Evaluating weapon systems using ranking fuzzy numbers

In this paper, we will point out that Chen's (1996) paper has some errors. A weapon system is large and complex, it has multi-level, multi-factor and multi-hierarchy features. Chen's method does not normalize each criterion's scores, which will make a wrong decision under the following conditions: (I) there are many levels for rank scores; (II) a criterion has many factors; (III) the total scores of systems have a larger difference under this criterion, and (IV) one criterion's weight is larger than the other criteria (numerical illustration is shown in Section 5). Therefore, Chen's method is not a general method for the evaluation of weapon systems. After pointing out some errors in Chen's paper, to overcome these errors, we will revise it and propose a general method for the evaluation of weapon systems. Our method utilizes fuzzy ratio scales 1, 3, 5, 7, 9 (the goal is normalizing heterogeneity into homogeneity) to indicate the relative strength of the factors in the corresponding criteria. Then, we build a judgement matrix through comparison of the total scores of performance, and use 1, 3, 5, 7, 9 to represent a weight vector among these criteria. We will derive the priority among the alternatives by multiplying the fuzzy judgement matrix with the corresponding fuzzy weight vector; the final results become a problem of ranking fuzzy numbers. Many triangular fuzzy numbers can easily rank its ordering by the intuition ranking method. Lee and Li (1988) pointed out that human intuition would favor a fuzzy number with the following characteristics: higher mean value and at the same time lower spread. If its ordering cannot rank by figures, we can use many other methods of ranking fuzzy numbers. Therefore, the best weapon selection can be obtained by ranking fuzzy numbers.