T ∞-Fuzzy observables
Tóm tắt
Observables are defined as homomorphisms from the Borelσ-algebra into a family of fuzzy sets considered with respect to the Giles connectives. Algebraic operations with observables are introduced and their relation to the corresponding operations with fuzzy random variables is explained.
Tài liệu tham khảo
Butnariu, D., and Klement, E. P. (1991). Triangular norm-based measures and their Markov kernel representation,Journal of Mathematical Analysis and Its Applications,162, 111–143.
Dvurečenskij, A., and Riečan, B. (1991). Fuzzy quantum models,International Journal of General Systems,20, 39–54.
Dvurečenskij, A., and Tirpáková, A. (1988). A note on a sum of observables inF-quantum spaces and its properties,Busefal,35, 132–137.
Höhle, U. (1976). Masse auf unscharfen Mengen,Zeitschrift für Wahrscheinlichtkeitstheorie und Verwandte Gebiete,36, 179–188.
Höhle, U. (1981). Representations theorems for fuzzy quantities,Fuzzy Sets and Systems,5, 83–107.
Klement, E. P. (1985). Integration of fuzzy valued functions,Revue Roumaine de Mathématiques Pures et Appliquées,30, 375–384.
Klement, E. P. (1987). Strong law of large numbers for random variables with values in the fuzzy real line,Communications of IFSA Mathematics Chapter,1987, 7–11.
Kolesárová, A., and Riečan, B. (1992).T-fuzzy observables,Tatra Mountains Mathematical Publications,1, 73–82.
Mesiar, R. (1993). Fuzzy measurable functions, to appear.
Pykacz, J. (1991) Fuzzy sets ideas in foundation of quantum mechanics, inIFSA 91, Brussels, Computer Management and System Science, D. Dubois, R. Lowen, and M. Rubens, eds., pp. 205–208.
Rodabaugh, S. E. (1982). Fuzzy addition in theL-fuzzy real line,Fuzzy Sets and Systems,8, 39–52.
Schweizer, B., and Sklar, A. (1983).Probabilistic Metric Spaces, North-Holland, Amsterdam.