ON METHODS OF COUNTING PREFERENTIAL FUZZY SUBGROUPS

V. Murali (South Africa) and B. B. Makamba (South Africa)

Received August 27, 2007

Abstract

We propose two different methods of computing the number of distinct preferential fuzzy subgroups of a finite group G using the notion of a pinned-flag which is a pair consisting of a maximal chain of subgroups and a keychain of real numbers in the unit interval. The first method is to count the number of fuzzy subgroups with a fixed maximal chain and a variable keychain, and the second is to count variable maximal chains with a fixed keychain. Each method throws an important light on the classification problem of preferential fuzzy subgroups. We illustrate with a typical example.

Keywords and phrases: preferential, fuzzy subgroup, maximal chain, keychain, pinned-flag.