Notes on “A survey of fuzzy implication algebras and their axiomatization”

• A correction of Theorem 2 in Pei's paper is presented.
• Conditions (I1)–(I5) in the definition of FI-algebras are independent.
• The class of all CFI-algebras forms an equational algebra class.

In this note, we present a correction of Theorem 2 in the paper [1], and show that all the conditions (I1)–(I5) in the definition of fuzzy implication algebras are independent of each other. In addition, we prove that the class of all commutative fuzzy implication algebras forms an equational algebra class.