×

zbMATH — the first resource for mathematics

Evidence measures based on fuzzy information. (English) Zbl 0596.62007
The evidence theory of A. P. Dempster [see J. R. Stat. Soc., Ser. B 30, 205-232 (1968; Zbl 0169.213) and Ann. Math. Stat. 38, 325-339 (1967; Zbl 0168.175)] is extended to the case of fuzzy observations and fuzzy events. The evidence measures defined are used for decision evaluation when the available knowledge is poor. In this sense the classical model of decision-making under uncertainty is thus extended to the case when the consequences of a decision are only roughly described and their probabilities of occurrence are modeled by intervals or fuzzy numbers.
Reviewer: L.Pardo

MSC:
62C99 Statistical decision theory
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
62B10 Statistical aspects of information-theoretic topics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baas, S.; Kwakernaak, H., Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, 47, (1977) · Zbl 0363.90010
[2] Baldwin, J.; Pilsworth, B.W., Fuzzy truth definition of possibility measure for decision classification, Int. J. man-machine studies, 11, 351, (1979) · Zbl 0407.94021
[3] Dempster, A.P., Upper and lower probabilities induced by a multivalued mapping, Ann. math. statist., 38, 325, (1967) · Zbl 0168.17501
[4] Dempster, A.P., A generalization of Bayesian inference, J. R. statist. soc., 30, 205, (1968), Series B · Zbl 0169.21301
[5] Dubois, D., Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications aux techniques d’aide à la décision, () · Zbl 0546.94036
[6] Dubois, D.; Prade, H., Mathematics in sciences and engng series, ()
[7] Dubois, D.; Prade, H., Additions of interactive fuzzy numbers, IEEE aut. control, AC-26, 926, (1981)
[8] Dubois, D.; Prade, H., A unifying view of comparison indices in a fuzzy set-theoretic framework, (), 3-13
[9] Dubois, D.; Prade, H., On several representations of an uncertain body of evidence, (), 167-182
[10] Dubois, D.; Prade, H., The use of fuzzy numbers in decision analysis, (), 309-322
[11] Dubois, D.; Prade, H., Upper and lower possibilistic expectations and some applications, () · Zbl 0562.94023
[12] Dubois, D.; Prade, H., Fuzzy sets and statistical data, () · Zbl 0607.00019
[13] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. sci., 30, 183, (1983) · Zbl 0569.94031
[14] Dubois, D.; Prade, H., The Mean value of a fuzzy number, (1985), In preparation · Zbl 0582.03040
[15] Freeling, A.N.S., Fuzzy sets and decision analysis, IEEE trans. syst., man and cybernet, 10, 341, (1980)
[16] Goguen, J.A., Concept representation in natural and artificial languages: axioms of fuzzy sets, Int. J. man-machine studies, 6, 513, (1974) · Zbl 0321.68055
[17] Huber, P.J., The use of Choquet capacities in statistics, Bull. int. stat. inst., 45, 181, (1973)
[18] Ishizuka, M., Inference methods based on extended Dempster-Shafer theory for problems with uncertainty/fuzziness, New generat. comput., 1, 159, (1983)
[19] Ishizuka, M.; Fu, K.S.; Yao, J.T.P., A rule-based inference with fuzzy set for structural damage assessment, (), 261-268
[20] /KampéDe Feriet, J., Interpretation of membership functions of fuzzy sets, in terms of plausibility and belief, (), 93-100
[21] Klement, E.P., Construction of fuzzy σ-algebras using triangular norms, J. math. anal. appl., 85, 543, (1982) · Zbl 0491.28003
[22] Kwakernaak, H., Random fuzzy variables. part I: definitions and theorems, Inform. sci., 15, 1, (1978) · Zbl 0438.60004
[23] Kwakernaak, H., Random fuzzy variables. part II: algorithms and examples for the discrete case, Inform. sci., 17, 253, (1979) · Zbl 0438.60005
[24] Moore, R., ()
[25] Prade, H., Compatibilité. qualification. modification. niveau de précision, (), 71
[26] Prade, H., Modèles mathématiques de l’imprécis et de l’incertain en vue d’applications au raisonnement naturel, (), June 1982 · Zbl 0491.68092
[27] Prade, H., Modal semantics and fuzzy set theory, (), 232-246
[28] Sage, A.P., Sensitivity analysis in systems for planning and decision support, J. franklin inst., 312, 265, (1981) · Zbl 0495.93024
[29] Sanchez, E., Inverses of fuzzy relations, Application to possibility distributions and medical diagnosis, Fuzzy sets and systems, 2, 75, (1979) · Zbl 0399.03040
[30] Savage, L.J., ()
[31] Shafer, G., ()
[32] Shafer, G., Constructive probability, Synthese, 48, 1, (1981) · Zbl 0522.60001
[33] Smets, P., The degree of belief in a fuzzy event, Inform. sci., 25, 1, (1981) · Zbl 0472.62005
[34] Smets, P., Probability of a fuzzy event: an axiomatic approach, Fuzzy sets and systems, 7, 153, (1982) · Zbl 0479.60009
[35] Sugeno, M., Theory of fuzzy integral and its applications, () · Zbl 0733.28014
[36] Watson, S.R.; Weiss, J.J.; Donnell, M., Fuzzy decision analysis, IEEE trans. syst., man and cybernet., 9, 1, (1979)
[37] Yager, R.R., Generalized probabilities of fuzzy events from fuzzy belief structures, () · Zbl 0525.60006
[38] Yager, R.R., Probabilities from fuzzy observations, () · Zbl 0549.60004
[39] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338, (1965) · Zbl 0139.24606
[40] Zadeh, L.A., Probability measures of fuzzy events, J. math. anal. appl., 23, 421, (1968) · Zbl 0174.49002
[41] Zadeh, L.A., Quantitative fuzzy semantics, Inform. sci., 3, 159, (1971) · Zbl 0218.02057
[42] Zadeh, L.A., Theory of fuzzy sets, () · Zbl 0377.04002
[43] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3, (1978) · Zbl 0377.04002
[44] Zadeh, L.A., PRUF: a meaning-representation language for natural languages, Int. J. man-machine studies, 10, 395, (1978) · Zbl 0406.68063
[45] Zadeh, L.A., On the validity of Dempster’s rule of combination of evidence, ()
[46] Zadeh, L.A., Fuzzy sets and information granularity, (), 3-18 · Zbl 0377.04002
[47] Zadeh, L.A., The role of fuzzy logic in the management of uncertainty in expert-systems, Fuzzy set and systems, 11, 199, (1983) · Zbl 0553.68049
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.