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A three-way Pythagorean fuzzy correlation coefficient approach and its applications in deciding some real-life problems

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Abstract

Correlation coefficient (CC) is a reliable information measure for measuring interrelationship between Pythagorean fuzzy sets (PFSs). Some approaches for calculating CC of PFSs have been considered. These hitherto approaches assess only the strength of relationship between PFSs, and are described within the interval [0,1]. This paper proposes a three-way approach for the computation of CC between PFSs by using the concepts of variance and covariance, respectively. This new approach is defined within the interval [− 1,1] akin to classical statistics, shows the strength of relationship between the considered PFSs and indicates whether the PFSs are either positively or negatively correlated. By including the three conventional parameters of PFSs in the proposed technique, the possibility of error due to information leakage is reasonably minimized. The new technique is validated with some theoretical results to show its suitability as reliable information measure. Some numerical examples are considered to show the edges of the new methods over similar methods. From the comparative analysis, the proposed methods of computing CCPFSs give more reliable and reasonable results compare to similar existing methods as presented in Table 13. Certain decision-making problems involving recognition of patterns and diagnostic medicine are resolved with the aid of the new method. The three-way technique of computing correlation coefficient between PFSs can solve decision-making problems that are multi-attributes in nature.

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Acknowledgements

This work is supported by the Foundations of Chongqing Municipal Key Laboratory of Institutions of Higher Education ([2017]3), Chongqing Development and Reform Commission (2017[1007]), and Chongqing Three Gorges University.cle.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing and Control, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Paul Augustine Ejegwa & Yuming Feng

  2. Department of Mathematics, University of Agriculture, P.M.B. 2373, Makurdi, Nigeria

    Paul Augustine Ejegwa

  3. Australian AI Institute, University of Technology Sydney, Ultimo, NSW, 2007, Australia

    Shiping Wen

  4. Chongqing Engineering Research Center of Internet of Things and Intelligent Control Technology, Chongqing Three Gorges University, Wanzhou, Chongqing, 404100, China

    Yuming Feng, Wei Zhang & Jinkui Liu

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  1. Paul Augustine Ejegwa
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  3. Yuming Feng
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  4. Wei Zhang
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  5. Jinkui Liu
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Correspondence to Yuming Feng.

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Ejegwa, P.A., Wen, S., Feng, Y. et al. A three-way Pythagorean fuzzy correlation coefficient approach and its applications in deciding some real-life problems. Appl Intell 53, 226–237 (2023). https://doi.org/10.1007/s10489-022-03415-5

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