Choquet integral-based GRA method with linguistic interval-valued q-Rung orthopair fuzzy sets

Volume 40, Issue 3, pp 368--404 https://dx.doi.org/10.22436/jmcs.040.03.06

Publication Date: July 17, 2025 Submission Date: April 11, 2025 Revision Date: May 15, 2025 Accteptance Date: June 02, 2025

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 275 Downloads
• 844 Views

Authors

J. Ali - Institute of Numerical Sciences, Kohat University of Science and Technology, KPK, Kohat 26000, Pakistan. A. Khan - Institute of Numerical Sciences, Kohat University of Science and Technology, KPK, Kohat 26000, Pakistan. I.-L. Popa - Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania. - Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania.

Abstract

Linguistic interval-valued q-rung orthopair fuzzy (LIVq-ROF) sets offer a powerful framework for modeling uncertainty and vagueness in complex decision-making environments. This study leverages the expressive strength of LIVq-ROF sets to develop novel aggregation operators-specifically, the LIVq-ROF Choquet integral averaging and geometric operators-which are designed to capture interdependencies among attributes in multiple attribute group decision-making (MAGDM) scenarios. The theoretical properties of these operators are rigorously established. Building on this foundation, we propose a Choquet integral-based grey relational analysis (GRA) method tailored for MAGDM under uncertainty. The proposed model is applied to a real-world case study involving the selection of the optimal neural network model for predicting crop yields. Results demonstrate the model’s effectiveness in identifying the best-performing alternative. A thorough sensitivity analysis and comparison with existing approaches confirm the robustness and superior performance of the proposed method.

Share and Cite

Keywords

• Linguistic interval-valued q-rung orthopair fuzzy set
• Choquet integral
• decision-making
• software development
• GRA method

MSC

•  03E72
•  91B06
•  90B50
•  68T37

References

• [1] J. Ali, A q-rung orthopair fuzzy MARCOS method using novel score function and its application to solid waste management, Appl. Intell., 52 (2022), 8770–8792
  • View Article
  • Google Scholar


• [2] Z. Ali, Fairly aggregation operators based on complex p, q-rung orthopair fuzzy sets and their application in decision-making problems, Spec. Oper. Res., 2 (2025), 113–131
  • View Article
  • Google Scholar


• [3] J. Ali, WASPAS-based decision aid approach with Dombi power aggregation operators under disc spherical fuzzy framework, Math. Found. Comput., (2025), 27 pages
  • View Article
  • Google Scholar


• [4] O. Alptekin, N. Alptekin, B. Sarac, Evaluation of low carbon development of European union countries and Turkey using grey relational analysis, Teh. Vjesn., 25 (2018), 1497–1505
  • View Article
  • Google Scholar


• [5] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87–96
  • View Article
  • MathSciNet
  • Google Scholar


• [6] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Manag. Sci., 17 (1970/71), B141–B164
  • View Article
  • MathSciNet
  • Google Scholar


• [7] Z. Chen, P. Liu, Z. Pei, An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers, Int. J. Comput. Intell. Syst., 8 (2015), 747–760
  • View Article
  • Google Scholar


• [8] G. Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble), 5 (1953/54), 131–295
  • View Article
  • MathSciNet
  • Google Scholar


• [9] T. Demirel, N. Ç. Demirel, C. Kahraman, Multi-criteria warehouse location selection using choquet integral, Expert Syst. Appl., 37 (2010), 3943–3952
  • View Article
  • Google Scholar


• [10] Z. Gong, Novel entropy and distance measures of linguistic interval-valued q-rung orthopair fuzzy sets, J. Intell. Fuzzy Syst., 44 (2023), 7865–7876
  • View Article
  • Google Scholar


• [11] S. H. Gurmani, H. Chen, Y. Bai, The operational properties of linguistic interval valued q-rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making, J. Intell. Fuzzy Syst., 41 (2021), 7063–7079
  • View Article
  • Google Scholar


• [12] F. Herrera, L. Martinez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst., 8 (2000), 746–752
  • View Article
  • Google Scholar


• [13] K. Jabeen, Q. Khan, K. Ullah, T. Senapati, S. Moslem, An approach to MADM based on Aczel-Alsina power Bonferroni aggregation operators for q-rung orthopair fuzzy sets, IEEE Access, 11 (2023), 105248–105261
  • View Article
  • Google Scholar


