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Multicriteria group decision making based on projection measures on complex Pythagorean fuzzy sets

Granular Computing volume 8, pages 137–155 (2023)Cite this article

Abstract

Complex Pythagoran fuzzy (C-PyF) set is an efficient tool to handle two dimensional periodic uncertain information which have various applications in fuzzy modeling and decision making. It is known that the aggregation operators influence decision making processes. Frank algebraic operator is one of the important and widely used operators in decision making techniques that deal with uncertain problems. This paper investigates arithmetic and geometric complex Pythagorean fuzzy Frank aggregation operators with the help of Frank operational laws. Further the necessary properties of the developed aggregation operators (AOs) are discussed. The distance and similarity measures of two C-PyF sets is still an open problem and distinguished research have been conducted. The complex projection measure is also one of the unexplored research areas in complex fuzzy scenario. The major part of this paper is dedicated to utilize C-PyF sets to develop complex Pythagorean fuzzy projection measure between alternatives and the relative complex Pythagorean fuzzy ideal solution (RCPFIS). Further, these AOs and complex projection measures have been employed in modeling a multicriteria group decision making (MCGDM) method. Then the proposed weighted C-PyF projection based MCGDM model is illustrated with an experimental analysis on frequency identification. Finally, a comparative study is conducted to show the validity of the proposed C-PyF projection model.

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Acknowledgements

This research was supported by Don Bosco Research grant, Sacred Heart College (Autonomous), Tirupattur, Tirupattur District, 635601, Tamilnadu, India.

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  1. J. Aldring and D. Ajay contributed equally to this work.

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  1. Department of mathematics, Sacred Heart College (Autonomous), Tirupattur District, 635601, Tamilnadu, India

    J. Aldring & D. Ajay

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  1. J. Aldring
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Correspondence to J. Aldring.

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Appendix A

Appendix A

The following tables such as Table 9, 10, 11 and 12 are added in the appendix section.

Table 9 Fused complex Pythagorean fuzzy decision matrix \(D_{ij}\)
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Table 10 Fused complex Pythagorean fuzzy decision matrix \(D_{ij}\) with indeterminacy values
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Table 11 complex Pythagorean score fuzzy valued decision matrix \(S_{ij}\)
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Table 12 The final result values of decision making methods using \(S_{ij}\)
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Aldring, J., Ajay, D. Multicriteria group decision making based on projection measures on complex Pythagorean fuzzy sets. Granul. Comput. 8, 137–155 (2023). https://doi.org/10.1007/s41066-022-00321-6

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  • DOI: https://doi.org/10.1007/s41066-022-00321-6

Keywords

  • Complex Pythagorean fuzzy set
  • Projection model
  • Frank operational laws
  • Aggregation operators
  • Decision making