Modelos e métodos de tomada de decisões multiobjetivo em ambiente com incertezas e suas aplicações

Abstract

This work is dedicated to the development of general approaches and methods for decision making with the consideration of uncertainty and multicriteria factors using fuzzy set theory. The methodological ground for the development of this work is related to the Bellman-Zadeh approach to decision making in a fuzzy environment for the analysis of multiobjective decisions making (<X, M> models). This approach served as a basis for the development of a general scheme for multiobjective decision making, which allows one to use mechanisms for modeling the preferences of a decision maker in natural language by the use of linguistic terms and the corresponding fuzzy sets. The use of these mechanisms permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving the solutions quality. The use of the Bellman-Zadeh approach, together with the generalization of the classical approach to decision making under uncertainty environment, allowed the construction of two general approaches to the consideration of the uncertainty of the initial quantitative information in multicriteria decision making problems. The first approach is associated with the construction and analysis of payoff matrices that reflect the effects of different solution alternatives in different scenarios. The second approach is based on using aggregated objective functions, constructed from the evaluation functions proposed in the classical approach to solutions analysis under uncertainty environment. The use of the results of this work should increase the adequacy of the constructed multiobjective decision-making models and, consequently, the foundation and factual efficiency of solutions obtained on the basis of these models. From the viewpoint of technological applications, the approaches developed in this work were used to solve problems of multiobjective resource allocation (or their shortage) and multiobjective optimization of network configuration in distribution systems. The results have a universal character and can be used in the design, planning, operation, and control of systems and processes of different natures.