Models and methods of decision making in fuzzy environment and their applications to power engineering problems (original) (raw)
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The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective ( , X M models) and multiattribute ( , X R models) problems are considered. The analysis of , X M models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of , X R models. A review of the authors' results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use of , X M and , X R models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.
Fuzzy set based multicriteria decision making and power engineering problems
Proceedings of the 2013 Joint International Fuzzy Systems Associations (IFSA) World Congress, North American Fuzzy Information Processing Society (NAFIPS) Annual Meeting., 2013
This paper presents results of research into the use of models and methods of multicriteria decision making in a fuzzy environment for solving power engineering problems. Two classes of models associated with multiobjective (<X, M> models) and multiattribute (<X, R> models) problems, as well as methods for their analysis are briefly discussed. A review of the authors' results related to the application of these models and methods for solving diverse types of planning and operation problems in power systems and subsystems is presented. The recent results associated with the allocation of reactive power sources and prioritization in maintenance planning in distribution systems, respectively, are discussed in more detail.
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Results of research into the use of fuzzy sets for handling various forms of uncertainty in optimization problems related to the design and control of complex systems are presented. Much attention is given to considering the uncertainty of goals that is associated with a multicriteria character of many optimization problems. The application of a multicriteria approach is needed to solve (1) problems in which solution consequences cannot be estimated on the basis of a single criterion, that involves the necessity of analyzing a vector of criteria, and (2) problems that may be considered on the basis of a single criterion but their unique solutions are not achieved because the uncertainty of information produces so-called decision uncertainty regions, and the application of additional criteria can serve as a convincing means to contract these regions. According to this, two classes of models ((X, M) and (X, R) models) are considered with applying the Bellman-Zadeh approach and techniques of fuzzy preference relations to their analysis. The consideration of (X, R) models is associated with a general approach to solving a wide class of optimization problems with fuzzy coefficients. This approach consists in formulating and analyzing one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective functions alone. It allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment with its analysis applying one of two techniques based on fuzzy preference relations. The results of the paper are of a universal character and are already being used to solve problems of power engineering.
Approach to decision making in fuzzy environment
Computers & Mathematics with Applications, 1999
A general approach to solving a wide class of optimization problems with fuzzy coefficients in objective functions and constraints is described. It is based on a modification of traditional mathematical programming methods and consists in formulating and solving one and the same problem within the framework of interrelated models with constructing equivalent analogs with fuzzy coefficients in objective function alone. This approach allows one to maximally cut off dominated alternatives from below as well as from above. The subsequent contraction of the decision uncertainty region is associated with reduction of the problem to multicriteria decision making in a fuzzy environment. The approach is applied within the context of fuzzy discrete optimization models, that is based on a modification of discrete optimization algorithms. The results of the paper are of a universal character and are already being used to solve problems of the design and control of power systems and subsystems. (~) 1999 Elsevier Science Ltd. All rights reserved. Keywords-Discrete optimization, Fuzzy coefficients, Nonfuzzy analog, Multicriteria selection of alternatives in fuzzy environment.
A Fuzzy Multi-Criteria Decision-Making Approach for Power Generation Problem Analysis
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The abundance of different energy sources such as coal, natural gas, and crude oil are in the Africa region, yet one of the lowest electric energy per capita consumption. Different factors have been attributed to this abysmal energy failure in the literature, leading to her slow economic and industrial advancement. These factors include poor maintenance of power generation infrastructure and lack of policy continuity, among others. The purpose of this article is to prioritize these power generation problems for proper budgetary allocation by managers of electric power. The fuzzy VIKOR technique is presented for the evaluation and ranking of these power generation problems. The analysis showed that poor maintenance is the most critical challenge of bedeviling power generation in Nigeria. The Fuzzy VIKOR produces the same result as the classical VIKOR used previously in resolving the problem. The proposed technique addresses the challenge of uncertainty and subjectivity by applying li...
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There exist two major classes of problems, which need the use of a multicriteria approach: problems whose solution consequences cannot be estimated with a single criterion and problems that, initially, may require a single criterion, but their unique solutions are unachievable, due to the existence of decision uncertainty regions, which can be contracted using additional criteria. According to this, two classes of multicriteria models ( > < M X , and > < R X , models) can be constructed. The Bellman-Zadeh approach to decision making in a fuzzy environment is utilized for analyzing > < M X , models. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The analysis of > < R X , models (which contain fuzzy preference relations as criteria of optimality) is based on fourth techniques for fuzzy preference modeling. They permit the evaluation, comparison, selection, prioritization, and/or ordering of alternatives with the use of quantitative as well as qualitative estimates based on knowledge, experience, and intuition of professionals. With the availability of different techniques, the most appropriate one can be chosen, considering possible sources of information and its uncertainty. The analysis of > < M X , and > < R X , models serves as parts of a general scheme for multicriteria decision making under information uncertainty. This scheme is also associated with a generalization of the classic approach to considering the uncertainty of information (based on analyzing payoff matrices constructed for different combinations of solution alternatives and states of nature) in monocriteria decision making to multicriteria problems. 2.
Fuzzy preference relations in models of decision making
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Analysis of X, R models is considered as part of a general approach to solving optimization problems with fuzzy coefficients. This approach involves a modification of traditional optimization methods and is associated with formulating and solving one and the same problem within the framework of mutually interrelated models by constructing equivalent analogs with fuzzy coefficients in objective functions alone. The use of the approach allows one to maximally cut off dominated alternatives. The subsequent contraction of the decision uncertainty region is based on reducing the problem to multiobjective choice of alternatives in a fuzzy environment. Three techniques for processing of fuzzy preference relations reflecting criteria of quantitative as well as qualitative character are discussed. The results of the paper are universally applicable and are already being used to solve power engineering problems.
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Computers & Mathematics With Applications, 2006
This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand's and Tsetlin's “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems.
Impact on some planning decisions from a fuzzy modelling of power systems
IEEE Transactions on Power Systems, 1994
In this paper, system component reinforcements are analyzed from the perspective of their impact in increasing flexibility in system design. The proposed framework integrates a fuzzy optimal power flow model through which one can derive, as a function of load uncertainties, possibility distributions for generation, power flows and power not supplied. Exposure and robustness indices, based on risk analysis concepts, are defined. These indices can be used to rank the expansion alternatives, giving the planner insight to system behavior in face of adverse futures. Their use in conjunction with investment assessments is proposed as a necessary step in a decision making methodology.