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...

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...

This is a continuation of [6]. In this article, we proved that convex combination on convex family is convex. and [9] provide the notation and terminology for this paper. 1. CONVEX COMBINATIONS ON CONVEX FAMILY The following propositions are true: (1) For every non empty RLS structure V and for all convex subsets M, N of V holds M ∩ N is convex. (2) Let V be a real unitary space-like non empty ...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

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...