Abstract. In this paper, first we define the notion of involutive operator
on bounded involutive equality algebras and by using it, we introduce a new
class of equality algebras that we called it a tense like equality algebra. Then
we investigate some properties of tense like equality algebra. For two involutive bounded equality algebras and an equality homomorphism between
them, we prove that the tense like equality algebra structure can be transfer
by this equality homomorphism. Specially, by using a bounded involutive
equality algebra and quotient structure of it, we construct a quotient tense
like equality algebra. Finally, we investigate the relation between tense like
equality algebras and tense MV-algebras.