New approach towards different ideals using bipolar valued intuitionistic neutrosophic set of an ordered semigroups

Abstract

This paper introduces the notion of bipolar valued intuitionistic neutrosophic subsemigroup (BIntNS), bipolar valued intuitionistic neutrosophic left ideal (BIntNLI), bipolar valued intuitionistic neutrosophic right ideal (BIntNRI), bipolar valued intuitionistic neutrosophic ideal (NI), and bipolar valued intuitionistic neutrosophic bi-ideal (BIntNBI) of an ordered semigroups, along with some of its properties. A new extension over ordered semigroups of the bipolar valued intuitionistic neutrosophic ideal. The lower level set is a subsemigroup (BV LI, BV RI, BV BI) of an ordered semigroup. Examples are provided to exemplify our results, however the contrary may not be true. Every BIntNS is a BIntNS of an ordered semigroup. © 2025, University of New Mexico. All rights reserved.