The main purpose of this paper is to introduce a concept of L-fuzzifying topological vector spaces (here L is a completely distributive lattice) and study some of their basic properties. Also, a characterization of such spaces in terms of the corresponding L-fuzzifying neighborhood structure of the zero element is given. Finally, the conclusion that the category of L-fuzzifying topological vect...

The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhoo...

the main purpose of this paper is to introduce a concept of$l$-fuzzifying topological groups (here $l$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. we prove that its corresponding $l$-fuzzifyingneighborhood structure is translation invariant. a characterizationof such topological groups in terms of the corresponding$l$-fuzzifying neighborhoo...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

We study L-categories of lattice-valued convergence spaces. Suchcategories are obtained by fuzzifying" the axioms of a lattice-valued convergencespace. We give a natural example, study initial constructions andfunction spaces. Further we look into some L-subcategories. Finally we usethis approach to quantify how close certain lattice-valued convergence spacesare to being lattice-valued topologi...

By fuzzifying the number of occurrences of an element of a multiset, we obtain a new fuzzy structure; similarly, by fuzzifying the number of occurrences of an element of a hybrid set, we obtain another new fuzzy structure. The aim of the present work is twofold: to provide a concise definition of these new fuzzy structures and their properties and to apply them in natural computing. More specif...

Engineering analysis often involves the accurate numerical solution of boundary value problems in discrete form. Hierarchical quadtree (or octree) grid generation offers an efficient method for the spatial discretisation of arbitrary-shaped two- (or three-) dimensional domains. It consists of recursive algebraic splitting of sub-domains into quadrants (or cubes), leading to an ordered hierarchi...

The concept of a fuzzifying topology was given in [1] under the name L-fuzzy topology. Ying studied in [9, 10, 11] the fuzzifying topologies in the case of L = [0,1]. A classical topology is a special case of a fuzzifying topology. In a fuzzifying topology τ on a set X , every subset A of X has a degree τ(A) of belonging to τ, 0 ≤ τ(A) ≤ 1. In [4], we defined the degrees of compactness, of loca...

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.