A Study of Rough Bipolar Soft Ideals in Terms of Semigroups

Nosheen Malik, Muhammad Shabir, Rizwan Gul

Abstract


Rough set (RS) theory is a valuable mathematical tool to address incomplete knowledge. In contrast, bipolar soft sets (BSSs) can handle the uncertainty and the bipolarity of the data in various scenarios. In this article, we have developed the notions of rough bipolar soft ideals in semigroup (SG) by combining RS theory and BSSs. Then, the idea of bipolar soft left ideals (BS-LIs), bipolar soft right ideals (BS-RIs), bipolar soft two-sided ideals (BS-2SIs), bipolar soft interior ideals (BS-IIs)
and bipolar soft bi-ideals (BS-BIs) over the SG ¨Θ is developed. Moreover, it is observed that Cr and complete Cr (CCr) are critical in developing rough approximations of bipolar soft ideals. Therefore, their related characteristics are studied via Cr and CCr.


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