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Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering

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Abstract

Distance and similarity measures are popular due to various applications across different fields, including clustering, classification, information retrieval, decision-making, and image and pattern recognition. Pythagorean fuzzy sets (PFSs) are more efficient than fuzzy sets (FSs) and intuitionist fuzzy sets (IFSs) in dealing with all kinds of uncertain and incomplete information related to real life. Since PFSs and interval-valued fuzzy sets (IVFs) are isomorphic to each other, so the interval values can be used to represent the distance between two PFSs uniquely. Therefore, in this article, we utilize the concept of Pythagorean fuzzy interval values to construct a new distance between two PFSs based on Lp metric. Furthermore, the suggested distance is used to construct several similarity measures between PFSs using simple and reasonable functions. Newly established distance and similarity measures between Pythagorean fuzzy sets satisfy all the required axioms. To show the reasonability, comparison analysis is conducted with existing one in an application to pattern recognition. The numerical comparison results reveal that our proposed method works better than the existing method. To reveal practical applicability and usefulness, we put forwarded an algorithm Pythagorean Vlsekriterijumsko Kompromisno Rangiranje in Serbian, means multicriteria optimization and compromise solution (P-VIKOR) based on our suggested method and applied it to solve daily life issues involving complex multicriteria decision-making (MCDM) process. Finally, we utilize our proposed similarity measure to establish Pythagorean clustering. Numerical results and practical applications demonstrate that the given approaches are practically applicable, reasonable, and reliable in dealing with a variety of complex problems carrying uncertainty and vague information in everyday life.

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Authors and Affiliations

  1. Department of Mathematical Science, Karakoram International University, Gilgit-Baltistan, 15100, Pakistan

    Zahid Hussain, Hafeeza Afzal, Rashid Hussain &  Nasimullah

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  1. Zahid Hussain
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  2. Hafeeza Afzal
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  3. Rashid Hussain
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  4. Nasimullah
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All the authors have contributed equally to this work.

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Correspondence to Zahid Hussain.

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Communicated by Graçaliz Pereira Dimuro.

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Hussain, Z., Afzal, H., Hussain, R. et al. Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering. Comp. Appl. Math. 42, 301 (2023). https://doi.org/10.1007/s40314-023-02420-9

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