Ranking Interval-Valued Fuzzy Numbers with Intuitionistic Fuzzy Possibility Degree and Its Application to Fuzzy Multi-Attribute Decision Making

In this paper, we present the concept of intuitionistic fuzzy possibility degree (IFPD) for ranking interval-valued fuzzy numbers. This method overcomes the shortcomings of the previous techniques by giving the possibility degree in the form of intuitionistic fuzzy value, which contains positive degree, negative degree, and hesitant degree to compare any two intervals. The prominent characteristic of this method is that it can deal with the incomparable cases effectively, i.e., the two interval numbers have the same center or one interval number is nested in another one. As an application of the proposed method, a fuzzy multi-attribute decision-making method based on the IFPD is studied. Finally, we use a numerical example of selecting a laptop to illustrate the application of the proposed method.