Note on "Fuzzy universal algebras on L-sets"

This note is the continuation of the paper entitled "Fuzzy universal algebras on L-sets" (IJFS, Volume 16, Number 4, (2019), pp. 175-187) and it focuses on Q-valued (universal) algebras on Q-typed sets. When Q is an involutive quantaloid, some basic related notions in Q-valued algebra such as subalgebra, quotient algebra, homomorphism, congruence, direct product and variety etc are given and the properties of them are studied. When Q is still a symmetric quantaloid, the Q-valued algebra is lifted to Q-valued power algebra, and the power isomorphism theorem is given. As a special case of Q-valued algebra, the fuzzy universal algebra on L-set is presented naturally when L is a commutative and divisible quantale.