Abstract
The Dubois–Prade operator can transform its parameter into different values when processing data, which can make it more flexible. Interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) give decision-makers more degrees of freedom. Combining the flexibility of the Dubois–Prade operators and the degrees of freedom of IVq-ROFSs, this paper proposes the interval-valued q-rung orthopair fuzzy Dubois–Prade (IVq-ROFDP) operations and the interval-valued q-rung orthopair Dubois–Prade ordered weighted average (IVq-ROFDPOWA) operator under IVq-ROFSs. Built upon this, considering the interaction between the membership degree and nonmembership degree, the interval-valued q-rung orthopair fuzzy interactive Dubois–Prade (IVq-ROFIDP) operations and the interval-valued q-rung orthopair fuzzy interactive Dubois–Prade ordered weighted average (IVq-ROFIDPOWA) operator are further proposed, and their properties are studied. Finally, a new group decision-making method based on the IVq-ROFIDPOWA operator is proposed to solve the multiattribute group decision-making (MAGDM) problem. The results of two case implementations and the sensitivity analysis show that the proposed operator and group decision-making method are feasible and effective. Furthermore, the comparative analysis shows that the group decision-making method proposed in this paper can better reflect the differences between alternatives.
Similar content being viewed by others
Data availability statement
All relevant data are within the paper.
References
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96. https://doi.org/10.1016/s0165-0114(86)80034-3
Atanassov KT, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3):343–349. https://doi.org/10.1016/0165-0114(89)90205-4
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Heidelberg
Boukezzoula R, Galichet S, Foulloy L (2007) MIN and MAX operators for fuzzy intervals and their potential use in aggregation operators. IEEE Trans Fuzzy Syst 15(6):1135–1144. https://doi.org/10.1109/TFUZZ.2006.890685
Chen S, Chiou CH (2014) Multiattribute decision making based on interval-valued intuitionistic fuzzy sets, PSO techniques, and evidential reasoning methodology. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/tfuzz.2014.2370675
Chen S, Niou SJ (2011) Fuzzy multiple attributes group decision-making based on fuzzy preference relations. Expert Syst Appl 38(4):4097–4108. https://doi.org/10.1016/j.eswa.2010.09.047
Chen S, Phuong BDH (2017) Fuzzy time series forecasting based on optimal partitions of intervals and optimal weighting vectors. Knowl Based Syst 118:204–216. https://doi.org/10.1016/j.knosys.2016.11.019
Chen S, Wang CH (2009) Fuzzy risk analysis based on ranking fuzzy numbers using α-cuts, belief features and signal/noise ratios. Expert Syst Appl 36:5576–5581. https://doi.org/10.1016/j.eswa.2008.06.112
Dong J, Wan S, Chen S (2021) Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Inf Sci 547:1080–1104. https://doi.org/10.1016/j.ins.2020.09.014
Dubois D, Prade H (1980) New results about properties and semantics of fuzzy set-theoretic operators. Springer, US. https://doi.org/10.1007/978-1-4684-3848-2_6
Duuren EV, Plantinga A, Scholtens B (2016) ESG integration and the investment management process: fundamental investing reinvented. J Bus Ethics 138(3):525–533. https://doi.org/10.1007/s10551-015-2610-8
Farid H, Riaz M (2021) Some generalized q-rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws. Int J Intell Syst 36(12):7239–7273. https://doi.org/10.1002/int.22587
Feng F, Zhang C, Akram M, Zhang J (2022) Multiple attribute decision making based on probabilistic generalized orthopair fuzzy sets. Granul Comput. https://doi.org/10.1007/s41066-022-00358-7
Ganie AH (2022) Multicriteria decision-making based on distance measures and knowledge measures of Fermatean fuzzy sets. Granul Comput. https://doi.org/10.1007/s41066-021-00309-8
Gao H, Ju Y, Zhang W, Ju D (2019) Multi-attribute decision-making method based on interval-valued q-rung orthopair fuzzy Archimedean Muirhead mean operators. IEEE Access 7:74300–74315. https://doi.org/10.1109/ACCESS.2019.2918779
Gao H, Ran L, Wei G, Wei C, Wu J (2020) VIKOR method for MAGDM based on q-rung interval-valued orthopair fuzzy information and its application to supplier selection of medical consumption products. Int J Environ Res Public Health 17(2):525–538. https://doi.org/10.3390/ijerph17020525
Garg H (2021) A new possibility degree measure for interval-valued q-rung orthopair fuzzy sets in decision-making. Int J Intell Syst 36(1):526–557. https://doi.org/10.1002/int.22308
Gupta MM, Qi J (1991) Theory of T-norms and fuzzy inference methods. Fuzzy Sets Syst 40(3):431–450. https://doi.org/10.1016/0165-0114(91)90171-L
Hamacher H (1975) Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. Progress in Cybernetics and Systems Research 3
