Abstract
The main objective of this paper is to formulate an “uncertain” counterpart of a minimum-norm problem in the form of primary and secondary optimization problems using the concept of uncertain norms.
Similar content being viewed by others
References
Luenberger, D. G.,Optimization by Vector Space Methods, Wiley, New York, New York, 1969.
Poincaré, H.,Science and Hypothesis, Science Press, Lancaster, Pennsylvania, 1905.
Schweppe, F. C.,Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
Kacprzyk, J.,Multistage Decision Making under Fuzziness, Verlag TUV Rheiland, Cologne, Germany, 1983.
Dubois, D., andPradé, H.,Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York, New York, 1980.
Mizumoto, M., andZimmermann, H. J.,Comparison of Fuzzy Reasoning Methods, Fuzzy Sets and Systems, Vol. 8, pp. 253–283, 1982.
Swierniak, A.,What Is Optimal in a Fuzzy Environment? International Journal of Control, Vol. 50, pp. 1763–1770, 1989.
Menger, K.,Statistical Metrics, Proceedings of the National Academy of Sciences, USA, Vol. 28, pp. 535–537, 1942.
Schweizer, B., andSklar, A.,Statistical Metric Spaces, Pacific Journal of Mathematics, Vol. 10, pp. 313–334, 1960.
Schweizer, B., andSklar, A.,Probabilistic Metric Spaces, North-Holland, Amsterdam, Holland, 1983.
Klement, E. P.,Construction of Fuzzy σ-Algebras Using Triangular Norms, Journal of Mathematical Analysis and Applications, Vol. 85, pp. 543–565, 1982.
Leitmann, G., Editor,Multicriteria Decision Making and Differential Games, Plenum Press, New York, New York, 1976.
Author information
Authors and Affiliations
Additional information
Communicated by W. Stadler
This work was supported partly by the Committee of Scientific Research (KBN).
Rights and permissions
About this article
Cite this article
Swierniak, A.P. On optimality in an uncertain environment. J Optim Theory Appl 71, 189–193 (1991). https://doi.org/10.1007/BF00940046
Issue Date:
DOI: https://doi.org/10.1007/BF00940046