Ehresmann semigroups may be viewed as biunary equipped with domain and range operations satisfying some equational laws. Motivated by of the main examples, we here define ordered semigroups, consider their basic properties well special cases in which order is algebraically definable. In particular, one two-sided restriction natural orders are characterized within class semigroups. The result an...

We consider the fuzzification of the notion of a positive implicative ordered filter in implicative semigroups. We show that every fuzzy positive implicative ordered filter is both a fuzzy ordered filter and a fuzzy implicative ordered filter. We give examples that a fuzzy (implicative) ordered filter may not be a fuzzy positive implicative ordered filter. We also state equivalent conditions of...