Evaluating weapon system using fuzzy analytic hierarchy process based on entropy weight

The performance evaluation of weapon systems is a multiple criteria decision making problem. The descriptions and judgements on weapon systems are usually linguistic and fuzzy. The traditional methods using the analytic hierarchy process (AHP) are mainly used in crisp (non-fuzzy) decision applications with a very unbalanced scale of judgements. To overcome these problems the author proposes a new and general decision making method for evaluating weapon systems using fuzzy AHP based on entropy weight. The authors uses symmetric triangular fuzzy numbers 1¯ to 9¯ to indicate the relative strength of the elements in the hierarchy, and to build fuzzy judgement vectors (matrix) through comparison of the performance scores. The author derives the priority among the alternatives by the entropy weight through the use of interval arithmetic, α-cuts, and index of optimism (the degree of optimism of the decision maker) to estimate the degree of satisfaction of the judgement. In this way it does not require a series of pairwise comparison judgements as required by the traditional AHP method. By multiplying the fuzzy subjective weight vector W¯ with the corresponding fuzzy judgement matrix X¯ (the orderly list of fuzzy judgement vectors x¯_i for every criterion C_i), a fuzzy problem can be solved and a weapon system selection example is used to illustrate the method and to compare it with other methods