Projection Model-Based Approaches to Intuitionistic Fuzzy Multi-Attribute Decision Making

Abstract

Xu and Hu (2010) investigate intuitionistic fuzzy multi-attribute decision making problems where the attribute values are expressed in IFNs or IVIFNs. They introduce some concepts, such as the relative intuitionistic fuzzy ideal solution, the relative uncertain intuitionistic fuzzy ideal solution, the modules of IFNs and IVIFNs, etc. They also introduce the cosine of the included angle between the attribute value vectors of each alternative and the relative intuitionistic fuzzy ideal solution, and the cosine of the included angle between the attribute value vectors of each alternative and the relative uncertain intuitionistic fuzzy ideal solution. They further establish two projection models to measure the similarity degrees between each alternative and the relative intuitionistic fuzzy ideal solution, and between each alternative and the relative uncertain intuitionistic fuzzy ideal solution. Based on the projection models, the given alternatives can be ranked and then the most desirable one can be selected.