Making modules fuzzy (Q1823300)

The paper shows that the notion of fuzzy module [cf. \textit{F. Z. Pan}, Fuzzy Sets Syst. 21, 105-113 (1987; Zbl 0616.16013)] is closely connected with diverse notions from module theory. E.g. the pseudonorm on a module or the hierarchy function on a category of modules generate a fuzzy module, conversely, the quasidecomposition function on a module category can be generated by a family of fuzzy modules [for suitable definitions cf. e.g. the author, Torsion theories (1986; Zbl 0657.16017)].