A Novel Study on Ordered Anti-Involution LA-Semihypergroups

Abstract

In this study, we introduce a new concept called “anti-involution” in relation to ordered LA-semihypergroups. An anti-involution is basically an involuntary automorphism, which is just a fancy term for a mathematical function that can be reversed. We looked at several fundamental results before introducing anti-involution hyperideals. We studied the anti-involution hyperideals of ordered anti-involution LA-semihypergroups using the rough set theory. In an ordered anti-involution LA-semihypergroup, the $\rho$ -upper and $\rho$ -lower rough approximations of anti-involution hyperideals are an anti-involution hyperideals.