T-Bipolar soft groups and their fundamental laws

The notion of a T-bipolar soft set (T - BSftS) is the structure that has the ability to discuss the two-sided aspects of certain situations like the effects and side effects of a medicine. Moreover, T - BSftS has the ability to discuss the parametrization tool as well. Also, notice that a group is an algebraic structure that is the key tool in many branches of mathematics. In many decision-making situations, we have to discuss the two-sided aspects of a certain situation and we can see that T - BSftS is the only structure that can handle it. So based on a characteristic of T - BSftS and groups theory there is a need to define the combined notion of T - BSftS and group. So, based on these valuable structures, in this manuscript, we aim to introduce the notion of T-bipolar soft groups by generalizing T-bipolar soft sets. Based on this newly defined structure, we have defined the basic operational laws like extended union, extended intersection, restricted union, restricted intersection, AND product, and OR product for T-bipolar soft groups. Moreover, we have observed the impact of these newly defined notions on T-bipolar soft groups.