Interval-valued intuitionistic fuzzy envelopment analysis and preference fusion

Abstract

The interval-valued intuitionistic fuzzy set (IIFS) is an effective tool to describe qualitative evaluations using two interval values from two perspectives of “good” and “bad”. In this study, a new decision-making method based on the envelopment efficiency of IIFS is proposed, which can be introduced to select the optimal alternative and improve the inefficient ones. To do this, we firstly propose the ratio comparison rules of IIFS, based on which the interval-valued intuitionistic fuzzy envelopment analysis (IIFEA) is demonstrated. After that, we develop the IIFEA-N and IIFEA-M models on the basis of non-membership and membership. Their dual forms are derived so that the IIFEA-N and IIFEA-M models can be transformed into linear programming, which are calculable. With respect to the attributes’ difference, we further construct the preference IIFEA (PIIFEA) model by fusing subjective preference rather than quantitative weights. Therefore, the optimal alternative can be selected based on the decision makers’ preference, and the development approaches also can be given to the inefficient alternatives. Subsequently, a complete decision-making process is provided. At last, an example for the CEO of an international hotel to select a GM of the biggest branch in China is illustrated to show the effectiveness of the proposed methods.