Fuzzy set based multiobjective allocation of resources and its applications (original) (raw)
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Fuzzy set based models and methods of decision making and power engineering problems
Engineering, 2013
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.
Numerical Linear Algebra with Applications, 2007
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.
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.
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.
Reference Point and Fuzzy Approaches for Decision Support in Multiobjective Programming
IFAC Proceedings Volumes, 2002
The study of the interactions between the energy sector, its effects on the environment and the corresponding impacts on a national economy must explicitly address multiple, conflicting and incommensurate aspects of evaluation. Multiple objective programming models enable the decision makers to rationalize the comparisons among distinct alternative solutions, providing them with a better perception of the conflicting aspects under evaluation and the ability to grasp the tradeoffs to be made. Reference point approaches provide a framework to aid decision makers to search for "satisfactory" efficient solutions. Moreover, it is possible to interpret the degree of satisfaction with the values of the objective functions by means of fuzzy membership functions.
A Fuzzy System for Multiobjective Problems
IFIP — The International Federation for Information Processing
In this study, an intelligent fuzzy system is used instead of mathematical models. The main core of the system is fuzzy rule base which maps decision space (Z) to solution space (X). The system is designed on noninferior region and gives a big picture of this region in the pattern of fuzzy rules. In addition, numerical examples of well-known NP-hard problems (i.e. multiobjective traveling salesman problem and multiobjective knapsack problem) are provided to clarify the accuracy of developed system.
Fuzzy sets and models of decision making
Computers & Mathematics with Applications, 2002
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.
A general approach to solving a wide class of fuzzy optimization problems
Fuzzy Sets and Systems, 1998
Results of research into the use of fuzzy sets for handling various forms of uncertainty in the optimal design and control of complex systems are presented. A general approach to solving a wide class of optimization problems containing fuzzy coefficients in objective functions and constraints is described. It involves a modification of traditional mathematical programming methods and is associated with formulating and solving one and the same problem within the framework of mutually conjugated models. 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 general approach is applied within the context of a fuzzy discrete optimization model that is based on a modification of discrete optimization algorithms. Prior to application of these algorithms there is a transition from a model with fuzzy coefficients in objective functions and constraints to an equivalent analog with fuzzy coefficients in objective functions alone. The results of the paper are of a universal character and are already being used to solve problems of power engineering.
Multiobjective fuzzy optimization method
The paper proposes a new multiobjective optimization method, based on fuzzy techniques. The method performs a real multiobjective optimization, every parameter modification taking into account the unfulfillment degrees of all the requirements. It uses fuzzy sets to define fuzzy objectives and fuzzy systems to compute new parameter values. The strategy to compute new parameter values uses local gradient information and encapsulates human expert thinking. After introducing our optimization method, we optimize the design of a finite response filter.