On fuzzy independence set systems

Abstract

The concept of fuzzy pre-independence set system and that of fuzzy independence set system are introduced and investigated in this paper. The properties "to be closed", "to be perfect" and "to be strongly regular" of a fuzzy independence set system are also considered. Several propositions concerning bases of closed perfect fuzzy independence set systems are presented. An important subclass of perfect fuzzy independence set systems, are fuzzy matroids, introduced by Goetschel and Voxman [Fuzzy Sets and Systems 27 (1988) 291; 31 (1989) 253]. © 1997 Elsevier Science B.V.