

Basing on the existing theory of crisp matroids and fuzzy matroids, the paper studies mainly closed regular fuzzy matroids including its sub-matroid when it's good-base; the exchange of fuzzy bases; the relations between the fuzzy bases and the fuzzy circuits; defining the base-graph and studying its properties.(1) Whether the sub-matroid of closed regular and good-base fuzzy matroids is closed regular or not is studied basing on the sub-matroid of fuzzy matroids.(2) Getting"the exchange theorem of bases"and many results of closed regular fuzzy matroids with the help of"the exchange theorem of bases"of crisp matroids.(3) The relations between the fuzzy bases and the fuzzy circuits in closed regular fuzzy matroids are investigated. Moreover, necessary and sufficient conditions for some fuzzy independent set to be a fuzzy base, getting some fuzzy circuits from a fuzzy base and getting some fuzzy bases from a fuzzy circuit are find out.(4) The base-graph of closed regular fuzzy matroids is defined, then in base-graph the connectivity, the distance of two random vectors, the properties of paths and circuits together with the relations between the degree of connectivity and the rest rank of the brought matroid are investigated.These aspects include nearly all properties of closed regular fuzzy matroids. Especially, by constructing the base-graph the relations between the fuzzy bases in closed regular fuzzy matroids are discovered more easily. Because these are all important subjects in the research fields of fuzzy matroids, they will enrich the theory of fuzzy matroids greatly and become significant foundations for the further researches.