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RETRACTED ARTICLE: Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information

  • Fuzzy systems and their mathematics
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This article was retracted on 01 October 2022

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Abstract

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method.

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Acknowledgements

This study work was supported by Higher Education Commission (HEC), Pakistan under National Research Program for University (NRPU), Project title: Fuzzy Mathematical Modeling for Decision Support Systems and Smart Grid Systems (No. 10701/KPK/NRPU/R & D/HEC/2017).

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Pakistan

    Shahzaib Ashraf & Saleem Abdullah

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  1. Shahzaib Ashraf
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  2. Saleem Abdullah
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Correspondence to Shahzaib Ashraf or Saleem Abdullah.

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This article has been retracted. Please see the retraction notice for more detail: https://doi.org/10.1007/s00500-022-07558-y

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Ashraf, S., Abdullah, S. RETRACTED ARTICLE: Decision aid modeling based on sine trigonometric spherical fuzzy aggregation information. Soft Comput 25, 8549–8572 (2021). https://doi.org/10.1007/s00500-021-05712-6

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