×

Connections between some criteria to compare fuzzy information systems. (English) Zbl 0705.94027

Summary: In previous papers we have examined the extension of some methods to compare random experiments to the case in which the available experiment information is fuzzy. In this paper we analyze the relationships between the criteria based on Blackwell’s sufficiency and some criteria based on well-known information measures.

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
94A17 Measures of information, entropy
94A15 Information theory (general)
Full Text: DOI

References:

[1] Bezdek, J. C., Pattern Recognition with Fuzzy Objective Function Algorithms (1981), Plenum Press: Plenum Press New York · Zbl 0503.68069
[2] Blackwell, D. A., Comparison of experiments, (Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability (1981), University of California Press: University of California Press Berkeley, CA), 93-102 · Zbl 0044.14203
[3] Blackwell, D. A., Equivalent comparison of experiments, Ann. Math. Statist., 24, 265-272 (1953) · Zbl 0050.36004
[4] Csiszár, I., Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar., 2, 299-318 (1967) · Zbl 0157.25802
[5] DeGroot, M. H., Optimal Statistical Decisions (1979), McGraw-Hill: McGraw-Hill New York
[6] Ferentinos, K.; Papaioannou, T., New parametric measures of information, Inform. and Control, 51, 193-208 (1981) · Zbl 0524.62005
[7] Ferentinos, K.; Papaioannou, T., Information in experiments and sufficiency, J. Statist. Plann. Inference, 6, 309-317 (1982) · Zbl 0492.62004
[8] García-Carrasco, M. P., Cantidad de información de Fisher, Trabajos Estadíst. Investigación Oper., 32, 13-42 (1981) · Zbl 0508.62008
[9] Gil, M. A., On the loss of information due to fuzziness in experimental observation, Ann. Inst. Statist. Math., 40, 627-639 (1988) · Zbl 0692.62004
[10] M.A. Gil and M.T. López, The Fisher information associated with a fuzzy information system, Inform. Sci.; M.A. Gil and M.T. López, The Fisher information associated with a fuzzy information system, Inform. Sci. · Zbl 0778.62006
[11] Gil, M. A.; López, M. T.; Gil, P., Comparison between fuzzy information systems, Kybernetes, 13, 242-251 (1984) · Zbl 0552.94030
[12] Gil, M. A.; López, M. T.; Gil, P., Quantity of information; comparison between information systems: 1. Nonfuzzy states. 2. Fuzzy states, Fuzzy Sets and Systems, 15, 129-145 (1985) · Zbl 0559.94003
[13] Goel, P. K.; DeGroot, M. H., Comparison of experiments and information measures, Ann. Statist., 7, 1066-1077 (1979) · Zbl 0412.62004
[14] Kale, K., A note on the loss of information due to grouping of observations, Biometrika, 51, 495-497 (1964) · Zbl 0137.12801
[15] Kullback, S., Information Theory and Statistics (1968), John Wiley: John Wiley New York · Zbl 0149.37901
[16] Le Cam, L., Sufficiency and approximate sufficiency, Ann. Math. Statist., 35, 1419-1455 (1964) · Zbl 0129.11202
[17] Lehmann, E. L., Comparing location experiments, Ann. Statist., 16, 521-533 (1988) · Zbl 0672.62008
[18] Lindley, D. V., On a measure of the information provided by an experiment, Ann. Math. Statist., 27, 986-1005 (1956) · Zbl 0073.14103
[19] Menéndez, M. L., Tratamiento de la Información en Sistemas de Información Difusos, (Ph.D. Thesis (1986), Universidad Politécnica: Universidad Politécnica Madrid)
[20] Menéndez, M. L.; Pardo, J. A.; Pardo, L., Sufficient fuzzy information systems, Fuzzy Sets and Systems, 32, 81-89 (1989) · Zbl 0674.94030
[21] Pardo, L.; Menéndez, M. L.; Pardo, J. A., The \(f^∗- divergence\) as a criterion of comparison between fuzzy information systems, Kybernetes, 15, 189-194 (1986) · Zbl 0606.94002
[22] Pardo, L.; Menéndez, M. L.; Pardo, J. A., The information energy gain as a criterion of comparison between fuzzy information systems, (Proceedings Eighth European Meeting on Cybernetics and Systems Research (1986), Kluwer: Kluwer Dordrecht), 599-606 · Zbl 0617.94016
[23] Pardo, L.; Menéndez, M. L.; Pardo, J. A., A sequential selection method of a fixed number of fuzzy information systems based on the information energy gain, Fuzzy Sets and Systems, 25, 97-105 (1988) · Zbl 0642.94053
[24] Puri, M. L.; Ralescu, D. A., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1985) · Zbl 0592.60004
[25] Puri, M. L.; Ralescu, D. A., The concept of normality for fuzzy random variables, Ann. Probab., 13, 1373-1379 (1986) · Zbl 0583.60011
[26] Ruspini, E., A new approach to clustering, Inform. and Control, 15, 22-32 (1969) · Zbl 0192.57101
[27] Ruspini, E., Numerical methods for fuzzy clustering, Inform. Sci., 2, 319-350 (1970) · Zbl 0205.21301
[28] Stone, M., Non-equivalent comparisons of experiments and their use for experiments involving location parameters, Ann. Math. Statist., 32, 326-332 (1961) · Zbl 0113.34303
[29] Tanaka, H.; Okuda, T.; Asai, K., Fuzzy information and decision in statistical model, (Advances in Fuzzy Sets Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 303-320
[30] Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606
[31] Zadeh, L. A., Probability measures of fuzzy events, J. Math. Anal. Appl., 23, 421-427 (1968) · Zbl 0174.49002
[32] Zadeh, L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1, 3-28 (1978) · Zbl 0377.04002
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.