We add here some further characterizations to the characterizations of strongly regular ordered $��$-semigroups already considered in Hacettepe J. Math. 42 (2013), 559--567. Our results generalize the characterizations of strongly regular ordered semigroups given in the Theorem in Math. Japon. 48 (1998), 213--215, in case of ordered $��$-semigroups. The aim of writing this paper is not just to add a publication in $��$-semigroups but, mainly, as a continuation of the paper "On regular duo $po$-$��$-semigroups in Math. Slovaca 61 (2011), 871--884, to publish a paper which serves as an example to show what a $��$-semigroup is and give the right information about this structure.