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The strong law of large numbers for fuzzy random variables. (English) Zbl 0571.60039
Sequences of independent and identically distributed fuzzy random variables are considered. It is shown that the strong law of large numbers holds also for fuzzy random variables. This result is used to give a consistent estimator for the expectation of a fuzzy random variable.

MSC:
 60F15 Strong limit theorems 03E72 Theory of fuzzy sets, etc. 62F10 Point estimation
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References:
 [1] Kwakernaak, H., Fuzzy random variables. part 1: definitions and theorems, Inform. sci., 15, 1-15, (1978) · Zbl 0438.60004 [2] Kwakernaak, H., Fuzzy random variables. part 2: algorithms and examples for the discrete case, Inform. sci., 17, 253-278, (1979) · Zbl 0438.60005 [3] Mizumato, M.; Tanaka, K., Some properties of fuzzy numbers, (), 153-165 [4] Zadeh, L.A., The concept of a linguistic variable and its application in approximate reasoning, Inform. sci., 8, 301-357, (1975), Part 2 · Zbl 0404.68074 [5] Nguyen, H.T., On fuzziness and linguistic probabilities, J. math. anal. appl., 61, 658-671, (1977) · Zbl 0374.68057 [6] Nahmias, S., Fuzzy variables, Fuzzy sets and systems, 1, 97-110, (1978) · Zbl 0383.03038 [7] Nahmias, S., Fuzzy variables in a random environment, (), 165-180 [8] Stein, W.E.; Talati, K., Convex fuzzy random variables, Fuzzy sets and systems, 6, 217-283, (1981) · Zbl 0467.60005 [9] Hirota, K., Concepts of probabilistic set, Fuzzy sets and systems, 5, 31-46, (1981) [10] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic New York · Zbl 0444.94049 [11] Negoita, C.V.; Ralescu, D.A., Applications of fuzzy sets to system analysis, (1975), BirkhĂ¤user Basel · Zbl 0326.94002 [12] Rohatgi, V.K., An introduction to probability theory and mathematical statistics, (1976), Wiley New York · Zbl 0354.62001
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