Comparison between fuzzy information systems. (English) Zbl 0552.94030

In the statistical decision problem, the decision maker can choose among several actions whose consequences depend upon the state of nature. This choice is usually made on the basis of the outcome of an experiment selected from a set of potential experiments for which the distribution depends upon the state of nature.
When the information provided by the performance of a potential experiment can only be known in an approximate way, we assimilate this information with a fuzzy information and the decision problem with a fuzzy decision problem [H. Tanaka, T. Okuda and K. Asai, Adv. Fuzzy Sets Theor. Appl., 303-320 (1979; Zbl 0434.94026)].
In this paper a selection among the possible experiments providing fuzzy information is suggested. This selection compares two of them by means of the worth of information of a fuzzy information system (defined by H. Tanaka et. al. as an extension of the ”expected value of sample information” [cf. H. Raiffa and R. Schlaifer, Applied statistical decision theory (1968; Zbl 0181.218)] to the fuzzy case). The suitability of the suggested method is proven by examining several natural properties.


94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
62C10 Bayesian problems; characterization of Bayes procedures
Full Text: DOI


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