In this article, we introduce bipolar hypersoft topological spaces over the collection of bipolar
hypersoft sets. It is proven that a bipolar hypersoft topological space gives a parametrized …

The main objective of this study is to define a new class of bipolar soft (BS) separation
axioms known as BS T˜˜ i-space (i= 0, 1, 2, 3, 4). This type is defined in terms of ordinary …

The basic of bipolar soft set theory stands for a mathematical instrument that bringstogether
the soft set theory and bipolarity. Its definition is based on two soft sets, a set thatprovides …

The concept of soft set theory can be used as a mathematical tool for dealing with problems
that contain uncertainty. Then, a new mixed mathematical model called the bipolar soft set is …

Mappings are significant mathematical tools with many applications in our daily lives. The
bipolar hypersoft set is one of the effective tools for dealing with ambiguity and vagueness …

The purpose of this paper is to define bipolar soft generalized compact sets and bipolar soft
generalized compact spaces. The structures of ̃̃g-centralized bipolar soft generalized closed …

Activation functions are critical components of neural networks, helping the model learn
highly-intricate dependencies, trends, and patterns. Non-linear activation functions allow the …

Connectedness represents the most significant and fundamental topological property. It
highlights the main characteristics of topological spaces and distinguishes one topology …

The striking idea of soft sets was frst claimed that by Molodtsov as a new mathematical tool
for dealing with uncertainties which is free from the other theories limitations. After the …

In this paper, we introduce the concept of bipolar soft supra topological space and provide a
characterization of the related concepts of bipolar soft supra closure and bipolar soft supra …