Document Type : Research Paper

Authors

1 UNIVERSITY OF LAGOS

2 DEPARTMENT OF MATHEMATICS, UNIVERSITY OF IBADAN, IBADAN, NIGERIA WEST AFRICA.

3 DEPARTMENT OF MATHEMATICS, YABA COLLEGE OF TECHNOLOGY, LAGOS, NIGERIA.

Abstract

Abstract. This theory of fuzzy sets has a wide range of applications, one

of which is that of fuzzy groups . The Fuzzy sets were introduced by Zadeh.

Even though, the story of Fuzzy logic started much earlier, it was specially designed mathematically to represent uncertainty and vagueness. It was

also, to provide formalized tools for dealing with the imprecision intrinsic to

many problems. The term fuzzy logic is generic as it can be used to describe

the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory and fuzzy data analysis which are customarily called

fuzzy set theory. A group is nilpotent if it has a normal series of a finite length

n: By this notion, every finite p-group is nilpotent. The nilpotence property

is an hereditary one. Thus, every finite p-group possesses certain remarkable

characteristics. In this paper, the explicit formulae is given for the number

of distinct fuzzy subgroups of the Cartesian product of the dihedral group of

order 23 with a cyclic group of order of an m power of two for, which m > 3

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