Multicriteria Decision-Making Under Conditions of Uncertainty

4<X, F> Models of Multicriteria Decision‐Making and Their Analysis

In this chapter, we concentrate on the construction, analysis, and application of models of multiobjective decision‐making (in the form of <X, F> models). The basic concepts related to multicriteria decision‐making are presented. The commonly utilized approaches to multiobjective decision‐making are discussed. A great deal of attention is paid to the Bellman–Zadeh approach to decision‐making in a fuzzy environment and its applications to multicriteria problems. Its application helps one to develop harmonious solutions, providing a rigorous as well as a computationally effective method of analyzing multiobjective models. The last circumstance opens a way for solving problems of short‐term planning, operation, and control on a multicriteria basis. The questions of applying the ordered weighted average (OWA) operator are discussed. Its use is crucial to the implementation of several concepts of optimality, taking into account the level of optimism or pessimism of a DM. An important class of problems of multiobjective allocation of resources or their shortages is considered separately. The corresponding <X, F> models are constructed with the use of an original approach to the homogeneous and expert‐acceptable formulation of specific objectives. The use of the presented results is illustrated by solving problems coming from power engineering area as well as problems of strategic planning.

4.1 Models of Multiobjective ...