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Statistical estimation with linguistic data. (English) Zbl 0588.62006
Suppose the distribution of a population is characterized by a parameter \(\Gamma\), whose value is not numerical, as usually is the case, but linguistic. The problem is to make a good guess about \(\Gamma\), especially in the case when only linguistic data are available. In this paper the theory of fuzzy random variables is used to solve this problem: A method for the construction of consistent and unbiased estimates is given.

62B10 Statistical aspects of information-theoretic topics
62A01 Foundations and philosophical topics in statistics
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
Full Text: DOI
[1] Mizumoto, M.; Tanaka, K., Some properties of fuzzy numbers, (), 153-165
[2] Kwakernaak, H., Fuzzy random variables. part 1: definitions and theorems, Inform. sci., 15, 1-15, (1978) · Zbl 0438.60004
[3] Kwakernaak, H., Fuzzy random variables. part 2: algorithms and examples for the discrete case, Inform. sci., 17, 253-278, (1979) · Zbl 0438.60005
[4] Kruse, R., The strong law of large numbers for fuzzy random variables, Inform. sci., 28, 233-241, (1982) · Zbl 0571.60039
[5] Kruse, R., Schätzfunktionen für parameter von unscharfen zufallsvariablen, (1983), Habilitationsschrift Braunschweig
[6] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its applications to approximate reasoning. part 3, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[7] Rohatgi, V.K., An introduction to probability theory and mathematical statistics, (1976), Wiley New York · Zbl 0354.62001
[8] Miyakoshi, M.; Shimbo, M., A strong law of large numbers for fuzzy random variables fuzzy sets and systems, 12, 133-142, (1984) · Zbl 0551.60035
[9] Ralescu, D., Fuzzy logic and statistical estimation, () · Zbl 0503.62009
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