States on EQ-algebras

Article type: Research Article

Authors: Borzooei, RA^* | Saffar, B. Ganji

Affiliations: Department of Mathematics, Payamnour University, G.C., Tehran, Iran

Correspondence: [*] Correspondence to: R. A. Borzooei, Department of Mathe-matics, Shahid Beheshti University, G.C., Tehran, Iran. Tel.: +9821 29902920; Fax: +98 21 22431652; E-mail: [email protected].

Abstract: The notion of state is an analogue to probability measure and it has been studied for different types of structures such as MV-algebras, BL-algebras and BCK algebra. In this paper we define the notion of state on EQ-algebras which is algebraic structure of higher order fuzzy logic and we investigate some properties of them. Then we characterize representable class of state EQ-algebras.

Keywords: EQ-algebra, state EQ-algebra, state ideals, state (pre)filters

DOI: 10.3233/IFS-151588

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 209-221, 2015