• [14] D. Julong, Introduction to grey system theory, J. Grey Syst., 1 (1989), 1–24
  • View Article
  • Google Scholar


• [15] M. S. A. Khan, A. S. Khan, I. A. Khan, W. K. Mashwani, F. Hussain, Linguistic interval-valued q-rung orthopair fuzzy TOPSIS method for decision making problem with incomplete weight, J. Intell. Fuzzy Syst., 40 (2021), 4223–4235
  • View Article
  • Google Scholar


• [16] S. H. Kim, B. S. Ahn, Interactive group decision making procedure under incomplete information, Eur. J. Oper. Res., 116 (1999), 498–507
  • View Article
  • Google Scholar


• [17] C.-Y. Kung, K.-L. Wen, Applying grey relational analysis and grey decision-making to evaluate the relationship between company attributes and its financial performance—a case study of venture capital enterprises in taiwan, Decis. Support Syst., 43 (2007), 842–852
  • View Article
  • Google Scholar


• [18] Y. Kuo, T. Yang, G.-W. Huang, The use of grey relational analysis in solving multiple attribute decision-making problems, Comput. Ind. Eng., 55 (2088), 80–93
  • View Article
  • Google Scholar


• [19] M. Lin, X. Li, L. Chen, Linguistic q-rung orthopair fuzzy sets and their interactional partitioned heronian mean aggregation operators, Int. J. Intell. Syst., 35 (2020), 217–249
  • View Article
  • Google Scholar


• [20] A. Malek, S. Ebrahimnejad, R. Tavakkoli-Moghaddam, An improved hybrid grey relational analysis approach for green resilient supply chain network assessment, Sustainability, 9 (2017), 28 pages
  • View Article
  • Google Scholar


• [21] M. Mir, M. Dayyani, T. Sutikno, M. Mohammadi Zanjireh, N. Razmjooy, Employing a Gaussian particle swarm optimization method for tuning multi input multi output-fuzzy system as an integrated controller of a micro-grid with stability analysis, Comput. Intell., 36 (2020), 225–258
  • View Article
  • MathSciNet
  • Google Scholar


• [22] N. Nabipour, A. Mosavi, E. Hajnal, L. Nadai, S. Shamshirband, K.-W. Chau, Modeling climate change impact on wind power resources using adaptive neuro-fuzzy inference system, Eng. Appl. Comput. Fluid Mech., 14 (2020), 491–506
  • View Article
  • Google Scholar


• [23] S. Petchimuthu, B. Palpandi, P. Pirabaharan, M. F. Banu, Sustainable urban innovation and resilience: Artificial intelligence and q-rung orthopair fuzzy expologarithmic framework, Spectr. Decis. Mak. Appl., 2 (2025), 242–267
  • View Article
  • Google Scholar


• [24] X. Qi, Z. Ali, T. Mahmood, P. Liu, Multi-attribute decision-making method based on complex interval-valued q-rung orthopair linguistic Heronian mean operators and their application, Int. J. Fuzzy Syst., 25 (2023), 1338–1359
  • View Article
  • Google Scholar


• [25] S. S. Rawat, Komal, P. Liu, Z. Stevic, T. Senapati, S. Moslem, A novel group decision-making approach based on partitioned hamy mean operators in q-rung orthopair fuzzy context, Complex Intell. Syst., 10 (2024), 1375–1408
  • View Article
  • Google Scholar


• [26] N. Razmjooy, M. Ramezani, N. Ghadimi, Imperialist competitive algorithm-based optimization of neuro-fuzzy system parameters for automatic red-eye removal, Int. J. Fuzzy Syst., 19 (2017), 1144–1156
  • View Article
  • Google Scholar


• [27] M. R. Rouhani-Tazangi, B. Feghhi, D. Pamucar, E-procurement readiness assessment in hospitals: A novel hybrid fuzzy decision map and grey relational analysis approach, Spectr. Decis. Mak. Appl., 2 (2025), 356–375
  • View Article
  • Google Scholar


• [28] A. Saha, F. Ecer, P. Chatterjee, T. Senapati, E. K. Zavadskas, q-rung orthopair fuzzy improved power weighted aggregation operators and their applications in multi-criteria group decision-making issues, Informatica, 33 (2022), 593–621
  • View Article
  • Google Scholar


