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Congruence lattices of intransitive G-Sets and flat M-Sets

Steve Seif (2013)

Commentationes Mathematicae Universitatis Carolinae

An M-Set is a unary algebra 〈 X , M 〉 whose set M of operations is a monoid of transformations of X ; 〈 X , M 〉 is a G-Set if M is a group. A lattice L is said to be represented by an M-Set 〈 X , M 〉 if the congruence lattice of 〈 X , M 〉 is isomorphic to L . Given an algebraic lattice L , an invariant Π ( L ) is introduced here. Π ( L ) provides substantial information about properties common to all representations of L by intransitive G-Sets. Π ( L ) is a sublattice of L (possibly isomorphic to the trivial lattice), a Π -product lattice. A Π -product...

Congruences in ordered sets

Ivan Chajda, Václav Snášel (1998)

Mathematica Bohemica

A concept of congruence preserving upper and lower bounds in a poset P is introduced. If P is a lattice, this concept coincides with the notion of lattice congruence.

Congruences in ordered sets and LU compatible equivalences

Václav Snášel, Marek Jukl (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A concept of equivalence preserving upper and lower bounds in a poset P is introduced. If P is a lattice, this concept coincides with the notion of lattice congruence.

Construction of uninorms on bounded lattices

Gül Deniz Çaylı, Funda Karaçal (2017)

Kybernetika

In this paper, we propose the general methods, yielding uninorms on the bounded lattice ( L , ≤ , 0 , 1 ) , with some additional constraints on e ∈ L ∖ { 0 , 1 } for a fixed neutral element e ∈ L ∖ { 0 , 1 } based on underlying an arbitrary triangular norm T e on [ 0 , e ] and an arbitrary triangular conorm S e on [ e , 1 ] . And, some illustrative examples are added for clarity.

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