The L-fuzzy Nakano hypergroup

  • Authors:

  • Ath. Kehagias;K. Serafimidis

  • Affiliations:

  • Division of Mathematics, Department of Mathematics, Physics and Computer Sciences, Aristotle University of Thessaloniki, Box 464, 54124 Thessaloniki, Greece;Division of Mathematics, Department of Mathematics, Physics and Computer Sciences, Aristotle University of Thessaloniki, Box 464, 54124 Thessaloniki, Greece

  • Venue:
  • Information Sciences—Informatics and Computer Science: An International Journal
  • Year:
  • 2005

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Abstract

In this paper we start with a lattice (X, ∨, ∧) and define, in terms of ∨, a family of crisp hyperoperations ⊔p (one hyperoperation for each p∈X). We show that, for every p, the hyperalgebra (X, ⊔p) is a join space and the hyperalgebra (X, ⊔p, ∧) is very similar to a hyperlattice. Then we use the hyperoperations ⊔p as p-cuts to introduce an L-fuzzy hyperoperation ⊔ and show that (X, ⊔) is an L-fuzzy join space and the hyperalgebra (X, ⊔p, ∧) is very similar to an L-fuzzy hyperlattice.