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Distance And Similarity Measures For Soft Sets

Author

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  • ATHAR KHARAL

    (National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan)

Abstract

In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.

Suggested Citation

  • Athar Kharal, 2010. "Distance And Similarity Measures For Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 6(03), pages 321-334.
    • Handle: RePEc:wsi:nmncxx:v:06:y:2010:i:03:n:s1793005710001724
    DOI: 10.1142/S1793005710001724
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    Citations

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    Cited by:

    1. Iraklis Kollias & John Leventides & Vassilios G. Papavassiliou, 2024. "On the solution of games with arbitrary payoffs: An application to an over‐the‐counter financial market," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 1877-1895, April.
    2. Acharjee S, 2018. "There’s Plenty of Room at Bottom of Biostatistics and Biometrics," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 6(4), pages 116-117, April.
    3. Huarong Zhang & Minxia Luo, 2019. "The “Generator” of Int-Soft Filters on Residuated Lattices," Mathematics, MDPI, vol. 7(3), pages 1-10, March.
    4. Wei Yang, 2013. "New similarity measures for soft sets and their application," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 19-25, March.
    5. Santanu Acharjee, 2018. "On Connections of Soft Set Theory with Existing Mathematics of Uncertainties: A Short Discussion for Non-Mathematicians with Respect to Soft Set Theory," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-9, March.
    6. Santanu Acharjee, 2017. "New Results for Kharal’s Similarity Measures of Soft Sets," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 55-60, March.

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