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Volume 15
Issue 21
10.3390/app152111818
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Correction to Appl. Sci. 2019, 9(6), 1232.
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Correction

Correction: Bashir et al. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232

by
Zia Bashir
1,
Yasir Bashir
2,
Tabasam Rashid
3,
Jawad Ali
1 and
Wei Gao
4,*
1
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2
Faculty of Mathematics, COMSATS University Islamabad, Wah Campus 47040, Pakistan
3
University of Management and Technology, Lahore 54770, Pakistan
4
School of Information Science and Technology, Yunnan Normal University, Kunming 650092, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2025, 15(21), 11818; https://doi.org/10.3390/app152111818
Submission received: 6 August 2025 / Accepted: 25 August 2025 / Published: 6 November 2025
Versions Notes
There were a few errors in the original publication [1]. The number 0 was mistakenly inserted in some equations and should be deleted.
Corrections have been made to equations of Section 2 (Definition 3, Definition 5), Section 3 (Definition 8, Definition 13, Proof of Theorem 1), Section 4 (Definition 14, Definition 15), Section 5 (Subsection 5.1, Definitions 17–20; Subsection 5.2), and Section 7 (Subsection 7.1).
The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Reference

  1. Bashir, Z.; Bashir, Y.; Rashid, T.; Ali, J.; Gao, W. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232. [Google Scholar] [CrossRef]
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Share and Cite

MDPI and ACS Style

Bashir, Z.; Bashir, Y.; Rashid, T.; Ali, J.; Gao, W. Correction: Bashir et al. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232. Appl. Sci. 2025, 15, 11818. https://doi.org/10.3390/app152111818

AMA Style

Bashir Z, Bashir Y, Rashid T, Ali J, Gao W. Correction: Bashir et al. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232. Applied Sciences. 2025; 15(21):11818. https://doi.org/10.3390/app152111818

Chicago/Turabian Style

Bashir, Zia, Yasir Bashir, Tabasam Rashid, Jawad Ali, and Wei Gao. 2025. "Correction: Bashir et al. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232" Applied Sciences 15, no. 21: 11818. https://doi.org/10.3390/app152111818

APA Style

Bashir, Z., Bashir, Y., Rashid, T., Ali, J., & Gao, W. (2025). Correction: Bashir et al. A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets. Appl. Sci. 2019, 9, 1232. Applied Sciences, 15(21), 11818. https://doi.org/10.3390/app152111818

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