On fuzzification of matroids
The fuzzification of matroids is studied and a method for doing so is proposed. Different results from matroid theory are stated and fuzzy analogs are defined. A theorem establishes the existence of bases in a fuzzy preindependence space (fpis) and properties of its fuzzy cardinality. Then a fuzzy matroid (fm) is defined on a finite set of a fpis. Two theorems are proved for fixing properties of the fm. Similar steps are used for deriving theoretical properties of polymatroids. Duality for fm is studied. Three theorems are proved. They permit to establish relationships between the fuzzy rank and corank functions of a fm. Most of the basic properties of matroids are preserved for the derived fm when the proposed fuzzification is used.
scientific article; zbMATH DE number 487476