• [29] T. Senapati, G. Chen, I. Ullah, M. S. A. Khan, F. Hussain, A novel approach towards multiattribute decision making using q-rung orthopair fuzzy Dombi–archimedean aggregation operators, Heliyon, 10 (2024), 32 pages
  • View Article
  • Google Scholar


• [30] T. Senapati, L. Martínez, G. Chen, Selection of appropriate global partner for companies using q-rung orthopair fuzzy Aczel–Alsina average aggregation operators, Int. J. Fuzzy Syst., 25 (2023), 980–996
  • View Article
  • Google Scholar


• [31] M. Shams, N. Kausar, P. Agarwal, S. A. Edalatpanah, Fractional Caputo-type simultaneous scheme for finding all polynomial roots, In: Recent Trends in Fractional Calculus and its Applications, Academic Press, (2024), 261–272
  • View Article
  • Google Scholar


• [32] M. Shams, N. Kausar, P. Agarwal, S. Jain, M. A. Salman, M. A. Shah, On family of the Caputo-type fractional numerical scheme for solving polynomial equations, Appl. Math. Sci. Eng., 31 (2023), 20 pages
  • View Article
  • Google Scholar


• [33] M. Shams, N. Kausar, C. Samaniego, P. Agarwal, S. F. Ahmed, S. Momani, On efficient fractional Caputo-type simultaneous scheme for finding all roots of polynomial equations with biomedical engineering applications, Fractals, 31 (2023), 15 pages
  • View Article
  • Google Scholar
  • MATH


• [34] M. Shams, N. Rafiq, N. Kausar, P. Agarwal, N. A. Mir, Y.-M. Li, On highly efficient simultaneous schemes for finding all polynomial roots, Fractals, 30 (2022), 10 pages
  • View Article
  • Google Scholar
  • MATH


• [35] M. Shams, N. Rafiq, N. Kausar, P. Agarwal, C. Park, N. A. Mir, On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation, Adv. Differ. Equ., 2021 (2021), 1–18
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [36] M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, (1974)
  • View Article
  • Google Scholar


• [37] G. Sun, X. Guan, X. Yi, Z. Zhou, Grey relational analysis between hesitant fuzzy sets with applications to pattern recognition, Expert Syst. Appl., 92 (2018), 521–532
  • View Article
  • Google Scholar


• [38] G. Sun, M. Wang, Pythagorean fuzzy information processing based on centroid distance measure and its applications, Expert Syst. Appl., 236 (2024),
  • View Article
  • Google Scholar


• [39] Y.-S. Tan, H. Chen, S. Wu, Evaluation and implementation of environmentally conscious product design by using AHP and Grey relational analysis approaches., Ekoloji Derg., 28 (2019), 857–864
  • View Article
  • Google Scholar


• [40] G. Tian, H. Zhang, Y. Feng, D. Wang, Y. Peng, H. Jia, Green decoration materials selection under interior environment characteristics: A grey-correlation based hybrid MCDM method, Renew. Sustain. Energy Rev., 81 (2018), 682–692
  • View Article
  • Google Scholar


• [41] R. R. Yager, Pythagorean membership grades in multicriteria decision making, IEEE Trans. Fuzzy Syst., 22 (2013), 958– 965
  • View Article
  • Google Scholar


• [42] R. R. Yager, Generalized orthopair fuzzy sets, IEEE Trans. Fuzzy Syst., 25 (2016), 1222–1230
  • View Article
  • Google Scholar


• [43] A. Zeb, W. Ahmad, M. Asif, T. Senapati, V. Simic, M. Hou, A decision analytics approach for sustainable urbanization using q-rung orthopair fuzzy soft set-based Aczel–Alsina aggregation operators, Socio-Econ. Plan. Sci., 95 (2024),
  • View Article
  • Google Scholar


• [44] W. Zhang, H. Gao, Interpretable robust multicriteria ranking with TODIM in generalized orthopair fuzzy settings, Spec. Oper. Res., 3 (2026), 14–28
  • View Article
  • Google Scholar


• [45] Y. Zhang, F. Tang, Z. Song, J. Wang, Interval-valued linguistic q-rung orthopair fuzzy TODIM with unknown attribute weight information, Symmetry, 16 (2024), 14 pages
  • View Article
  • Google Scholar