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Measure in generalized fuzzy sets. (English) Zbl 1120.03312
Far East J. Math. Sci. (FJMS) 24, No. 2, 217-226 (2007).
Summary: In this article, using a construction of fuzzy sets without depending on a membership function, algebraic properties of a family of fuzzy sets, three notions, including rings of generalized fuzzy sets \(GF(X)\) of \(X\), complete Heyting algebras (cHa) which contain the power set \(P(X)\) of \(X\), extension lattices \(\overline{B(L)}\), where \(B=P(X)\), and sets of \(L\)-fuzzy sets, where \(L=\{L_x\mid x\in X\}\), definitions of fuzzy \(\sigma\)-algebra and fuzzy measure are generalized. We obtain some results using these definitions, which include a generalization of Proposition 2 in [E. P. Klement and W. Schwyhla, Fuzzy Sets Syst. 7, 57–70 (1982; Zbl 0478.28006)].

MSC:
03E72 Theory of fuzzy sets, etc.
28E10 Fuzzy measure theory
06D20 Heyting algebras (lattice-theoretic aspects)