The Method of Determining Importance of Criteria in a Multicriteria Decision Problem
Multi-criteria group decision-making tasks require the weights of the criteria. Assigning weights importance criteria By Decision-makers (PDS) means, in essence, a priori assignment options for the winner. There are a number of problematic situations: 1) evaluate alternatives represent a degree of satisfying the basic requirements of applicants. The assessment matrix is a small variation, and a very large number of indicators (criteria); 2) application of cognitive maps for modeling of problem situations. If the alternatives are only considered pure strategies (options affect the concepts), the matrix of evaluations is small size. If the task as alternatives to the use of mixed strategies (for example, 25% of the impacts on the concept 1, 50% to 10%, 2 concept for concept 3, etc), then the matrix estimates also is becoming more dimension and 3) etc. It is clear that in such cases the appointment of weighting criteria LPR becomes a problem.
The goal: to develop a new method to obtain the weight of each criterion according to alternatives from expert group upon receipt of examination results. First, this approach allows you to more accurately determine the rate the importance of each criterion, even with their large numbers. In the second it is now believed that the importance of the criterion of is constant and is independent of the expert, as well as from the problem situation, for which the conditions are evaluated.
Methodology: propose a method to find the distances from the trajectories of alternatives for each criterion to built a perfect trajectory defined by the last method of finding commonality.
The algorithm of the proposed method is as follows:
- When a large number of indicators are the main factors that replace a baseline.
- Are the regression coefficients for each criterion for generality.
- Each evaluation of the alternatives, multiplied by every criterion found in p. 2 regression coefficients. Thus, the trajectory of each alternative are subject to Community criteria laid down in the original estimates.
- On the path alternatives for each build criterion is the highest (or lowest depending on problem solving on Max or Min) score is a "record".
- According to various metrics is the matrix of distances of deviations from the ideal trajectory of alternatives (a record) of the path.
- The largest distance for each alternative, they are ranked and, thus, is the best.
Implementation of the suggested method showed full convergence with the known method of weighting criteria for entropy in the matrix of evaluations of alternatives (TOPSIS authors Hwang Ch-L, Lin M-J).