Aggregation distance measure and its induced similarity measure between intuitionistic fuzzy sets

• A method for aggregating distance measures is proposed.
• A general approach to constructing similarity measures is introduced.
• Some interesting examples in applications are presented.

Various distance and similarity measures in Atanassov’s intuitionistic fuzzy sets (IFSs) are applied to practical problems. However, it is difficult to decide which one is the most suitable for measuring the degree of distance or similarity, especially in the case of the occurrence of conflict results in practice. In this paper, we propose the concept of aggregation distance measure for IFSs based on aggregation functions without zero divisors to help decision makers to make final decisions. Furthermore, a novel technique is introduced to construct similarity measures from a given distance measure with respect to non-filling fuzzy negations, which gives a new direction for the construction method for similarity measures of IFSs. Some illustrative examples in applications such as pattern recognition, fuzzy clustering and decision making are used to investigate the effectiveness of the proposed measures.