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

Abstract

The performance evaluation of weapon systems are multiple criteria decision making problems. The descriptions and judgements on weapon systems are usually linguistic and fuzzy. The traditional method of Analytic Hierarchy Process (AHP) are mainly used in crisp (non-fuzzy) decision applications with a very unbalanced scale of judgements. To overcome these problems, we will propose a new and general decision making method for evaluating weapon systems using fuzzy AHP based on entropy weight. We will use symmetric triangular fuzzy number 1 to 9 to indicate the relative strength of the elements in the hierarchy, and build fuzzy judgement vectors (matrix) through comparison of the performance scores. We will derive 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 will be used to illustrate our method and compare it with other methods.