Fuzzy Bayes risk based on Mahalanobis distance and Gaussian kernel for weight assignment in labeled multiple attribute decision making

Attribute weight assignment plays a key role in multiple attribute decision making (MADM). For the issue of labeled multiple attribute decision making (LMADM), the existing methods of attribute weight determination that have been well developed for MADM usually ignore or do not take full advantage of the supervisory function of labels. As a result, the weights produced by these methods may not be ideal in practice. To make up for this deficiency, this paper develops an objective method based on Bayes risk. Specifically, the LMADM problem is first put forward, then a Gaussian kernel based loss function is proposed to cope with the drawback that the loss function in Bayes risk is usually determined by experts. Meanwhile, Mahalanobis distance and fuzzy neighborhood relationship are employed to measure the fuzziness of data set. Finally, a number of experiments, including the comparison experiments on UCI data and the effectiveness evaluation of fighter, are carried out to illustrate the superiority and applicability of the proposed method.