On The Cardinality Of Systems Of L-fuzzifying Matroids On A Finite Set

By listing technique (that is to list all systems of L-fuzzifying ma-troid independent sets on E and all L-cotowers consisting of systems of matroid independent sets on E, then get the cardinalities of the sets consisted of them), we study on the cardinalities of the set consisted of all systems of L-fuzzifying ma-troid independent sets on E and the set of all L-cotowers consisting of systems of matroid independent sets on E, where E is a set satisfying|E|≤3(where|E|denotes the cardinality of E), and L is a diamond lattice. Also,we prove the equal-ity|I(E,2,L)|=|Ict(E,L)|, and generalize the related conlcusion in crist matroid theorem.The key points and the main contents of this paper are as follows:Chapter one, preliminary knowledge, in which we give some concepts of the car-dinality of systems of L-fuzzifying matroids|I(E,2, L)|and all L-cotowers|Ict(E, L)|consisting of systems of matroid independent sets on a finite set.Chapter two is composed of three parts.In section2.1, by listing techniquewe, we study on all systems of L-fuzzifying matroid independent sets|I(E,2, L)|and all L-cotowers|Ict(E, L)|consisting of sys-tems of matroid independent sets on E, then to get the cardinalities of the sets consisted of them while E=(?) and E={x} by listing technique.In section2.2, by listing techniquewe,we concentrate on all systems of L-fuzzifying matroid independent sets|I(E,2,L)|and all L-cotowers|Ict(E,L)|con-sisting of systems of matroid independent sets on E, then to get the cardinalities of the sets consisted of them while E={x, y}(x≠y) by listing technique.In section2.3, by listing techniquewe, we focus on all systems of L-fuzzifying matroid independent sets|I(E,2, L)|and all L-cotowers|Ict(E, L)|consisting of sys-tems of matroid independent sets on E, then to get the cardinalities of the sets consisted of them while the cardinality of E={x, y, z} is3by listing technique.