Implicative and positive implicative prefilters of EQ-algebras

Article type: Research Article

Authors: Liu, Lianzhen | Zhang, Xiangyang

Affiliations: College of Science, Jiangnan University, Wuxi, China

Note: [] Corresponding author. Lianzhen Liu, College of Science, Jiangnan University, 214122 Wuxi, China. E-mail: lianzhen2003@yahoo.com

Abstract: EQ-algebras were introduced by Novák and De Baets with the intent to develop an algebraic structure of truth values for fuzzy type theory. In this paper, the notions of implicative prefilters and positive implicative prefilters in EQ-algebras are introduced and several characterizations of them are obtained. The relationship between implicative prefilters and positive implicative prefilters is considered. It is proved that implicative prefilters and positive implicative prefilters are equivalent on good IEQ-algebras. The extension theorems of implicative prefilters and positive implicative prefilters are obtained. Furthermore, the quotient algebras induced by positive implicative filters are studied.

Keywords: EQ-algebra, implicative prefilter, positive implicative prefilter

DOI: 10.3233/IFS-130884

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2087-2097, 2014