Summary: In a recent paper [ibid. 2012, Article ID 729758, 5 p. (2012; Zbl 1242.54032
)], F. Zheng
and X. Lian
proved a common fixed-point theorem for commutating mappings in
-complete fuzzy metric spaces and gave an example to illustrate the main result. In this note, we point out that the above example is incorrect because it does not satisfy the condition of
-completeness, and then two appropriate examples are given. In addition, we prove that the theorem proposed in [loc. cit.] actually holds in an
-complete fuzzy metric space. Our results improve and extend some existing results in the relevant literature.