Lattices of fuzzy objects (Q1922855)

The essence of fuzzification was examined by many authors [cf., e.g., \textit{J. A. Goguen}, Bull. Am. Math. Soc. 75, 622-624 (1969; Zbl 0177.02401); \textit{M. A. Erceg}, Fuzzy Sets Syst. 3, 75-82 (1980; Zbl 0421.03044); \textit{L. Biacino} and \textit{G. Gerla}, Inf. Sci. 33, 181-195 (1984; Zbl 0562.06004); \textit{L. Filep}, J. Fuzzy Math. 2, 871-892 (1994; Zbl 0822.20066)]. The paper introduces a new concept of fuzzification as a relation between complete lattices. The introduced model generalizes constructions known in fuzzy algebra and in fuzzy topology.