On fuzzy spaces and fuzzy group theory
The notion of fuzzy set was generalized in many directions, e.g.: \(L\)-fuzzy sets [\textit{J. A. Goguen}, J. Math. Anal. Appl. 18, 145--174 (1967; Zbl 0145.24404)], probabilistic sets [\textit{K. Hirota}, Fuzzy Sets Syst. 5, 31--36 (1981; Zbl 0442.60008)], intuitionistic fuzzy sets [\textit{K. Atanassov}, Fuzzy Sets Syst. 20, 87--96 (1986; Zbl 0631.03040)], Boolean fuzzy sets [\textit{C. A. Drossos}, Fuzzy Sets Syst. 37, 287--307 (1990; Zbl 0712.03045)]. Here a notion of fuzzy space is introduced and fuzzy groupoids on fuzzy spaces are examined (formally without structure of crisp groupoid, but practically with equivalent conditions). Results are compared to properties of Rosenfeld's fuzzy groupoids [cf. \textit{A. Rosenfeld}, J. Math. Anal. Appl. 35, 512--517 (1971; Zbl 0194.05501), \textit{L. Biacino, G. Gerla}, Inf. Sci. 33, 181--195 (1984; Zbl 0562.06004)].
scientific article; zbMATH DE number 694932