Implicative and positive implicative prefilters of EQ-algebras. (English) Zbl 1305.03061

Liu, Lianzhen; Zhang, Xiangyang

J. Intell. Fuzzy Syst. 26, No. 5, 2087-2097 (2014).

Summary: EQ-algebras were introduced by V. Novák and B. De Baets [Fuzzy Sets Syst. 160, No. 20, 2956–2978 (2009; Zbl 1184.03067)] 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.

MSC:

03G25	Other algebras related to logic
03B52	Fuzzy logic; logic of vagueness

Keywords:

EQ-algebra; implicative prefilter; positive implicative prefilter

Citations:

Zbl 1184.03067