A Recursive Formula for the Number of Fuzzy Subgroups of Finite Cyclic Groups

Journal of Advances in Computer Research

شناسنامه علمی شماره، دوره 4، شماره 1، فروردین 2013، صفحه 55-63   

نویسندگان

Mahdi Imanparast^{* 1}؛ Hamid Darabi²

¹Department of Computer Science, University of Bojnord, Bojnord, Iran

²Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

چکیده

Fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. Hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. The Main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group G Z p1 Z p 2 Z p 3 Z pk = ´ ´ ´´ , where k p , p ,..., p 1 2 are distinct prime numbers. We introduce a very simple recursive formula to count the number of subgroups of G.

کلیدواژه‌ها

Fuzzy groups؛ Lattice؛ Finite cyclic groups؛ Chains