A Novel Preference Scale Function Based on Poincaré Metric for Decision-Making

This paper proposes a novel preference scale function based on the Poincare metric for decision-making with Intuitionistic Fuzzy Sets (IFSs). We first introduce a pair of two-dimensional vectors expressing the IFSs in multi-criteria decision-making problems, which satisfy the Poincare metric, and then construct a preference scale function based on it. The proposed scale function can address, without resorting to the accuracy function, the issue of the existing score function for IFSs returning zero scores when membership and non-membership degrees of an element are the same. The advantages of the proposed scale function over the existing ones are demonstrated through illustrative examples.