Eight Innovative Dual Hesitant Fuzzy Aggregation Operators for Enhanced Decision Making

Abstract

Dual hesitant fuzzy elements can simultaneously capture the hesitancy and uncertainty of information. Although significant progress has been made in dual hesitant fuzzy elements aggregation for multi-attribute decision-making, existing aggregation operators still lack idempotency, potentially leading to biased decision outcomes. To address this issue, this study proposes a series of novel dual hesitant fuzzy elements aggregation operators, and further establishes a corresponding decision-making method. Specifically, we firstly propose two normalized Einstein operations for dual hesitant fuzzy elements and define a novel comparison rule. Furthermore, several normalized Einstein aggregation operators are developed based on the provided normalized Einstein operations. What’s more, we establish a decision-making method for solving practical multi-attribute decision-making problems. In addition, two practical cases are conducted to demonstrate the feasibility and practicality of our method.

Keywords

Dual hesitant fuzzy set / normalized Einstein aggregation operator / decision making / material selection

References

[1] Ahmad W, Zeb A, Asif M, Hou M. Bipolar fuzzy soft Hamacher aggregations operators and their application in triage procedure for handling emergency earthquake disaster. The Journal of Supercomputing, 2025, 81: 1-56.

[2] Atanassov K T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, 20: 87-96.

[3] Atanassov K T, Gargov G. Interval-valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1989, 31: 343-349.

[4] Aydemir S B, Gunduz S Y. Anovel approach to multi-attribute group decision making based on power neutrality aggregation operator for q-rung orthopair fuzzy sets. International Journal of Intelligent Systems, 2021, 36: 1454-1481.

[5] Beliakov G, Pradera A, Calvo TAggregation Functions: A Guide for Practitioners, 2007Heidelberg, Berlin, New YorkSpringer

[6] Caglayan N, Abbasi S, Yilmaz I, Erdebilli B. Bibliometric analysis on the distributed decision, decentralized decision, and fuzzy logic. Discrete Dynamics in Nature and Society, 20247305880

[7] Calache L D D R, Camargo V C B, Osiro L, Carpinetti L C R. A genetic algorithm based on dual hesitant fuzzy preference relations for consensus group decision making. Applied Soft Computing, 2022, 121: 108778.

[8] Dawlet O, Bao Y L. Normalized hesitant fuzzy aggregation operators for multiple attribute decision-making. International Journal of Fuzzy Systems, 2024

[9] Dawlet O, Bao Y L. A note on “Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making”. Journal of Intelligent & Fuzzy Systems, 2023, 45: 8197-8201

[10] Gao J, Xu Z S, Zhong C, Mao Y S. Multiplicative integral theory of generalized orthopair fuzzy sets and its applications. Journal of Systems Science and Systems Engineering, 2022, 31: 457-479.

[11] Garg H, Sun Y K, Liu X D. Dual hesitant fuzzy Correlation coefficient-based decision-making algorithm and its applications to Engineering Cost Management problems. Engineering Applications of Artificial Intelligence, 2023, 126: 107170.

[12] Gowtham R N, Hait S R, Guha D, Mahadevappa M. Classification of epileptic EEG signals with the utilization of Bonferroni mean based fuzzy pattern tree. Expert Systems with Applications, 2024, 239: 122424.

[13] Grabisch M, Marichal J L, Mesiar R, Pap EAggregation functions, 2009.

[14] Hao Z N, Xu Z S, Zhao H, Su Z. Probabilistic dual hesitant fuzzy set and its application in risk evaluation. Knowledge-Based Systems, 2017, 127: 16-28.

[15] Javeed S, Javed M, Shafique I, Shoaib M, Khan M S, Cui L, Askar S, Alshamrani A M. Complex q-rung orthopair fuzzy Yager aggregation operators and their application to evaluate the best medical manufacturer. Applied Soft Computing, 2024, 157: 111532.

[16] Ju Y B, Zhang W K, Yang S G. Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 2014, 27: 2481-2495

[17] Li L, Ji C L, Wang J. A novel multi-attribute group decision making method based on q-rung dual hesitant fuzzy information and extended power average operators. Cognitive Computation, 2021, 13: 1345-1362.

[18] Li L, Wang J, Ji C L. Multi-attribute decision-making based on q-rung dual hesitant power dual maclaurin symmetric mean operator and a new ranking method. Archives of Control Sciences, 2022, 32: 627-658

[19] Liang D C, Darko A P, Xu Z S, Wang M W. Aggregation of dual hesitant fuzzy heterogenous related information with extended Bonferroni mean and its application to MULTIMOORA. Computers & Industrial Engineering, 2019, 135: 156-176.

