Our aim in this paper is to lay the groundwork for, and provide some significant initial contributions to, the development of a comprehensive theory on the structure of residuated lattices – a class …

More generally, residuated lattices defined by monoid equations that are preserved under the powerset construction (by Theorem 3.34 (3), all monoid identities are preserved by nuclei) are …

It is important to observe that a given lattice may usually be residuated in several different ways. To give a simple example, consider the lattice of four elements i>a>b>z.

In this chapter we investigate the properties of a residuated lattice and the lattice of filters of a residuated lattice, we study the Boolean center of an FL w -algebra and we define and study …

A residuated lattice is an ordered algebraic structure. such that <L,∧,∨> is a lattice, <L,·, e> is a monoid, and \ and / are binary operations for which the equivalences hold for all a,b,c ∈ L.

Abstract commutative residuated lattice, is an ordered algebraic struc-ture L = (L, ·, ∧, ∨, →, e), where (L, ·, e) is a commutative monoid, (L, ∧, ∨) is a lattice, and the operation → satisfies the …

In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, …

Residuated lattices are 1-regular, and have distributive congruence lattices (since they have lattice reducts). A normal filter F is a subset of a residuated lattice where {1}, ↑F, F·F, (x·F)/x, …

Jan 1, 2017 · The residuated lattice is a basic algebraic structure accepted as a structure of truth values for fuzzy logic and fuzzy set theory. In general, it is an algebra

ilinear residuated lattices: their lattice is a union of disjoint incomparable chains, with bounds added. We we give two general constructions of unilinear residuated lattices, provide an …