Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuz...Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank function for a weighted greedoid, and discuss the rank closure of a fuzzy greedoid.展开更多
We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to ge...We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to get the lexicograpllically optima base of a submodular polyhedron which works on its dula superlnodular polyhedron.This dual algorithm completely agrees to the algorithm of Morton,G.and von Tandow,R.and Ringwald,K.[1985],where their underlying distributive lattice is a chaill poset greedoid.Finally we show that finding the lesicographically optimal base of a submodular system is essentially equivalent to finding the lexicographically optimal base of a simple submodular system,where its underlying distributive lattice is a poset greedoid.This fact.indicates the importance of greedoids in a further development of submodular system theory.展开更多
文摘Fuzzy greedoids were recently introduced as a fuzzy set generalization of (crisp) greedoids. We characterize fuzzy languages which define fuzzy greedoids, give necessary properties and sufficient properties of the fuzzy rank function of a fuzzy greedoid, give a characterization of the rank function for a weighted greedoid, and discuss the rank closure of a fuzzy greedoid.
文摘We show that for a submodular polyhedron and its dual supermodular polyhedron the exists a unique lexicographically optimal base with respect to a weight vector and they coincide.We also present a dual algorithm to get the lexicograpllically optima base of a submodular polyhedron which works on its dula superlnodular polyhedron.This dual algorithm completely agrees to the algorithm of Morton,G.and von Tandow,R.and Ringwald,K.[1985],where their underlying distributive lattice is a chaill poset greedoid.Finally we show that finding the lesicographically optimal base of a submodular system is essentially equivalent to finding the lexicographically optimal base of a simple submodular system,where its underlying distributive lattice is a poset greedoid.This fact.indicates the importance of greedoids in a further development of submodular system theory.
