Kibern. vyčisl. teh., 2015, Issue 179, pp 34-44.
Mashchenko Sergei O., Dr (Phys. & Math.), Professor of the Deparment of System Analysis and Decision Theory of Taras Shevchenko National University of Kyiv, Acad.Glushkova Ave., 4, Kiev, 03187, Ukraine, e-mail: email@example.com
Shusharin Yurii V., PhD (Phys. & Math.), Associate Professor of the Department of Higher Mathematics of the Vadim Hetman Kiev National Economic University, Victory Ave., 54/1, Kyiv, 03680, Ukraine, e-mail: firstname.lastname@example.org
MINIMAX REGRET CRITERION IN DECISION MAKING PROBLEMS WITH THE FUZZY SET OF STATES OF THE ENVIRONMENT
Introduction. In this work, the problem of alternatives rational choice in the conditions of uncertainties with the fuzzy set of states of the environment is considered. A need for the solving of such problems arises, when a decision making person cannot expressly indicate, what states of nature will affect the consequences of the alternatives choice in a problem which was appeared at the moment of the decision making. In this case, it can only set the belonging function of a fuzzy set of relevant nature states.
The purpose of the article is the application of the known minimax regret principle for construction of a fuzzy criterion of minimax regret in the conditions of uncertainties with the fuzzy set of nature states.
Methods. The methods of the fuzzy set theory, fuzzy mathematical programming, multicriterion optimization are used in this work.
Results. It is suggested to estimate every alternative of the decision making problem by a fuzzy set of the guaranteed regrets, which can be obtained as a set of maximal values function of results utility on the fuzzy set of nature states. The solving of the problem with a fuzzy set of nature states by the fuzzy criterion of minimax regret is determined as a fuzzy set of non-dominated alternatives according to a specially built fuzzy relation of preference. The method of choice of the best-by-regret alternative with the degree of membership to the fuzzy set of decisions not less than the set number is offered. For this purpose, it is suggested to solve the system of two problems of mathematical programming of the special kind.
Conclusion. The offered method of problem solving in the conditions of uncertainties with the fuzzy set of nature states can be easily generalized in the case of a fuzzy set of alternatives and fuzzy estimations of results utility. For this purpose, it is enough to use the known technique of defuzzification.
Keywords: decision making, uncertainties, fuzzy set, the L. Savage criterion, maximizing decision.
- Truhaev R.I. Models of decision making in the conditions of uncertainties. Moscow: Science, 1981, 258 p. (in Russian).
- Mashchenko S.O. Generalization Germeyer’s criterion in the decision making problem in conditions of uncertainty with the fuzzy set of nature states. Journal of Automation and Information Sciences, 2012, no. 5, pp. 102–110 (in Russian). https://doi.org/10.1615/JAutomatInfScien.v44.i10.20
- Orlovsky S.A. Problems of decision making at fuzzy initial information. Moscow: Science, 1981, 208 p. (in Russian).