A new approach to the fuzzification of groups

Article type: Research Article

Authors: Liu, Q. | Shi, Fu-Gui^{; *}

Affiliations: Beijing Key Laboratory on MCAACI, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 102488, P.R. China

Correspondence: [*] Corresponding author. Fu-Gui Shi, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China. E-mails: [email protected] (F.-G. Shi), [email protected] (Q.Liu).

Abstract: In the present paper we present a new approach to the fuzzification of groups, which is defined by the hazy associative law (a new fuzzy associative law) on hazy binary operations. It is also called an M-hazy group. The basic idea is to generalize the binary operation of classical algebras to fuzzy binary operation. Some properties of M-hazy groups and M-hazy subgroups are discussed. Besides, we also study the homomorphisms between two M-hazy groups.

Keywords: Hazy associative law, M-hazy group, M-hazy subgroup, M-hazy homomorphism

DOI: 10.3233/JIFS-180001

Journal: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 5, pp. 6429-6442, 2019