The paper discusses some issues on fuzzy and many-valued logic, since the difference between them seems not to be completely clear. Let us remark that the situation has changed after a thorough metamathematical analysis of fuzzy logic had been published [\textit{P. Hájek}, Metamathematics of fuzzy logic, Kluwer, Dordrecht (1998)] as well as a more detailed book on fuzzy logic itself [\textit{V. Novák, I. Perfilieva} and \textit{J. Močkoř}, Mathematical principles of fuzzy logic, Kluwer, Boston (1999)]. Though the authors of the reviewed paper could not know the mentioned books, their goal is analogous to them. They start from the concept of fuzzy logic developed by \textit{J. Pavelka} [Z. Math. Logik Grundlagen Math. 25, 45-52, 119-134, 447-464 (1979; Zbl 0435.03020, Zbl 0446.03015, Zbl 0446.03016)] and compare it with the well-known many-valued Łukasiewicz logic. The focus is on the proper choice of fuzzy implication operations. They try to clarify why some combinations of logical operations interpreting the connectives ``and'', ``or'', ``not'' should not be used. They formulate two requirements for fuzzy implication which fail for many of the definitions but are satisfied by Łukasiewicz logic. The composition rule of inference, originally introduced by L. A. Zadeh, is also addressed pointing out that the implication always corresponds with a certain conjunction, thus determining modus ponens.