Evaluating the best main battle tank using fuzzy decision theory with linguistic criteria evaluation

To face the reality of practical multiple criteria problems usually possessing characters of fuzziness, and to consider group decision making with various subjective–objective backgrounds usually participating in decision-making process. In this paper, the experts' opinions are described by linguistic terms which can be expressed in trapezoidal (or triangular) fuzzy numbers. To make the consensus of the experts consistent, we utilize fuzzy Delphi method to adjust the fuzzy rating of every expert to achieve the consensus condition. For the aggregate of many experts' opinions, we take the operation of fuzzy numbers to get the mean of fuzzy rating, {x∼}ij and the mean of weight, {w∼}−j. In multi-alternatives and multi-attributes cases, the fuzzy decision matrix {X∼}=[{x∼}ij]m×n is constructed by the mean of the fuzzy rating, {x∼}ij. Then, we can derive the aggregate fuzzy numbers by multiplying the fuzzy decision matrix with the corresponding fuzzy attribute weights. The final results become a problem of ranking fuzzy numbers. We also propose an easy procedure of using fuzzy numbers to rank aggregate fuzzy numbers Ãi. In this way, we can obtain the best selection for evaluating system. For practical application, we propose an algorithm for evaluating the best main battle tank by fuzzy decision theory and compare it with other method.