Generalized Grey Target Decision Method for Mixed Attributes Based on Connection Number

Abstract

Grey target decision model for mixed attributes including real numbers, interval numbers, triangular fuzzy numbers, and trapezoidal fuzzy numbers is complex for its data processing in different ways and information distortion in handling fuzzy numbers. To solve these problems, the binary connection number proposed in set pair analysis is applied to unify different types of index values with their parameters’ average values and standard deviations as determinacy-uncertainty vectors. Then the target center index vectors are determined by the modules of index vectors of all alternatives under different attributes. So the similarity of each index vector and its target center index vector called nearness degree can be calculated. Following, all the nearness degrees are normalized in linear method in order to be compared with each other. Finally, the optimal alternative can be determined by the minimum of all integrated nearness degrees. Case study demonstrated that this approach can not only unify different types of numbers, and simplify the calculation but also reduce the information distortion in operating fuzzy numbers.