Анализ чувствительности выбора к изменению параметров частичных отношений предпочтений
An approach to sensitivity (stability) analysis of nondominated alternatives to changes in the bounds of intervals of value tradeoffs, where the alternatives are selected based on interval data of criteria tradeoffs is proposed. Methods of computations for the analysis of sensitivity of individual nondominated alternatives and the set of such alternatives as a whole are developed.
The influence of the assumption about the existence of cardinal coefficients of criteria importance, consistent with the importance ordering of criteria (according to the definitions in the criteria importance theory), on the preference relation generated by this information, is investigated.
Influence of the assumption about the existence of quantitative coefficients of criteria importance, consistent with the criteria importance order (according to the definitions in the criteria importance theory), on the preference relation, generated by this information, is investigated.
We consider the problem of selecting a predetermined number of objects from a given finite set. It is assumed that the preferences of the decisionmaker on this set are only partially known. Our solution approach is based on the notions of optimal and non-dominated subsets. The properties of such subsets and the objects they contain are investigated. The implementation of the developed approach is discussed and illustrated by various examples.
This abstract offers a method for ranking alternatives in a decison making problem. It determines importance of the criteria with help of factor analysis. Though the alternatives are evaluated by each of the criteria by a group of experts, the weights for the criteria are to be found with the help of factor analysis.
The algorithm of the method is as follows:
1. Under the constraint that the problem handles several evaluation criteria, several items to compare (alternatives) and several experts to give their evaluation.
2. Find the principal components that replace the input criteria implicitly.
3. To find the final mark for each of the alternatives the marks given by experts are multiplied with the regression coefficients, found in the step 2.
4. The final marks are represented in axes „crieria“ and „mark“ so that each alternative is described with a curve (trajectory). These curves represent the map of graded alternatives. Depending on the problem to be solved (min or max,) a record for each main criteria is to be found.
5. With help of special deviation measure procedures (Minkowski, Chebyshev e.t.s) a matrix of deviations from ideal solution is to be built.
6. The alternatives are to be rated in accordance to the deviation from the ideal trajectory.
To prove the effectiveness of the method it was applied to a problem for 5 alternatives, 3 experts and 38 evaluation criteria. The problem was also solved with the help of most popular method of Weighted Sum Model (WSM) and TOPSIS method. The problem was also being solved by finding the geometric mean for each alternative. The results for approaches were compared and the method, offered in this abstrat, proved itself as a feasible one.
WE present a general approach to the solution of the multicriteria choice problem by methods of the Criteria importance theory. The overview of methods of vector estimates comparison by preference using various types of information about the preferences of the decision-maker is given. These methods are implemented in the computer system DASS.