University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 An introduction to bipolar fuzzy soft hypervector spaces 15 35 8846 10.22124/jart.2025.27891.1687 EN O. R. Dehghan Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran Journal Article 2024 07 16 The purpose of this document is to present the concept of bipolar fuzzy soft hypervector spaces and explore their fundamental characteristics‎. ‎To begin with‎, ‎a new operation and an external hyperoperation are introduced for bipolar fuzzy soft sets on the hypervector space $\mathcal{V}$‎, ‎which are connected to the operation and external hyperoperation of $\mathcal{V}$‎. ‎Then the notion of bipolar fuzzy soft hypervector space is defined‎, ‎supported by non-trivial examples‎, ‎and it is investigated whether 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 investigated. https://jart.guilan.ac.ir/article_8846_f12ae4a99c4cb11a5a8b047c61c04eca.pdf