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Distance measures of r,s,t-spherical fuzzy sets and their applications in MCGDM based on TOPSIS

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Abstract

The T-spherical fuzzy set is a useful generalization of other fuzzy structures such as fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, picture fuzzy, q-rung orthopair fuzzy, and spherical fuzzy sets. The notion of r,s,t-spherical fuzzy set was defined by the researchers as a generalization of T-spherical fuzzy sets. In this paper, the set operations of r,s,t-spherical fuzzy sets are defined and the arithmetic operations between the r,s,t-spherical fuzzy numbers are redefined, and some results related to defined operations are derived. Also, distance measures between two r,s,t-spherical fuzzy sets based on Hamming, Hausdorff, and Euclidean distance measures are introduced. Furthermore, a multi-criteria group decision-making (MCGDM) method is developed based on the TOPSIS method by using the proposed distance measure. Finally, to show the process of the proposed MCGDM method, a numerical example is given.

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No datasets were generated or analyzed during the current study.

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Funding

The authors declare that they have not received any funds, grants, or other support during the preparation of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Çankırı Karatekin University, 18100, Çankırı, Turkey

    Fatih Karamaz & Faruk Karaaslan

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  1. Fatih Karamaz
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  2. Faruk Karaaslan
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The project was developed and designed by Fatih Karamaz and Faruk Karaaslan. They also conducted the data analysis and prepared the report.

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Correspondence to Faruk Karaaslan.

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Karamaz, F., Karaaslan, F. Distance measures of r,s,t-spherical fuzzy sets and their applications in MCGDM based on TOPSIS. J Supercomput 81, 173 (2025). https://doi.org/10.1007/s11227-024-06560-5

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