Graded fuzzy topological spaces

In this paper, graded fuzzy topological spaces based on the notion of neighbourhood system of graded fuzzy neighbourhoods at ordinary points are introduced and studied. These graded fuzzy neighbourhoods at ordinary points and usual subsets played the main role in this study

The metrizability of L-topological groups

In this study, we study the metrizability of the notion of L-topological group defined by Ahsanullah 1988. We show that for any (separated) L-topological group there is an L-pseudo-metric (L-metric), in sense of Gähler which is defined using his notion of L-real numbers, compatible with the L-topology of this (separated) L-topological group. That is, any (separated) L-topological group is pseudo-metrizable (metrizable)

Soft closure spaces via soft ideals

This paper was devoted to defining new soft closure operators via soft relations and soft ideals, and consequently new soft topologies. The resulting space is a soft ideal approximation. Many of the well known topological concepts were given in the soft set-topology. Particularly, it introduced the notations of soft accumulation points, soft continuous functions, soft separation axioms, and soft connectedness. Counterexamples were introduced to interpret the right implications. Also, a practical application of the new soft approximations was explained by an example of a real-life problem

Double Fuzzy Ideal Multifunctions

In this paper, we introduce the notion of p,q-fuzzy local function and DF-ideal topological space. Also, we introduce the concepts DFU-ð-continuous and DFL-ð-continuous, almost ð-continuous, weakly ð-continuous and almost weakly ð-continuous multifunctions. Several properties and characterizations of the introduced multifunctions and types of continuity are established. Some examples are given to explain the correct implications between these notions