Quotient bipolar fuzzy soft sets of hypervector spaces and bipolar fuzzy soft sets of quotient hypervector spaces

Abstract

In this paper, two related quotient structures are investigated utilizing the concept of coset. At first, a new hypervector space F/V = (F/V,\circ,\circledcirc,K) is created, which is composed of all cosets of a bipolar fuzzy soft set (F;A) over a hypervector space V . Then it will be shown that dim F/V = dim V/W, where the quotient hypervector space V/W includes all cosets of an especial subhyperspace W of V. Also, three bipolar fuzzy soft sets over the quotient hypervector space V/W are presented and in this way some new bipolar fuzzy soft hypervector spaces are defined.