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Bipolar is one of the Multiple Attribute Decision Making methods, based on the concept of Bipolar reference objectives, proposed by Konarzewska-Gubala. The essence of the analysis in the Bipolar method consists in a fact that the decision... more
Bipolar is one of the Multiple Attribute Decision Making methods, based on the concept of Bipolar reference objectives, proposed by Konarzewska-Gubala. The essence of the analysis in the Bipolar method consists in a fact that the decision alternatives are not compared directly to each other, but they are confronted to the two sets of reference objects: desirable and non-acceptable. Practical application of the method showed some its shortcomings. It may happen that a decision alternative can be evaluated as better than a desirable reference object and simultaneously as worse than a non-acceptable object. The aim of the paper is to formulate modifications of the classical Bipolar approach to overcome such difficulties.
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ABSTRACT This paper presents a model of dynamic, discrete, decision-making problem with partially ordered set (exactly the set with transitive and antisymmetric relation). We also show Bellman’s principle of this kind of a problem by... more
ABSTRACT This paper presents a model of dynamic, discrete, decision-making problem with partially ordered set (exactly the set with transitive and antisymmetric relation). We also show Bellman’s principle of this kind of a problem by means of properties of maximal elements. Numerical procedures are formulated and all example is given for illustrative purposes. In this example we apply fuzzy parameters of the model.
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AbstractMulti-criteria, multi-period discrete decision problems are considered. It is assumed that the decision maker has fixed single hierarchy in the set of multi-period criteria.The paper aims at discribing hierarchical approach to... more
AbstractMulti-criteria, multi-period discrete decision problems are considered. It is assumed that the decision maker has fixed single hierarchy in the set of multi-period criteria.The paper aims at discribing hierarchical approach to multi-criteria discrete dynamic programming. Then, a new interactive hierarchical dynamic programming technique based on the concept of period structure of considered solution is introduced. In the following stages we consider next criteria, one by one, using single objective dynamic programming method and we reduce sets of states and decisions according to the decision maker’s period requirments. After the last stage the decision maker is asked to point to one solution which suits him best. This solution is tested and, if it is not efficient, the set of efficient solutions better than the chosen one is constructed and presented. The decision maker can choose the final solution among the indicated solutions. If he is not satisfied, he can:– point to another solution and repe...
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Dynamic programming is classically concerned with maximization of the value assigned by a real-valued function defined over sequences of decisions. Multi-criteria (multi-objective) dynamic programming extends the approach to a... more
Dynamic programming is classically concerned with maximization of the value assigned by a real-valued function defined over sequences of decisions. Multi-criteria (multi-objective) dynamic programming extends the approach to a vector-valued criterion function. The main purpose of the paper is to give new definitions of separability and monotonicity which allow to extend the theory of discrete multiobjective dynamic programming. The vector principle of optimality and theorems applied in decomposition methods are formulated. Numerical algorithms for such problems are briefly described. The paper ends with examples which illustrate the numerical aspects of the procedures.
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This paper describes problems arising in multiple objective discrete dynamic programming with single and group hierarchy of criteria. Computer implementation of numerical procedures are also shortly presented.
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Research Interests: Mathematics and ELECTRE
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In this paper we consider a multi-stage, multi-criteria discrete decision process under risk. We use a discrete, stochastic dynamic programming approach based on Bellman’s principle of optimality. We assume that the decision maker... more
In this paper we consider a multi-stage, multi-criteria discrete decision process under risk. We use a discrete, stochastic dynamic programming approach based on Bellman’s principle of optimality. We assume that the decision maker determines a quasi-hierarchy of the criteria considered; in other words, he or she is able to determine to what extent the optimal expected value of a higher-priority criterion can be made worse to improve the expected value of a lower-priority criterion. The process of obtaining the final solution can be interactive. Based on the observations of the consecutive solutions, the decision maker can modify the aspiration levels with respect to the criteria under consideration, finally achieving a solution which satisfies him/her best. The method is illustrated on an example based on fictitious data.
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Multi-stage, multi-criteria discrete decision processes under risk are considered and Bellmans principle of optimality is applied. Quasi-hierarchy of multi-period criteria is determined by the decision maker. The aim of the paper is to... more
Multi-stage, multi-criteria discrete decision processes under risk are considered and Bellmans principle of optimality is applied. Quasi-hierarchy of multi-period criteria is determined by the decision maker. The aim of the paper is to propose an algorithm to solve quasi-hierarchical problem according to decision maker’s requirements. The process of obtaining the final solution is interactive.