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q-Rung orthopair fuzzy soft Hamacher aggregation operators and their applications in multi-criteria decision making

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Abstract

Soft sets (\({S}_{t}\) S) theory provides a general mechanism for handling uncertainty based on the point of view of parameterization tools. The main theme of this manuscript is to extend the notion of Hamacher operators by establishing an interesting connection between two mathematical concepts \({S}_{t}\) S theory and q-rung orthopair fuzzy sets (q-ROFS). To be specific, we develop some new Hamacher operations for q-rung orthopair fuzzy soft sets (q-ROF \({S}_{t}\) S). In light of these operational laws, we further propose some q-rung orthopair fuzzy soft Hamacher aggregation operators, i.e., q-ROF soft Hamacher averaging and q-ROF soft Hamacher geometric aggregation operators, such as q-ROF soft Hamacher weighted averaging (q-ROF \({S}_{t}\) HWA), q-ROF soft Hamacher ordered weighted averaging (q-ROF \({S}_{t}\) HOWA) and q-ROF soft Hamacher hybrid averaging (q-ROF \({S}_{t}\) HHA) operators. Furthermore, based on Hamacher operator laws, we discuss some geometric aggregation operators such as q-ROF soft Hamacher weighted geometric (q-ROF \({S}_{t}\) HWG), q-ROF soft Hamacher ordered weighted geometric (q-ROF \({S}_{t}\) HOWG) and q-ROF soft Hamacher hybrid geometric (q-ROF \({S}_{t}\) HHG) operators. Meanwhile, the important properties of the developed operators are investigated in detail. Then, a technique for multi-criteria decision making and a stepwise algorithm for decision making are demonstrated by utilizing the proposed approach. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is performed. The derived results demonstrate that the investigated models are more effective and useful than the existing approaches.

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Acknowledgements

The authors would like to thank the Editor-in-Chief, an Associate Editor, and the anonymous referees for detailed and valuable comments which helped to improve this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Basic and Applied Sciences, International Islamic University, Islamabad, Pakistan

    Azmat Hussian & Tahir Mahmood

  2. Islamic Girls Public School and College Parachinar, Parachinar, Pakistan

    Azmat Hussian

  3. Department of Mathematics, Islamabad Model College for Boys, F-10/3, Islamabad, Pakistan

    Muhammad Irfan Ali

  4. Department of Digital Systems, University of Thessaly, Larissa, Greece

    Vassilis C. Gerogiannis & Dimitrios Tzimos

  5. Ministry of Education, Experimental School of Larissa, Larissa, Greece

    Dimitrios Giakovis

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  1. Azmat Hussian
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  2. Tahir Mahmood
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  3. Muhammad Irfan Ali
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  4. Vassilis C. Gerogiannis
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  5. Dimitrios Tzimos
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Correspondence to Azmat Hussian or Vassilis C. Gerogiannis.

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Communicated by Junsheng Qiao.

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Hussian, A., Mahmood, T., Ali, M.I. et al. q-Rung orthopair fuzzy soft Hamacher aggregation operators and their applications in multi-criteria decision making. Comp. Appl. Math. 43, 22 (2024). https://doi.org/10.1007/s40314-023-02477-6

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