The Research Of Fuzzy Submatroids On Closed Fuzzy Motriods

The study of fuzzy matroids is based on the theory of crisp matroids. At present,the basic frame of Fuzzy matroids has been set up. It’s possible to discuss some deeperconcepts of fuzzy matroids. The paper studies mainly the fuzzy submatroids of closedfuzzy matroids, quasi-fuzzy graph matroid and closed regular fuzzy matroids.(1) We had studied the T-vertical truncatures, the k-vertical truncatures,the horizontal truncatures and the k-horizontal truncatures of fuzzy matroids. Wehave gotten the important result which the T-vertical truncatures, the k-verticaltruncatures, the horizontal truncatures and the k-horizontal truncatures of closedfuzzy matroids are also closed fuzzy matroids;(2) According to quasi-fuzzy graph matroids, the paper had investigated theT-vertical truncatures, the fuzzy contraction matroids on basis set, the k-verticaltruncatures, and the k-horizontal truncatures of quasi-fuzzy graph matroids. We haveobtained the result what the T-vertical truncatures, the fuzzy contraction matroids onbasis set, the k-vertical truncatures and the k-horizontal truncatures of quasi-fuzzygraph matroids are quasi-fuzzy graph matroids;(3) With help of the examples, we have found that the T-vertical truncatures of closedregular fuzzy matroids is possible to be not closed regular fuzzy matroids, thek-vertical truncatures of closed regular fuzzy matroids is possible to be not closedregular fuzzy matroids and the horizontal truncatures of closed regular fuzzymatroids is possible to be not closed regular fuzzy matroids;(4) We had studied the k-horizontal truncatures of closed regular fuzzy matroids,and found out what the k-horizontal truncatures of closed regular fuzzy matroids areclosed regular fuzzy matroids;(5) As the opposite of matroids, we had studied the sum of quasi-fuzzy graphmatroids and closed regular fuzzy matroids, and have got results which the sum ofquasi-fuzzy graph matroids is quasi-fuzzy graph matroids and the sum of closed regularfuzzy matroids is closed regular fuzzy matroids.