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

  • Authors:

  • K. Serafimidis;Ath Kehagias

  • Affiliations:

  • Faculty of Engineering, Department of Mathematics, Physical and Computational Sciences, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;Faculty of Engineering, Department of Mathematics, Physical and Computational Sciences, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2006

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Abstract

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.