An Introduction to Bipolar Fuzzy Soft Hypervector Spaces

TL;DR

This paper introduces bipolar fuzzy soft hypervector spaces, defining new operations, exploring their properties, and analyzing their behavior under linear transformations, expanding the mathematical framework of fuzzy hyperstructures.

Contribution

It presents the novel concept of bipolar fuzzy soft hypervector spaces, including their operations, properties, and behavior under linear transformations, which is a new extension in fuzzy hyperstructure theory.

Findings

Defined new operations on bipolar fuzzy soft sets over hypervector spaces

Established that certain constructed sets are bipolar fuzzy soft hypervector spaces

Analyzed the behavior of these spaces under linear transformations

Abstract

The aim of this paper is to introduce the notion of bipolar fuzzy soft hypervector spaces and study their basic properties. In this regard, at first some new operation and external hyperoperation are defined on bipolar fuzzy soft sets over hypervector space V, related to the operation and external hyperoperation of V. Then the notion of bipolar fuzzy soft hypervector space is defined, supported by non-trivial examples, and it is investigated that the new bipolar fuzzy soft sets, constructed by the mentioned operation and hyperoperation, are bipolar fuzzy soft hypervector spaces. Finally, the behavior of bipolar fuzzy soft hypervector spaces under linear transformations is studied.