In this paper, we study the least strongly regular equivalence relation containing a given binary relation on a semihypergroup. Also, we discuss the least fuzzy strongly regular equivalence relation greater than or equal to a given fuzzy relation on a semihypergroup. As an application of the results of this paper, the fundamental relation β∗ and the least fuzzy strongly regular equivalence relation on a semihypergroup are obtained. Furthermore, we respectively give descriptions of the greatest strongly regular equivalence relation contained in a given equivalence relation containing β∗ and the greatest fuzzy strongly regular equivalence relation less than or equal to a given fuzzy equivalence relation greater than or equal to on a semihypergroup.
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