Linguistic terms are often used to represent the truth degree or credibility degree to manage the uncertainty or imprecision as one of popular ways of knowledge representation in the perception-based decision making problem. This present work represents the credibility of uncertain knowledge using linguistic values. The linguistic-valued credibility is then modeled based on a lattice ordered lo...

Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified L-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified L-right semi-topo...

This paper presents an investigation of many valued lattices from the point of view of enriched category theory. For a bounded partially ordered set P , the conditions for P to become a lattice can be postulated as existence of certain adjunctions. Reformulating these adjunctions, by aid of enriched category theory, in many valued setting, two kinds of many valued lattices, weak -lattices and -...

The aim of this paper is to introduce some classes of aggregation functionals when the evaluation scale is a complete lattice. We focus on the notion of quantile of a lattice-valued function which have several properties of its real-valued counterpart and we study a class of aggregation functionals that generalizes Sugeno integrals to the setting of complete lattices. Then we introduce in the r...

*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...

The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant Z3-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain Z3-valued, additive quantity. Implications for continuous QCD are discussed.

Hopf solitons in the Skyrme-Faddeev model — S 2-valued fields on R 3 with Skyrme dynamics — are string-like topological solitons. In this Letter, we investigate the analogous lattice objects, for S 2-valued fields on the cubic lattice Z 3 with a nearest-neighbour interaction. For suitable choices of the interaction, topological solitons exist on the lattice. Their appearance is remarkably simil...

Recently, I. Stubbe constructed an isomorphism between the categories of right Q-modules and cocomplete skeletal Q-categories for a given unital quantale Q. Employing his results, we obtain an isomorphism between the categories of Q-algebras and Q-quantales, where Q is additionally assumed to be commutative. As a consequence, we provide a common framework for two concepts of lattice-valued fram...

In this note we present a new treatment of the pointfree version of the semicontinuous quasi-uniformity based on the new tool of the ring of arbitrary (not necessarily continuous) real-valued functions made available recently by J. Gutiérrez Garćıa, T. Kubiak and J. Picado [Localic real functions: a general setting, Journal of Pure and Applied Algebra 213 (2009) 1064-1074]. The purpose is to sh...