\((\alpha,\beta)\)-fuzzy mappings
It is well known that relations, mappings, cardinal numbers and ordinal numbers are the quintessence of set theory. Analogously, these problems, especially fuzzy mappings, are the basic ones followed with interest in fuzzy set theory. Dubois and Prade gave a definition for fuzzy mappings and Liu Yingming gave the concept of fuzzy points. Based on these results, the authors put forward a concept for fuzzy mapping, \((\alpha,\beta)\)-fuzzy mappings, which has its substance by means of the cut sets of fuzzy sets. (It is worth noting that the reviewer has also given a definition of fuzzy mappings by using cut sets [the reviewer, \textit{Luo Chengzhong} and \textit{Wang Peizhuang}, ibid. 55, No. 1, 61-77 (1993; Zbl 0786.04005)]. Then the authors of this paper discuss some properties from their definition, for instance, \((\alpha,\beta)\)-fuzzy injectivity, \((\alpha,\beta)\)-fuzzy surjectivity and an application to fuzzy algebra.
scientific article; zbMATH DE number 496163