State operators on pseudo EQ-algebras

Article type: Research Article

Authors: Guo, Qing^a | Xin, Xiao Long^{b; a; *}

Affiliations: [a] School of Mathematics, Northwest University, Xi’an, China | [b] School of Science, Xi’an Polytechnic University, Xi’an, China

Correspondence: [*] Corresponding author. Xiao Long Xin, E-mail: xlxin@nwu.edu.cn.

Abstract: Pseudo EQ-algebras were introduced by X.L. Xin as possible algebraic semantics for fuzzy type theory. The main goal of this paper is to investigate pseudo EQ-algebras with internal states. To begin with, we introduce the notion of pseudo EQ-algebras with internal state(simplify, ISPEQ-algebra) and study its properties. Moreover, we discuss the relation between ISPEQ-algebras and states on pseudo EQ-algebras. In the following, we study state filters(simplify S-fliters) and state prefilters(simplify S-prefliters) of ISPEQ-algebras. We construct ISPEQ-algebras from S-fliters and derive congruence relation θ of ISPEQ-algebras. In the end, we give the generating formula of prefilters on residuated pseudo EQ-algebras and based on that we get the generating formula of S-prefilters on residuated pseudo EQ-algebras.

Keywords: Pseudo EQ-algebra, state operator, S-fliter, S-prefliter, generating formula

DOI: 10.3233/JIFS-212723

Journal: Journal of Intelligent & Fuzzy Systems, vol. 43, no. 1, pp. 1189-1202, 2022