Characterization of ordered semigroups in terms of fuzzy soft ideals (Q454592)

Applying the concept of fuzzy soft sets, for an ordered semigroup, the concepts of \((\in_\gamma,\;\in_\gamma\vee q_\delta)\)-fuzzy soft left (right) ideals, \((\in_\gamma,\;\in_\gamma\vee q_\delta)\)-fuzzy soft bi-ideals and \((\in_\gamma,\;\in_\gamma\vee q_\delta)\)-fuzzy soft quasi-ideals are introduced and some of their properties are given. Then, the intra-regular, the left (right) quasi-regular, and the ordered semigroups which are both intra-regular and left quasi-regular in terms of \((\in_\gamma,\;\in_\gamma\vee q_\delta)\)-fuzzy soft left (right) ideals, \((\in_\gamma,\;\in_\gamma\vee q_\delta)\) fuzzy soft bi-(quasi)-ideals are characterized. Reviewer's remark: A subset \(X\) of an ordered semigroup is called idempotent if \(X=(X^2]\).