Abstract
The author proposes a method to solve a mathematical programming problem with a fuzzy set of the indices of constraints. A mapping of the membership of a fuzzy set of type 2 is constructed, which is the set of its feasible alternatives. The properties of this set are analyzed and problems of the choice of rational decisions are considered.
Similar content being viewed by others
References
R. E. Bellman and L. A. Zadeh, “Decision making in a fuzzy environment,” Manag. Sci., 17, 141–162 (1970).
S. A. Orlovskii, Decision-Making Problems under Fuzzy Initial Information [in Russian], Nauka, Gl. Red. Fiz.-Mat. Lit., Moscow (1981).
Yu. P. Zaichenko, Operations Research: Fuzzy Optimization. A Handbook [in Russian], Vyshcha Shkola, Kyiv (1991).
N. V. Semenova, L. N. Kolechkina, and A. M. Nagirna, “Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives,” Cybern. Syst. Analysis, 47, No. 2, 250–259 (2011).
S. O. Mashchenko, “Fuzzy individual-optimal equilibria,” Kibern. Vych. Tekhn., Issue 159, 19–29 (2010).
V. V. Podinovskii and V. D. Nogin, Pareto-Optimal Solutions of Multicriteria Problems [in Russian], Fizmatlit, Moscow (2007).
L. A. Zadeh, “The Fundamentals of a New Approach to the Analysis of Complex Systems and Decision-Making Processes,” in: Mathematics Today [in Russian], Znanie, Moscow (1974), pp. 5–49.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika I Sistemnyi Analiz, No. 1, January–February, 2013, pp. 73–81.
Rights and permissions
About this article
Cite this article
Mashchenko, S.O. A mathematical programming problem with the fuzzy set of indices of constraints. Cybern Syst Anal 49, 62–68 (2013). https://doi.org/10.1007/s10559-013-9485-4
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-013-9485-4