This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

The purpose of this paper is to introduce and study a new concept of strong fuzzy real-valued double Aconvergence sequences with respect to an Orlicz function. Also, some properties of the resulting fuzzy real-valued sequence spaces are examined. In addition, we define the double A-statistical convergence and establish some connections between the spaces of strong double A-convergence sequence ...

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...

Vector-valued L p-convergence of orthogonal series and Lagrange interpolation. Abstract We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of L p-functions in terms of Jacobi polynomi...

In this paper, it is shown that the category of stratified $L$-generalized convergence spaces is monoidal closed if the underlying truth-value table $L$ is a complete residuated lattice. In particular, if the underlying truth-value table $L$ is a complete Heyting Algebra, the Cartesian closedness of the category is recaptured by our result.

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...