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) 10451050], 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. © 2011 Elsevier Ltd. All rights reserved.
Zhu, P., & Wen, Q. (2011). Homomorphisms between fuzzy information systems revisited. Applied Mathematics Letters, 24(9), 1548–1553. https://doi.org/10.1016/j.aml.2011.03.044