[20] Liu J B, Malik M A, Ayub N, Siddiqui H. Distance measures for multiple-attributes decision-making based on connection numbers of set pair analysis with dual hesitant fuzzy sets. IEEE Access, 2020, 8: 9172-9184.

[21] Liu Y, Yang Z J, He J L, Yu L J, Zhong Y. Some intuitionistic cubic fuzzy muirhead mean operators with their application to multicriteria decision making. International Journal of Intelligent Systems, 20239891355

[22] Mahmood T, Ullah K, Khan Q, Jan N. An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Computing and Applications, 2019, 31: 7041-7053.

[23] Mo JM, Huang H L. Archimedean geometric Heronian mean aggregation operators based on dual hesitant fuzzy set and their application to multiple attribute decision making. Soft Computing, 2020, 24: 14721-14733.

[24] Ning B Q, Wei G W, Lin R, Guo Y F. A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection. Expert Systems with Applications, 2022, 204: 117419.

[25] Pan L, Xu Z S. Confidence-based consensus model for multi-attribute group decision making: Exploring the bounded trust propagation and personalized adjustment willingness. Journal of Systems Science and Systems Engineering, 2023, 32: 483-513.

[26] Sarkar A, Moslem S, Esztergar-Kiss D, Akram M, Jin L S, Senapati T. Ahybrid approach based on dual hesitant q-rung orthopair fuzzy Frank power partitioned Heronian mean aggregation operators for estimating sustainable urban transport solutions. Engineering Applications of Artificial Intelligence, 2023, 124: 106505.

[27] Singh S. Knowledge and accuracy measure based on dual-hesitant fuzzy sets with application to pattern recognition and site selection for solar power plant. Granular Computing, 2023, 8: 157-170.

[28] Tang X A, Yang S L, Pedrycz W. Multiple attribute decision-making approach based on dual hesitant fuzzy Frank aggregation operators. Applied Soft Computing, 2018, 68: 525-547.

[29] Thilagavathy A, Mohanaselvi S. T-Spherical fuzzy TOPSIS method based on distance measures and Hamacher Heronian mean averaging aggregation operators and its application to waste management. Applied Soft Computing, 2024, 162: 111868.

[30] Torra V. Hesitant fuzzy sets. International Journal of Intelligent Systems, 2010, 25: 529-539

[31] Wang L, Shen Q G, Zhu L. Dual hesitant fuzzy power aggregation operators based on Archimedean t-conorm and t-norm and their application to multiple attribute group decision making. Applied Soft Computing, 2016, 38: 23-50.

[32] Yiarayong P. Enhancing multicriteria decision-making in smart farming using (p, q)rung orthopair fuzzy hypersoft sets and weighted aggregation operators. International Journal of Information Technology, 2024

[33] Yu D J, Zhang W Y, Huang G. Dual hesitant fuzzy aggregation operators. Technological and Economic Development of Economy, 2013, 52: 395-407

[34] Yu Q, Hou F J, Zhai Y B, Du Y Q. Some hesitant fuzzy Einstein aggregation operators and their application to multiple attribute group decision making. International Journal of Intelligent Systems, 2016, 31: 722-746.

[35] Zadeh LA. Fuzzy sets. Information and Control, 1965, 8: 338-353.

[36] Zeng W Y, Ma R, Liu Z P, Yin Q, Xu Z S. Some novel distance measures between dual hesitant fuzzy sets and their application in medical diagnosis. International Journal of Intelligent Systems, 2022, 37: 8653-8671.

[37] Zeng W Y, Xi Y, Yin Q, Guo P. Weighted dual hesitant fuzzy set and its application in group decision making. Neurocomputing, 2021, 458: 714-726.

[38] Zhao X F, Wei G W. Some intuitionistic fuzzy Einstein hybrid aggregation operators and their application to multiple attribute decision making. Knowledge-Based Systems, 2013, 37: 472-479.

[39] Zhao H, Xu Z S, Liu S S. Dual hesitant fuzzy information aggregation with Einstein t-conormand t-norm. Journal of Systems Science and Systems Engineering, 2017, 26: 240-264.

[40] Zhu B, Xu Z S, Xia M M. Dual hesitant fuzzy sets. Journal of Applied Mathematics, 2012, 12: 879629.

RIGHTS & PERMISSIONS

Systems Engineering Society of China and Springer-Verlag GmbH Germany

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.