On Uniform Effect Measure Functions and a Weighted Multi-attribute Grey Target Decision Model

A novel multi-attribute grey target decision model is proposed and demonstrated with a practical case study. First, a grey target is defined as a satisfying region, which a decision maker wants to reach, with an inside ideal point across multiple objectives. To facilitate the uniform distance measure of a decision strategy to the pre-defined grey target, four kinds of measure procedures are designed including the effect measures for benefit type objectives and cost type objectives, the lower effect measure for moderate type, and the upper effect measure for moderate type according to three types of decision objective including benefit objective, cost objective, and non-monotonic objective with a most preferred middle value. Then, a matrix of synthetic effect measures can be easily obtained based on the uniform distance measure of a decision strategy to the grey target over different objectives. Based upon the obtained matrix information, different decision strategies can be easily evaluated comprehensively. The proposed method has a clear physical meaning as missing target, hitting target as well as hitting performance. Finally, the proposed model is applied to a supplier selection problem for a commercial aircraft design.