Group decision focusing on outliers

This paper investigates a group decision problem focusing on outliers in a group. The group decision in this paper is considered as approximation of all individual opinions, which are given normalized crisp or interval values. The difference of an individual opinion from the group opinion represents his/her compromise in order to reach a consensus so that it should be minimized. The first step is to detect outliers in a group and assign outlier degree to individual. The outlier degree is distance of an individual from the group of others and defined as the reduction of compromise by excluding him/her from the group. The outlier degree of a unique individual is more than those of other general individuals. Similarly to outlier degree, inlier degree is closeness of others to an individual and defined as the compromise of the group without him/her. The second step is to approximate individual opinions so as to be a group opinion. The weighted sum of compromises of all individuals is minimized introducing the outlier degrees as the weights of individuals. In this model, outliers are considered positively into account for a group opinion. Therefore, based on compromises of individuals, the models to define outlier degree and to obtain group opinion by approximating individual opinions are proposed in this paper.