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A characterization of triangular norm based tribes

In: Tatra Mountains Mathematical Publications, vol. 3, no. 2
Mirko Navara
Detaily:
Rok, strany: 1993, 161 - 166
O článku:
We study collections of fuzzy sets which are closed under complementation and under countable products (interpreted as “fuzzy intersectionsrdquo;). We characterize them as certain spaces of functions measurable with respect to the $σ$-algebra of crisp elements. This solves the problem stated in [R. Mesiar: Fundamental triangular norm based tribes and measures, J. Math. Anal. Appl. 177 (1993), 633–640] and [R. Mesiar: Fuzzy sets and probability theory, Tatra Mountains Math. Publ. 1 (1992), 105–123] and enables a generalization of results of [D. Butnariu, E. P. Klement: Triangular norm-based measures and their Markov-kernel representation, J. Math. Anal. Appl. 162 (1991), 111–143], [E. P. Klement: Construction of fuzzy $σ$-algebras using triangular norms, J. Math. Anal. Appl. 85 (1982), 543–565], [E. P. Klement, R. Lowen, W. Schwyhla: Fuzzy probability measures, Fuzzy Sets and Systems 5 (1981), 21–30], [R. Mesiar: Fundamental triangular norm based tribes and measures, J. Math. Anal. Appl. 177 (1993), 633–640].
Ako citovať:
ISO 690:
Navara, M. 1993. A characterization of triangular norm based tribes. In Tatra Mountains Mathematical Publications, vol. 3, no.2, pp. 161-166. 1210-3195.

APA:
Navara, M. (1993). A characterization of triangular norm based tribes. Tatra Mountains Mathematical Publications, 3(2), 161-166. 1210-3195.