based on a complete heyting algebra l, the relations between lfuzzifyingconvergence spaces and l-fuzzifying topological spaces are studied.it is shown that, as a reflective subcategory, the category of l-fuzzifying topologicalspaces could be embedded in the category of l-fuzzifying convergencespaces and the latter is cartesian closed. also the specialization l-preorderof l-fuzzifying convergenc...

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topologica...

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...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

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...

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

A new so-called fuzzifying measurable theory that generalizes the classical measurable theory is established and the structures of such new theory are discussed very detailed. In the last, we study the product of two fuzzifying measures and consider a problem, which is like the third of the open problems in fuzzy measure presented by Z. Wang. We have solved this problem satisfactorily in the ne...