Abstract
An LP (Linear Programing) problem is studied under the assumption that the right hand sides of the contraint inequalities are independently distributed normal r.v.’s (random variables) with fuzzy mean values and fuzzy standard deviations.
A version of Charnes-Cooper’s method is formulated and possible extensions of the approach are suggested.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications. Academic Press, New York (1980).
Dubois, D. and Prade, H., Ranking fuzzy numbers in the setting of possibility theory. Information Science 30, 183–224 (1983).
Dubois, D., Linear pragramming with fuzzy data, in: J.C.Bezdek (Ed.), The Analysis of Fuzzy Information, C.R.C. Press, Boca Raton (1986).
Luhandjula, M.K., Linear pragramming under randomness and fuzziness. Fuzzy Sets and System, 10, 45–55 (1983).
Orlovski, S.A., Problems of Decision-Making with Fuzzy Information. Nauka Publishers, Moscow (1981) in Russian.
Ruszkowski, J. and Rosłonek, E., The Bayesian sequential model with the range-based probability estimation. Kybernetika 18, 278–289 (1982).
Vajda, S., Probabilistic Programming. Academic Press, New York (1972).
Wierzchoń, S.T., Linear programming with fuzzy sets: A general approach. Mathl. Modelling 9, 447–459, 1987.
Yager, R.R., Fuzzy prediction based on regression models. Information Sciences 26, 45–63 (1982).
Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–29 (1978).
Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning.Information Sciences (Part 2) 8, 301–357 (1975).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Wierzchoń, S.T. (1988). Randomness and Fuzziness in a Linear Programming Problem. In: Kacprzyk, J., Fedrizzi, M. (eds) Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46644-1_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-46644-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50005-6
Online ISBN: 978-3-642-46644-1
eBook Packages: Springer Book Archive