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Displaying similar documents to “Characterization of the order induced by uninorm with the underlying drastic product or drastic sum”

On skew lattices. II.

Václav Slavík (1973)

Commentationes Mathematicae Universitatis Carolinae

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Classification systems and their lattice

Sándor Radeleczki (2002)

Discussiones Mathematicae - General Algebra and Applications

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We define and study classification systems in an arbitrary CJ-generated complete lattice L. Introducing a partial order among the classification systems of L, we obtain a complete lattice denoted by Cls(L). By using the elements of the classification systems, another lattice is also constructed: the box lattice B(L) of L. We show that B(L) is an atomistic complete lattice, moreover Cls(L)=Cls(B(L)). If B(L) is a pseudocomplemented lattice, then every classification system of L is independent...

About the equivalence of nullnorms on bounded lattice

M. Nesibe Kesicioğlu (2017)

Kybernetika

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In this paper, an equivalence on the class of nullnorms on a bounded lattice based on the equality of the orders induced by nullnorms is introduced. The set of all incomparable elements w.r.t. the order induced by nullnorms is investigated. Finally, the recently posed open problems have been solved.

Finite atomistic lattices that can be represented as lattices of quasivarieties

K. Adaricheva, Wiesław Dziobiak, V. Gorbunov (1993)

Fundamenta Mathematicae

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We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].

Residuation in orthomodular lattices

Ivan Chajda, Helmut Länger (2017)

Topological Algebra and its Applications

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We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one. ...