Abstract
We concern ourselves with the problem of determining the overall degree or measure of realization of an object based upon its occurrence in a collection of individual phenomena. We show that while probability is the classic measure of this type, it is but one of a whole family of possible such measures. We use the OWA operator to provide this family of measures. We investigate the situation in which our observations are both specific elements and subsets of some base set.
Similar content being viewed by others
References
Dubois, D. and Prade, H.: 1982, ‘A class of fuzzy measures based on triangular norms’, International Journal of General Systems 8, 43–61.
Dubois, D. and Prade, H.: 1985, ‘A review of fuzzy sets aggregation connectives’, Information Sciences 36, 85–121.
Dubois, D. and Prade H.: 1988, ‘Modeling uncertainty and inductive inference: A survey of recent additive probability systems’, Acta Psychogica.
Shafer, G.: 1976, A Mathematical Theory of Evidence, Princeton, N.J.: Princeton University Press.
Sugeno, M.: 1974, Theory of Fuzzy Integrals and its Application, Doctoral Thesis, Tokyo Institute of Technology.
Yager, R. R. and Rubinson, T. C.: 1981, ‘Linguistic summaries of data bases’, Proc. IEEE Conf. on Decision and Control, San Diego, pp. 1094–1097.
Yager, R. R.: 1988, ‘On ordered weighted averaging aggregation operators in multicriteria decision making’, IEEE Transactions on Systems, Man and Cybernetics 18, 183–190.
Zadeh, L. A.: 1979, ‘Fuzzy sets and information granularity’, in Advances in Fuzzy Set Theory and Applications, Gupta, M. M., Ragade, R. K. and Yager, R. R. (Eds.), Amsterdam: North-Holland, pp. 3–18.
Zadeh, L. A.: 1982, ‘Possibility theory as a basis for meaning representation’, in Proceedings of Sixth Wittgenstein Symposium, Kirchberg, pp. 253–261.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yager, R.R. On generalized measures of realization in uncertain environments. Theor Decis 33, 41–69 (1992). https://doi.org/10.1007/BF00133982
Issue Date:
DOI: https://doi.org/10.1007/BF00133982