In this paper, we propose a new algorithm for evaluating weapon systems by Analytical Hierarchy Process (AHP) based on fuzzy scales, which is a multiple criteria decision making approach in a fuzzy environment. We use the triangular fuzzy number to build the judgement matrices through the pair-wise comparison technique. From Kaufmann and Gupta [Fuzzy Mathematical Models in Engineering and Management Science (North-Holland, Amsterdam, 1988)], P = (1/a3, 1/a2, 1/a1) only approximates the inverse of triangular fuzzy number A-1 (where A = (a1, a2, a3)), which is due to A-1 is maybe no longer a fuzzy number. Therefore, we revise Juang and Lee's fuzzy number 9 [IFES (1991) 415-4211 more accurately. In order to estimate the fuzzy eigenvectors of this matrix, we utilize interval arithmetic, alpha-cuts, together with optimism of index A. In this way, performance scores of the alternatives and the weights of the different attributes can finally be obtained and compared. For easy computation, we use the MATHCAD package to calculate all results. At last, we apply and verify this new algorithm to a weapon system evaluation and selection problem.
