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Bipolar fuzzy soft Hamacher aggregations operators and their application in triage procedure for handling emergency earthquake disaster

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Abstract

When immediate care cannot be delivered because of a lack of resources, the triage procedure is used in the field of medical. The system provides care to those who need it most urgently and who stand to benefit from it the most. A model for early care in emergency circumstance based on triage is presented in this paper. But before that, some aggregation operators for information based on bipolar fuzzy soft set are introduced. The concepts of Hamacher t-norm and t-conorm are utilized in order to introduce these operators. We have developed some new operational principles for bipolar fuzzy soft numbers based on Hamacher t-norm and t-conorm. Further, based on these operational laws, we have introduced bipolar fuzzy soft Hamacher weighted averaging, geometric and their respective ordered aggregation operators. We have provided an approach to resolve multi-attribute decision-making issues in a bipolar fuzzy soft environment using the suggested operators. The triage procedure has been elaborated, with detailed information on classifying patients and providing care during the process. Particular attention is given to those affected by war and natural disasters, following a priority system designed to enhance survival rates. The novel operators are utilized in categorizing dead, most seriously injured and those with little injuries following the triage procedure in an earthquake situation. Varying performance of the novel operators has been examined through sensitivity analysis by tuning the controlling parameter and their stability, and flexibility has been provided by the comparative analysis with some existing methods.

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Acknowledgements

This work was supported by the projects of the Natural Science Foundation of the province Under Grant 2022JJ30673 and Changsha Major Science and Technology Special Project under the Grant No. kh2401008.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Waseem Ahmad, Aurang Zeb, Muhammad Asif & Muzhou Hou

  2. Key Laboratory of High Impact Weather(Special), China Meteorological Administration, Changsha, 410083, China

    Muzhou Hou

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  1. Waseem Ahmad
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  2. Aurang Zeb
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Appendices

Proof of Theorem 3.1

Proof

By mathematical induction, for Eq. (14) becomes,

Similarly, For we have so that

Hence the result is true for and . Now suppose the result is true for and , i.e.,

and

Now for

We have,

Hence true for . Thus, the result is true for

Moreover, and \(\acute{r}>0\) then,

And and \(\acute{r}>0\) then,

Thus the aggregated value obtained by BFSHWA operator is again a BFSN \(\square \)

Proof of Theorem 3.10

Proof

  Eq (18) becomes,

Similarly, we have, so that

Hence the result is true for and . Now suppose the result is true for and , i.e.,

and

Now for we have,

Hence true for . Thus, the result is true for

Moreover, and \(\acute{r}>0\) so that

And and \(\acute{r}>0\) so,

Thus the aggregated value obtained by BFSHWA operator is again a BFSN. \(\square \)

Tables

See Tables 11, 1213, 14, 15 and 16.

Table 11 Aggregated values by BFSHWA operator
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Table 12 Aggregated values by BFSHOWA operator
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Table 13 Aggregated values by BFSHWG operator
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Table 14 Aggregated values by BFSHOWG operator
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Table 15 Score values of alternatives by the BFSHWA and BFSHOWA operators
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Table 16 Score values of alternatives by the BFSHWG and BFSHOWG operators
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Ahmad, W., Zeb, A., Asif, M. et al. Bipolar fuzzy soft Hamacher aggregations operators and their application in triage procedure for handling emergency earthquake disaster. J Supercomput 81, 294 (2025). https://doi.org/10.1007/s11227-024-06757-8

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