Generalized fuzzy n-ary subpolygroups endowed with interval valued membership functions

Article type: Research Article

Authors: Davvaz, B. | Kazanci, O. | Yamak, S.

Affiliations: Department of Mathematics, Yazd University, Yazd, Iran | Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey

Note: [] Corresponding author. E-mail: davvaz@yazduni.ac.ir; kazancio@yahoo.com; syamak@ktu.edu.tr.

Abstract: Recently, fuzzy n-ary polygroups were introduced and analyzed by Davvaz, Corsini and Leoreanu-Fotea. Fuzzy n-ary polygroups are suitable generalizations of n-ary polygroups and a special case of fuzzy n-ary hypergroups. The aim of this paper is to introduce the notion of an interval-valued fuzzy n-ary subpolygroup of an n-ary subpolygroup and to extend the fuzzy n-ary subpolygroup to interval-valued (∈, ∈, ∨q)-fuzzy n-ary subpolygroup. We also consider the concept of implication-based interval-valued fuzzy n-ary sub-polygroup in an n-ary polygroup, in particular, the implication operators in £ukasiewicz system of continuous-valued logic are discussed.

Keywords: n-ary polygroup, fuzzy n-ary subpolygroup, interval-valued (∈, ∈, ∨q)-fuzzy n-ary subpolygroup, fuzzy logic, implication operator

DOI: 10.3233/IFS-2009-0424

Journal: Journal of Intelligent & Fuzzy Systems, vol. 20, no. 4, 5, pp. 159-168, 2009