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

Abstract

SUMMARYResults 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.

Multicriteria analysis based on constructing payoff matrices and applying methods of decision making in fuzzy environment

“…The results of Ekel and Galperin (2003), Canha et al (2007), Ekel et al (2007) show that the use of the product operator leads to solution more harmonious than solutions obtained on the basis of the traditional multicriteria methods (in particular, scalarization techniques) (Rao 1996;Ehrgott 2005). However, the use of the min operator provides solutions more harmonious than solutions obtained with applying product operator.…”

“…Thus, it is possible to assert that the selection of the operators, to a significant extent, is experience-based. Considering this, the works of Ekel and Galperin (2003), Canha et al (2007), Ekel et al (2007) include results of computing experiments with the min operator as well as with the product operator (which is one of a family of t-norm operators, for instance Yager (1988), and has found quite visible position in decision making problems) reducing (6) to…”

“…In this context, two classes of models, so-called X, M and X, R , models may be constructed (Ekel 2002;Canha et al 2007). The X, M models correspond to multiobjective decision making problems (Lu et al 2007).…”

A consensus model for Delphi processes with linguistic terms and its application to chronic pain in neonates definition

“…In [18] a review of consensus models in a fuzzy environment can be found. There is, nowadays, a wide range of areas of application for these methods, from managerial to medical or engineering [6,8,10,30]. In particular, some fuzzy Delphi approaches have been proposed to deal with uncertainty and linguistic information [9,12,27].…”

Analysis of typical problems and methods in Higher Algebra

“…Only when students master the essential knowledge of advanced algebra can they have a thorough understanding of such courses. Therefore, we must recognize the fundamental role of higher algebra, higher algebra knowledge only through learning, students can study specialized knowledge for the follow-up basis and conditions, to lay the foundation for the better development after [4].…”