Multiobjective and multiattribute decision making in a fuzzy environment and their power engineering applications

•Two classes of problems requiring the use of a multicriteria approach are defined.•Fuzzy set theory serves for aggregating information arriving from diverse sources.•Combined branches of mathematics of uncertainty serve as a new decision making tool.•The use of fuzzy set based decision making in power system problems is described.•Benefits of applying fuzzy set theory in problems of power engineering are shown.

This work presents and generalizes our experience in the use of fuzzy set theory, including its combination with another branch of mathematics of uncertainty, in developing general approaches and methods for optimization and decision making with considering the uncertainty and multicriteria factors in problems of the design, planning, operation, and control of complex systems. Two major classes of situations that require the use of a multicriteria approach are identified. In accordance with this, two general classes of models related to multiobjective (〈X, F〉 models) and multiattribute (〈X, R〉 models) problems, respectively, are considered. Methods for their analysis based on the use of the Bellman–Zadeh approach to decision making in a fuzzy environment and fuzzy preference modeling techniques, respectively, are considered. Although, the use of 〈X, F〉 and 〈X, R〉 models is of an independent character, they also serve as parts of a general scheme for multicriteria decision making under conditions of uncertainty. This scheme is associated with the use of a generalization of the classic approach to considering the uncertainty of information to multicriteria problems, based on analyzing special aggregations of payoff matrices. The authors' experience in the use of the results indicated above for solving diverse classes of power system planning and operation problems is described. This experience convincingly demonstrates diverse advantages of applying fuzzy mathematics in optimization and decision making problems of power engineering.