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Parametric circular intuitionistic fuzzy information measures and multi-criteria decision making with extended TOPSIS

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Abstract

The representation of a circular intuitionistic fuzzy set (C-IFS) involves using a circle to symbolize the uncertainty associated with the membership and non-membership functions. A significant advantage of C-IFS is its ability to model the vagueness present in membership and non-membership degrees. This is accomplished through the structure of C-IFSs, which allows for the representation of information using points positioned on a circle with a defined center and radius. Using this structure, a C-IFS facilitates the making of more sensitive and nuanced decisions. In this study, a score function and an accuracy function are introduced to rank circular intuitionistic fuzzy values (C-IFVs). Then, we put forth novel parametric distance measures to calculate the difference between C-IFSs. This measure allows us to examine the impact of membership degree, non-membership degree, and radius on various applications. By observing these effects, we gain insights into the behavior and significance of these parameters in practical scenarios. We also give a similarity measure for computing the degree of similarity between C-IFSs. Furthermore, an extended version of the circular intuitionistic fuzzy Technique for Order of Preference by Similarity to Ideal Solution (C-IF TOPSIS) method is introduced by utilizing aggregation operators and distance measures. This extension incorporates distance measures and is harmonized specifically for C-IFSs. We apply this extended TOPSIS to a multi-criteria group decision making problem sourced from existing literature. Additionally, we evaluate sensitive analysis of proposed extended TOPSIS according to different parameters.

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Acknowledgements

The authors are grateful to the Referees for carefully reading the manuscript and for offering substantial comments and suggestions which enabled them to improve the paper. The research of Mahmut Can Bozyiğit has been supported by Scientific and Technological Research Council of Türkiye (TüBİTAK) Program 2211.

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  1. Faculty of Engineering and Natural Sciences, Department of Mathematics, Ankara Yıldırım Beyazıt University, 06420, Ankara, Turkey

    Mahmut Can Bozyiğit

  2. Faculty of Science, Department of Mathematics, Ankara University, 06100, Ankara, Turkey

    Mehmet Ünver

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  1. Mahmut Can Bozyiğit
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  2. Mehmet Ünver
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Bozyiğit, M.C., Ünver, M. Parametric circular intuitionistic fuzzy information measures and multi-criteria decision making with extended TOPSIS. Granul. Comput. 9, 43 (2024). https://doi.org/10.1007/s41066-024-00469-3

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