An Introduction to Bipolar Fuzzy Soft Hypervector Spaces

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.