×

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.

MSC:

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

References:

[1] DOI: 10.1108/eb005404 · Zbl 0332.90001 · doi:10.1108/eb005404
[2] DOI: 10.1108/eb005451 · Zbl 0372.62046 · doi:10.1108/eb005451
[3] DOI: 10.1016/S0019-9958(78)90151-1 · Zbl 0401.94050 · doi:10.1016/S0019-9958(78)90151-1
[4] Tanaka H., Advances in Fuzzy Sets Theory and Applications (North-Holland pp 303– (1979)
[5] Raiffa H., Applied Statistical Decision Theory (1961) · Zbl 0107.13603
[6] DOI: 10.1007/BF02888673 · Zbl 0437.62006 · doi:10.1007/BF02888673
[7] DOI: 10.1016/0022-247X(68)90078-4 · Zbl 0174.49002 · doi:10.1016/0022-247X(68)90078-4
[8] DOI: 10.1016/0022-247X(67)90189-8 · Zbl 0145.24404 · doi:10.1016/0022-247X(67)90189-8
[9] Zadeh L. A., Mem. UCB/ERL M77/1 (1977)
[10] DOI: 10.1016/S0020-7373(76)80003-X · Zbl 0335.02037 · doi:10.1016/S0020-7373(76)80003-X
[11] Warren R. H., Equivalent fuzzy sets (1981) · Zbl 0464.04005
[12] Gil M. A., R. A. I. R. O. Rech. Oper. 16 pp 319– (1982)
[13] Gil M. A., Statistica Anno XL11 1 pp 21– (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.