Anti-Imprecision in The Fuzzy Group Concerning Reference Function and Its Application

In this article, we first defined an anti-subgroup based on a reference function and then extended it to ‎an α-imprecise subgroup, α-imprecise cosets, an α-normal imprecise subgroup, and finally defined an α-anti-imprecise ‎subset. Additionally, we discuss some of their properties in detail. In this article, it has been proved that an ‎imprecise subgroup (normal imprecise subgroup) is again an α-imprecise subgroup (α-normal imprecise ‎subgroup), but the converse is not true, for which some examples are cited. Furthermore, we anticipated the ‎development of an application derived from an anti-imprecise subgroup that can be applied to a variety of ‎networking issues.