A method for multi-attribute group decision-making with triangular intuitionistic fuzzy numbers application to trustworthy service selection

The trustworthy service selection is a typical Multi-Attribute Group Decision- Making (MAGDM) problem. The aim of this paper is to develop a novel method for MAGDM with Triangular Intuitionistic Fuzzy Numbers (TIFNs) and apply it to the trustworthy service selection problem. Firstly, we define the mean-index, variance-index, and standard deviation of TIFN. Moreover, a new distance measure of TIFNs is proposed, and the corresponding proofs are given. Based on these concepts of mean-index and standard deviation, a ranking method for TIFNs is developed considering the risk preference of Decision Maker (DM). Further, according to the crisp relative closeness coefficient matrix with respect to the normalized TIFNs decision matrix, we use entropy measure to obtain attribute weights. The DMsʹ weights are calculated by the similarity between the individual and the average decisions. Then, a decision procedure is described to solve the MAGDM under triangular intuitionistic fuzzy environment. Finally, a real trustworthy service selection example is analyzed to verify the practicality and effectiveness of the developed method.