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On a dual proximity measure based on intuitionistic fuzzy sets

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Abstract

In this paper, we present a new approach for defining a dual proximity measure for intuitionistic fuzzy sets. The new approach utilizes an extended form of the restricted equivalence functions and receives their values as a two tuple. The two values in the two tuple are due to the dual character of the proximity measure under consideration. In fact, the computation of proximity between two intuitionistic fuzzy sets simultaneously provides the value of similarity as well as non-similarity between the intuitionistic fuzzy sets. So, the novel approach proposed in this paper provides a comprehensive information theoretic evaluation of intuitionistic fuzzy sets. Further, we investigate the application of the novel measure in pattern recognition and clustering analysis. We also contrast the performance of the proposed measure with the state-of-art in view of the structured linguistic variables, pattern classification and clustering analysis. The comparative analysis shows that the newly introduced two-valued proximity measure performs better in certain circumstances and encompasses the dualism of the human cognition.

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Acknowledgements

Authors are highly thankful to the anonymous reviewers for their constructive suggestions and bringing the paper in the present form.

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  1. Koushal Singh and Surender Singh have contributed equally to this work.

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  1. School of Mathematics, Faculty of Sciences, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, 182320, India

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Singh, K., Singh, S. On a dual proximity measure based on intuitionistic fuzzy sets. Neural Comput & Applic 35, 6293–6311 (2023). https://doi.org/10.1007/s00521-022-07946-3

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