On a refinement of method for solving possibilistic optimization problems of one class with mutually Tw-related parameters

I. S. Soldatenko

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 1 (2016), pp. 13-32

Résumé

We refine results that were obtained in [1-3]. In the mentioned papers an indirect method of solving the possibilistic optimization problem with fuzzy parameters of $\mathrm{(L,R)}$-type based on model of maximizing the level of fuzzy goal achievement in the context of weakest $t$-norm was constructed. In these works during the process of finding the distribution function of weighted sums involved in the construction of criteria and constraints it was assumed that the parameters of the optimization problem were mutually $T_W$-related. However later task's model space was being replaced while assuming that weighted sums and free terms are min-related. In this paper the above mentioned possibilistic optimization problem is investigated fully in the context of the weakest $t$-norm. A numerical example shows a comparative analysis of solving the optimization problem in 4 different cases: in "crisp" context, in mutaully min-related context, mutually $T_W$-related context and the dual $T_W$-$T_M$ context, based on the replacement of model set in the course of solving the problem.

Détail

Keywords: possibilistic optimization, aggregation of fuzzy information, the weakest triangular norm, indirect method.
Mots-clés : $t$-norm, $\mathrm{(L,R)}$-type distributions