(f, g)-derivation in residuated multilattices

Residuated Multilattices: a First Glimpse into Their Structures

We prove that when divisibility is added to a residuated multilattice, this causes the multilattice structure to collapse down to a residuated lattice. This motivates the study of semi-divisibility and regularity on residuated multilattices. The ordinal sum construction is also applied to residuated multilattices as a way to construct new examples of both residuated multilattices and consistent...

GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM

The aim of the present work is to study the  $F$-transform over a generalized residuated lattice.  We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.

f-DERIVATIONS AND (f; g)-DERIVATIONS OF MV -ALGEBRAS

Recently, the algebraic theory of MV -algebras is intensively studied. In this paper, we extend the concept of derivation of $MV$-algebras and we give someillustrative examples. Moreover, as a generalization of derivations of $MV$ -algebraswe introduce the notion of $f$-derivations and $(f; g)$-derivations of $MV$-algebras.Also, we investigate some properties of them.

Congruence Relations on Multilattices

Numerical Methods for Multilattices

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we revie...