A preference degree for ranking k-dimensional vectors of qualitative labels and its application in multi-attribute group decision-making

Abstract

ABSTRACT In this paper, a ranking procedure is proposed for the order-of-magnitude qualitative reasoning problem. To this end, a preference degree was suggested for comparing a set of k-dimensional vectors of qualitative labels to provide a criterion to interpret the concept of ‘preference’ between two k-dimensional vectors of qualitative labels. Some useful properties of the proposed preference degree were also examined and discussed. It was shown that the proposed preference degree can satisfy the common and desired properties expected in the space of k-dimensional vectors of qualitative labels. Numerical examples were also employed to illustrate the proposed ranking method. Three application examples were used to show the applicability of the proposed ranking method in a single criterion group decision-making (SAGDM) and multiple criteria group decision-making (MAGDM). Moreover, the proposed preference degree was compared with a conventional method in terms of ranking the k-dimensional vector of qualitative labels. Unlike the proposed method, the numerical evaluations revealed that the previous techniques are not applicable to some situations in decision-making.