Generalized fuzzy polygroups endowed with interval valued membership functions

Article type: Research Article

Authors: Davvaz, Bijan | Zhan, Jianming | Shum, K.P.

Affiliations: Department of Mathematics, Yazd University, Yazd, Iran | Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province, 445000, P.R. China | Faculty of Science, The Chinese University of Hong Kong, Shatin, Hong Kong (SAR), P.R. China

Note: [] Corresponding author. E-mail: davvaz@yazduni.ac.ir

Abstract: In this paper, the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set, which is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set, is introduced. Using this new idea, the notion of interval valued (α,β)-fuzzy sub-polygroups in a polygroup, which is a generalization of a fuzzy sub-polygroup, is defined, and related properties are investigated. In particular, the study of interval valued (∈,∈∨q)-fuzzy sub-polygroups in a polygroup is dealt with. Finally, we consider the concept of implication-based interval valued fuzzy sub-polygroups in a polygroups.

Keywords: Polygroup, interval valued (α,β)-fuzzy sub-polygroup, interval valued (∈,∈∨q)-fuzzy sub-polygroup, fuzzy logic, implication operator

Journal: Journal of Intelligent & Fuzzy Systems, vol. 19, no. 3, pp. 181-188, 2008