Developing Group Ordered Weighted Averaging Operator Weights for Group Decision Support

A few single decision-making methods under uncertainty (SDMUU) are available in the literature. The reason for such scarcity seems to be mainly due to too insufficient information to induce a reasonable result for effective decision support. Moreover their final outcomes on the same SDMUU problem may be different depending on which method is applied. A group decision-making method under uncertainty (GDMUU) extends a SDMUU in a sense that a group of individuals, each expressing different opinions, work together to solve a relevant problem. As in a SDMUU, we find that just a few methods are available to solve a GDMUU problem. In the paper, the ordered weighted averaging (OWA) method, originally devised for use with the SDMUU problem, is considered to deal with a GDMUU problem where individuals of a group express their degree of optimism in terms of attitudinal characters. We first find the extreme points corresponding to the attitudinal character and then solve a quadratic mathematical program which minimizes a squared distance from each extreme point identified. Thus the resulting OWA operator weights for the group are located at the center of the weights-space constructed by attitudinal characters. This idea is further extended to deal with uncertain attitudinal character expressed in the form of interval in situations where it is difficult to reliably obtain a precise attitudinal character due to time pressure and a limited domain knowledge and so on.