Study of Bipolar Fuzzy Soft Hypervector Spaces

Abstract

In this paper, three topics in bipolar fuzzy soft hypervector spaces are investigated. At first, four equivalent conditions for the definition of a bipolar fuzzy soft hypervector space are presented, from different points of view. Then some new bipolar fuzzy soft hypervector spaces are constructed using the notions of subhyperspace, level subset, generated subhyperspace, and previous bipolar fuzzy soft hypervector spaces. Finally, normal bipolar fuzzy soft hypervector spaces are studied as a special kind of bipolar fuzzy soft hypervector spaces. All concepts are supported by interesting examples.

Keywords: Hypervector space; Level subset; Bipolar fuzzy soft hypervector space; Subhyperspace; Normal bipolar fuzzy soft hypervector space.

2010 Mathematics Subject Classification. 06D72; 20N20; 08A72