The Computational Subgroups for the Finite Fuzzy NilpotentGroups Involving Indetermi-Nates (Varying) m; n - Adebisi, Sunday Adesina; Ogiugo, Mike; Enioluwafe, Michael (Optimality, 2025)
This theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups . The fuzzy sets were actually been 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 eight with a cyclic group of order of an m power of two for, which m is not less than three.