On Goetschel and Voxman fuzzy matroids

✍ Scribed by Ladislav Novak

• Book ID: 104293149
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 97 KB
• Volume: 117
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(98)00424-2

✦ Synopsis

The concepts of fuzzy pre-matroid and hereditary fuzzy pre-matroid are introduced and investigated. The property "to be perfect" for hereditary fuzzy pre-matroids is also considered. It is shown that Goetschel and Voxman fuzzy matroids coincide with perfect hereditary fuzzy pre-matroids. It is also shown that Goetschel and Voxman fuzzy matroids can be described via three fuzzy axioms, two of which are direct fuzzy counter-parts of the crisp matroid axioms in terms of elementary fuzzy sets and the third one is a decomposition axiom, also in terms of elementary fuzzy sets.