Analyzing and solving problems of decision making with parametric fuzzy

M. G. Matveev

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 4, pp. 14-29

Résumé

The method of solution of decision making problems presented as models with parameters in the form of LR fuzzy numbers is proposed. This methodic is based on using of $\alpha $-level representation of fuzzy numbers, their subsequent modification by a convex linear transformation of the boundaries of $\alpha $-intervals, preserving the basic characteristics of fuzziness, proposed algebra of modified fuzzy numbers and a convex linear combination of the boundaries of $\alpha$-change interval. Bounded growth of uncertainty in fuzzy information processing, preservation of natural interpretation of intermediate and final results of calculations and the possibility of algorithm realization in software environments working with real numbers are the advantages of the proposed method. The usage of the $\alpha$-level representation causes the problem of fuzzy solutions stability. We give the definition of stability for solutions in the form of a fuzzy point in $n$-dimensional space and in the form of a fuzzy function. For several kinds of problems we give a stability criteria, which is easily verified in practical calculations. We have examples of solving the problems with parametric fuzziness using the proposed method, confirming the validity of the results.

Détail

Keywords: the models with parametric fuzziness; LR-fuzzy numbers; $\alpha$-level representation; algebra of fuzzy numbers; stability of fuzzy solution.