Multi-criteria decision-making (MCDM) techniques play a crucial role in solving real-life problems with imprecision and uncertainty. The p, q, r-spherical fuzzy rough set (p, q, r-SFRS) is an important development over FS theory for flexible representation of hesitancy, membership, and non-membership degrees. In this paper, we present a nuanced decision-making approach named confidence levels. Moreover, p, q, r-spherical fuzzy rough Einstein Bonferroni ($ {C}_{p, q, r} $-SFREBOM) aggregation operators, such as the p, q, r-spherical fuzzy rough Einstein Bonferroni weighted geometric operator ($ {C}_{p, q, r} $-SFREBOMWG) and p, q, r-spherical fuzzy rough Einstein Bonferroni weighted average operator ($ {C}_{p, q, r} $-SFREBOMWA), plays a crucial role in providing a strong support for MCDM analysis. The method considers lower and upper approximations of alternatives and synthesizes judgments along criteria based on expert confidence levels. The operational laws, theorems, and properties of p, q, r-SFREBOMWG and q, r-SFREBOMWA are explained, showing the superiority and importance of the suggested work, providing more accurate results than existing approaches. Integrating the newly proposed operator with multi-decision-making techniques like criteria importance through intercriteria correlation (CRITIC) and combinative distance-based assessment (CODAS) is a unique approach. A case study was considered to validate the efficacy and usability of the proposed operators in prioritizing sustainable municipal solid waste treatment techniques with the CRITIC and CODAS techniques. The computed results were compared with approaches to further support the outcomes of the proposed work. The comparison was done with technique for order preference by similarity to ideal solution (TOPSIS), and weighted aggregated sum product assessment (WASPAS) to assess the proposed work's reliability. Additionally, comparative and sensitivity analyses were conducted to demonstrate the robustness and excellence of the $ {C}_{p, q, r} $-SFREBOM approach with that of conventional MCDM methods.
Citation: O. S. Deepa, Nandana Vasudevan. Integrating confidence level-based p, q, r-spherical fuzzy rough Einstein Bonferroni aggregation operators with the CRITIC-CODAS approach for prioritizing waste treatment techniques[J]. AIMS Mathematics, 2026, 11(3): 7353-7399. doi: 10.3934/math.2026303
Multi-criteria decision-making (MCDM) techniques play a crucial role in solving real-life problems with imprecision and uncertainty. The p, q, r-spherical fuzzy rough set (p, q, r-SFRS) is an important development over FS theory for flexible representation of hesitancy, membership, and non-membership degrees. In this paper, we present a nuanced decision-making approach named confidence levels. Moreover, p, q, r-spherical fuzzy rough Einstein Bonferroni ($ {C}_{p, q, r} $-SFREBOM) aggregation operators, such as the p, q, r-spherical fuzzy rough Einstein Bonferroni weighted geometric operator ($ {C}_{p, q, r} $-SFREBOMWG) and p, q, r-spherical fuzzy rough Einstein Bonferroni weighted average operator ($ {C}_{p, q, r} $-SFREBOMWA), plays a crucial role in providing a strong support for MCDM analysis. The method considers lower and upper approximations of alternatives and synthesizes judgments along criteria based on expert confidence levels. The operational laws, theorems, and properties of p, q, r-SFREBOMWG and q, r-SFREBOMWA are explained, showing the superiority and importance of the suggested work, providing more accurate results than existing approaches. Integrating the newly proposed operator with multi-decision-making techniques like criteria importance through intercriteria correlation (CRITIC) and combinative distance-based assessment (CODAS) is a unique approach. A case study was considered to validate the efficacy and usability of the proposed operators in prioritizing sustainable municipal solid waste treatment techniques with the CRITIC and CODAS techniques. The computed results were compared with approaches to further support the outcomes of the proposed work. The comparison was done with technique for order preference by similarity to ideal solution (TOPSIS), and weighted aggregated sum product assessment (WASPAS) to assess the proposed work's reliability. Additionally, comparative and sensitivity analyses were conducted to demonstrate the robustness and excellence of the $ {C}_{p, q, r} $-SFREBOM approach with that of conventional MCDM methods.
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O. S. Deepa, Nandana Vasudevan. Integrating confidence level-based p, q, r-spherical fuzzy rough Einstein Bonferroni aggregation operators with the CRITIC-CODAS approach for prioritizing waste treatment techniques[J]. AIMS Mathematics, 2026, 11(3): 7353-7399. doi: 10.3934/math.2026303
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