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The purpose of this paper is to introduce a novel similarity measure of intuitionistic fuzzy sets (IFSs). The proposed measure is based on the equivalence relation in the IFS-IBA approach. Due to the logic-based background, this measure compares IFS from a different viewpoint than the standard measures, emphasizing comprehension of intuitionism. The IFS-IBA similarity measure has a solid mathematical background and can be combined with various IF aggregation operators. Additionally, we define IFS-IBA distance function as a complement of IFS-IBA similarity. Both IFS-IBA similarity and distance functions may have different realizations that are easy to interpret. Hence, the measures are offering great descriptive power and the ability to model various problems. The benefits of the proposed measure are illustrated on the problem of pattern recognition and classification within k -NN algorithm. Finally, we show that the proposed measure is appropriate for IF hierarchical clustering on the problem of clustering Serbian medium-sized companies according to their financial ratios. Results obtained using the IFS-IBA measure are clear-cut and more meaningful compared to a standard IF distances regardless of the I-fuzzification method used. [ABSTRACT FROM AUTHOR]