Aczél–Alsina aggregation operators for bipolar $ (p, q) $-quasirung orthopair fuzzy information with application to MCDM

Shatha Abdulhadi Saleh Alharbi; Kholood Mohammad Alsager; Shatha Abdulhadi Saleh Alharbi; Kholood Mohammad Alsager

doi:10.3934/math.20261394

AIMS Mathematics

2026, Volume 11, Issue 11: 35957-36025. doi: 10.3934/math.20261394

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Research article

Aczél–Alsina aggregation operators for bipolar $ (p, q) $-quasirung orthopair fuzzy information with application to MCDM

Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia; 461216032@qu.edu.sa

Received: 14 September 2026 Revised: 11 October 2026 Accepted: 20 October 2026 Published: 03 November 2026
MSC : 03B52, 03E72

This study extends the Aczél–Alsina operational and aggregation framework for $ (p, q) $-quasirung orthopair fuzzy information to a four-component bipolar setting. Aczél–Alsina operational laws are formulated for bipolar $ (p, q) $-quasirung orthopair fuzzy numbers, and the corresponding weighted averaging and weighted geometric aggregation operators are developed. The resulting operators are shown to preserve the bipolar $ (p, q) $-quasirung orthopair fuzzy structure and satisfy the required aggregation properties. In addition, complement duality between the weighted averaging and geometric operators is established. The effect of the Aczél–Alsina parameter is characterized theoretically, showing the opposite responses of the positive- and negative-pole score components and demonstrating that monotonicity of the overall pole-weighted score does not follow in general. An explicit pole importance parameter $ \alpha $ is incorporated into the ranking mechanism, and pole agreement, pole conflict, and the corresponding preference-switching threshold are characterized analytically. The proposed mechanisms are integrated into a multicriteria decision-making procedure and illustrated through a sustainable supplier selection problem. Numerical analyses examine the effects of the bipolar structure, criterion weights, and the parameters $ p $, $ q $, $ \lambda $, and $ \alpha $. The leading alternative remains unchanged across the examined $ p $, $ q $, $ \lambda $, and criterion weight scenarios, whereas changes in $ \alpha $ can alter the leading alternative when the negative pole is heavily discounted. The complete ranking of the lower-ranked alternatives remains sensitive to the aggregation operator and parameter settings.
- bipolar fuzzy sets,
- $ (p, q) $-quasirung orthopair fuzzy sets,
- Aczél–Alsina aggregation operators,
- multicriteria decision-making,
- pole-sensitive ranking
Citation: Shatha Abdulhadi Saleh Alharbi, Kholood Mohammad Alsager. Aczél–Alsina aggregation operators for bipolar $ (p, q) $-quasirung orthopair fuzzy information with application to MCDM[J]. AIMS Mathematics, 2026, 11(11): 35957-36025. doi: 10.3934/math.20261394

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Abstract

This study extends the Aczél–Alsina operational and aggregation framework for $ (p, q) $-quasirung orthopair fuzzy information to a four-component bipolar setting. Aczél–Alsina operational laws are formulated for bipolar $ (p, q) $-quasirung orthopair fuzzy numbers, and the corresponding weighted averaging and weighted geometric aggregation operators are developed. The resulting operators are shown to preserve the bipolar $ (p, q) $-quasirung orthopair fuzzy structure and satisfy the required aggregation properties. In addition, complement duality between the weighted averaging and geometric operators is established. The effect of the Aczél–Alsina parameter is characterized theoretically, showing the opposite responses of the positive- and negative-pole score components and demonstrating that monotonicity of the overall pole-weighted score does not follow in general. An explicit pole importance parameter $ \alpha $ is incorporated into the ranking mechanism, and pole agreement, pole conflict, and the corresponding preference-switching threshold are characterized analytically. The proposed mechanisms are integrated into a multicriteria decision-making procedure and illustrated through a sustainable supplier selection problem. Numerical analyses examine the effects of the bipolar structure, criterion weights, and the parameters $ p $, $ q $, $ \lambda $, and $ \alpha $. The leading alternative remains unchanged across the examined $ p $, $ q $, $ \lambda $, and criterion weight scenarios, whereas changes in $ \alpha $ can alter the leading alternative when the negative pole is heavily discounted. The complete ranking of the lower-ranked alternatives remains sensitive to the aggregation operator and parameter settings.

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