Homomorphisms between fuzzy information systems revisited

Recently, Wang et al. discussed the properties of fuzzy information systems under homomorphisms in the work [C. Wang, D. Chen, L. Zhu, Homomorphisms between fuzzy information systems, Appl. Math. Lett. 22 (2009) 1045–1050], where homomorphisms are based upon the concepts of consistent functions and fuzzy relation mappings. In this work, we classify consistent functions as predecessor-consistent and successor-consistent, and then proceed to present more properties of consistent functions. In addition, we improve some characterizations of fuzzy relation mappings provided in the above cited work.