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Models and methods of decision making in fuzzy environment and their applications to power engineering problems

Results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems are presented. Two types of situations which need the application of a multicriteria approach are classified. According to this, two classes of models (〈X, M〉 and 〈X, R〉 models) are considered with utilizing the Bellman–Zadeh approach to decision making in a fuzzy environment and techniques for modelling of fuzzy preference relations for their analysis. The application of the Bellman–Zadeh approach for solving 〈X, M〉 problems conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analysing associated maxmin problems. Analysis of 〈X, R〉 models is considered as part of a general approach to solving problems with fuzzy coefficients. Three techniques for processing of fuzzy preferences relations are considered. The first technique is associated with building and analysing a membership function of a subset of non‐dominated alternatives considering all criteria simultaneously. The second technique is of a lexicographic character and consists in step‐by‐step consideration of criteria. The third technique is based on aggregating membership functions of subsets of non‐dominated alternatives for each criterion. The results of the paper are universally applicable and are already being used to solve power engineering problems. It is illustrated by considering problems of multicriteria power and energy shortage allocation, multicriteria power system operation, and substation planning with considering criteria of quantitative as well as of qualitative character. Copyright © 2007 John Wiley & Sons, Ltd.