On fuzzification of matroids
type: Item
instance of: scholarly article
title: On fuzzification of matroids
zbMATH Open document ID: 0789.05020
DOI: 10.1016/0165-0114(93)90403-5
author: Yuang-Cheh Hsueh
published in: Fuzzy Sets and Systems
publication date: 1994-01-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 487476
zbMATH Keywords: fuzzy matroids
zbMATH Keywords: fuzzy preindependence space
zbMATH Keywords: polymatroids
zbMATH Keywords: fuzzy rank
reviewed by: Carlos Narciso Bouza Herrera
MaRDI profile type: Publication
full work available at URL: 0165-0114(93)90403-5
OpenAlex ID: W2030604584
cites work: Q5684698
cites work: Fuzzy matroids
cites work: Bases of fuzzy matroids
cites work: Fuzzy matroid structures
cites work: Transversal theory. An account of some aspects of combinatorial mathematics
cites work: Q4111952
description: scientific article; zbMATH DE number 487476