Some remarks on congruences obtained from the L-fuzzy Nakano hyperoperation

• Published in: Information sciences 2006-02, Vol.176 (3), p.301-320
• Main Authors: Serafimidis, K., Kehagias, Ath
• Format: Article
• Language: English
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2004.11.002

In this paper we study relations which are congruences with respect to ∧ and ⊔ p , where ⊔ p is the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R 1 which is a congruence with respect to ∧ and ⊔ 1 and, for each p ∈ X, construct an equivalence relation R p which is a congruence with respect to ∧ and ⊔ p . Furthermore, for each x ∈ R p we construct a quotient hyperoperation ⊔ p and we show that the hyperalgebra ( X/ R p , ⊔ p ) is a join space and the hyperalgebra ( X/ R p , ⊔ p , ∧ p ) is a hyperlattice.