Intuitionistic fuzzy sets (IFS) represent a concept that addresses the analysis of not necessarily numerical variables by specifying, besides their membership and non-membership relations, a hesitancy factor to express the lack of knowledge about the membership or non-membership. Similarity measures between two IFSs are defined to evaluate their information against each other and may represent useful tools in areas involving decision making or pattern recognition. The weaknesses of many existing similarity measures are typically outlined by some counterexamples.

The goal of the paper is to introduce a new similarity measure between IFSs and to demonstrate its accuracy and discriminative power, compared to a range of existing similarity measures. The third section presents the new similarity measure and its weighted variant, and demonstrates how it accommodates the similarity axioms. The measures expression is based on the membership, non-membership, and hesitancy degrees; its originality is based on the fact that it does not seem to rely on any conventional approaches, such as distances or entropy. The next section investigates, by numerical examples, the effectiveness of the novel measure. A first series of numerical examples is selected from those generating counterintuitive cases for some existing measures. A second set concerns an abstract pattern recognition problem and the last a medical diagnosis case, both consisting of examples frequently occurring in IFS experiments. The new similarity measure agrees with the acknowledged pattern-recognition results and demonstrates more robustness concerning the counterintuitive cases. The paper also contains a historical record of the research produced in this field. The work is clearly explained, well organized, and creative. Maybe it would be interesting in the future to present the new measure in a more complex context.