An application-oriented view of modeling uncertainty. (English) Zbl 0955.91029

Zimmermann, H.-J.

Eur. J. Oper. Res. 122, No. 2, 190-198 (2000).

Summary: Uncertainty is involved in many real phenomena. Whether one considers uncertainty explicitly when modeling such a phenomenon is one of the modeling decisions, the result of which will depend on the context. If, however, the modeler decides to consider uncertainty, he or she will have to select the method for modeling it. Some scientists claim that one theory, e.g. probability theory, is sufficient to model all kinds of uncertainty. Here it is claimed, however, that the choice of the appropriate method is context dependent and an approach is suggested to determine context-dependently a suitable method to model uncertainty.

MSC:

91B30	Risk theory, insurance (MSC2010)
93A30	Mathematical modelling of systems (MSC2010)

Keywords:

modeling; risk analysis; uncertainty

References:

[1]	Atanassov, K.T., Intuitonistic fuzzy sets, Fuzzy sets and systems, 20, 87-96, (1986) · Zbl 0631.03040
[2]	Bellmann, R.; Zadeh, L.A., Decision-making in a fuzzy environment, Management science, 17B, 141-164, (1970)
[3]	Ben-Haim, Y.; Elishakoff, I., Convex models of uncertainty in applied mechanics, (1990), Elsevier Amsterdam · Zbl 0703.73100
[4]	Dubois, D.; Prade, H., Possibility theory, (1988), New York London
[5]	Dubois, D.; Prade, H., Fuzzy sets, probability and measurement, European journal of operational research, 40, 135-154, (1989) · Zbl 0663.90050
[6]	Goodman, I.R.; Nguyen, H.T., Uncertainty models for knowledge-based systems, (1985), North-Holland Amsterdam
[7]	()
[8]	Klein, R.L.; Methlie, L.B., Knowledge-based decision support systems, second ed, (1995), Wiley Chichester
[9]	Klir, G.J.; Folger, T.A., Fuzzy sets, uncertainty and information, (1988), Prentice-Hall Englewood Cliffs, NJ · Zbl 0675.94025
[10]	Klir, G.J., Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?, Fuzzy sets and systems, 24, 141-160, (1987) · Zbl 0633.94026
[11]	Newell, A.; Simon, H.A., Human problem solving, (1972), Prentice-Hall Englewood Cliffs, NJ
[12]	Pawlak, Z., Rough sets, Fuzzy sets and systems, 17, 99-102, (1985) · Zbl 0588.04004
[13]	Schneider, D., Meßbarkeit subjektiver wahrscheinlichkeiten als erscheinungsformen der ungewißheit, Zeitschrift für betriebswirtschaftliche forschung, 31, 89-122, (1979)
[14]	Shafer, G.A., 1976. A Mathematical Theory of Evidence. Princeton University Press, Princeton, NJ · Zbl 0359.62002
[15]	Sneath, P.H.A., Sokal, R., 1973. Numerical Taxonomy. San Francisco · Zbl 0285.92001
[16]	Turban, E., Decision support and expert systems, second ed, (1988), Macmillan New York
[17]	Zimmermann, H.-J.; Zysno, P., Latent connectives in human decision making, Fuzzy sets and systems, 4, 37-51, (1980) · Zbl 0435.90009
[18]	Zimmermann, H.-J., 1988. Uncertainties in Expert Models. In: Mitra, G. (Ed.), Mathematical Models for Decision Support. Springer, Berlin, pp. 613-630
[19]	Zimmermann, H.-J., 1996. Fuzzy Set Theory and its Applications, third ed., Boston · Zbl 0845.04006