Ilbahar E, Karaşan A, Cebi S, Kahraman C (2018) A novel approach to risk assessment for occupational health and safety using Pythagorean fuzzy AHP & fuzzy inference system. Saf Sci 103:124–136. https://doi.org/10.1016/j.ssci.2017.10.025
Joshi BP, Singh A, Bhatt PK, Vaisla KS (2018) Interval valued q-rung orthopair fuzzy sets and their properties. J Intell Fuzzy Syst 35(3):1–6. https://doi.org/10.3233/jifs-169806
Ju Y, Luo C, Ma J, Gonzalez ES, Wang A (2019) Some interval-valued q-rung orthopair weighted averaging operators and their applications to multiple-attribute decision making. Int J Intell Syst 34(10):2584–2606
Khaista R, Saleem A, Muhammad J, Muhammad YK (2018) Some generalized intuitionistic fuzzy einstein hybrid aggregation operators and their application to multiple attribute group decision making. Int J Fuzzy Syst 20(5):1567–1575. https://doi.org/10.1007/s40815-018-0452-0
Liu P, Liu J, Chen SM (2017) Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. J Oper Res Soc. https://doi.org/10.1057/s41274-017-0190-y
Liu Z, Wang S, Liu P (2018) Multiple attribute group decision making based on q-rung orthopair fuzzy Heronian mean operators. Int J Intell Syst 33(12):2341–2363. https://doi.org/10.1002/int.22032
Liu P, Chen S, Wang Y (2019) Multiattribute group decision making based on intuitionistic fuzzy partitioned Maclaurin symmetric mean operators. Inf Sci. https://doi.org/10.1016/j.ins.2019.10.013
Merigo JM (2012) The probabilistic weighted average and its application in multiperson decision making. Int J Intell Syst 27(5):457–476. https://doi.org/10.1002/int.21531
Peng X, Yong Y (2016) Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487. https://doi.org/10.1002/int.21790
Rawat SS, Komal (2022) Multiple attribute decision making based on q-rung orthopair fuzzy Hamacher Muirhead mean operators. Soft Comput 26(5):2465–2487. https://doi.org/10.1007/s00500-021-06549-9
Saad M, Rafiq A (2022) Correlation coefficients for T-spherical fuzzy sets and their applications in pattern analysis and multi-attribute decision-making. Granul Comput. https://doi.org/10.1007/s41066-022-00355-w
Saha A, Majumder P, Dutta D, Debnath BK (2020) Multi-attribute decision making using q-rung orthopair fuzzy weighted fairly aggregation operators. J Ambient Intell Humaniz Comput 12:8149–8171. https://doi.org/10.1007/s12652-020-02551-5
Wang J, Gao H, Wei G, Wei Y (2019a) Methods for multiple-attribute group decision making with q-rung interval-valued orthopair fuzzy information and their applications to the selection of green suppliers. Symmetry 11(1):56–82. https://doi.org/10.3390/sym11010056
Wang L, Garg H, Li NA (2019b) Interval-valued q-rung orthopair 2-tuple linguistic aggregation operators and their applications to decision making process. IEEE Access 7(1):131962–131977. https://doi.org/10.1109/ACCESS.2019.2938706
Wang J, Wei G, Wei C, Wu J (2019c) Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment. Defence Technol 16(5):1–34. https://doi.org/10.1016/j.dt.2019.11.007
Wang L, Garg H, Li N (2021) Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight. Soft Comput 25(2):973–993. https://doi.org/10.1007/s00500-020-05193-z
Yager RR (1994) Aggregation operators and fuzzy systems modeling. Fuzzy Sets Syst 67(2):129–145. https://doi.org/10.1016/0165-0114(94)90082-5
Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A Syst Hum 31(6):724–731. https://doi.org/10.1109/3468.983429
Yager RR (2013) Pythagorean fuzzy subsets. In: IFSA World Congress & NAFIPS Annual Meeting. IEEE
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965. https://doi.org/10.1109/tfuzz.2013.2278989
Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230. https://doi.org/10.1109/tfuzz.2016.2604005
Yang Y, Chen ZS, Rodriguez RM, Pedrycz W, Chin KS (2021) Novel fusion strategies for continuous interval-valued q-rung orthopair fuzzy information: a case study in quality assessment of SmartWatch appearance design. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-020-01269-2
Yucesan M, Kahraman G (2019) Risk evaluation and prevention in hydropower plant operations: a model based on Pythagorean fuzzy AHP. Energy Policy 126:343–351. https://doi.org/10.1016/j.enpol.2018.11.039
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zeng S, Chen S, Fan K (2020) Interval-valued intuitionistic fuzzy multiple attribute decision making based on nonlinear programming methodology and TOPSIS method. Inf Sci 506:424–442. https://doi.org/10.1016/j.ins.2019.08.027
Funding
There is no funder of the paper.
Author information
Authors and Affiliations
Contributions
YP did all the work for the paper, including conceptualization, methodology, data gathering, formal analysis and writing.
Corresponding author
Ethics declarations
Conflict of interest
The author declared no potential conflicts of interest with respect to the research, authorship, and publication of the paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Peng, Y. Interval-valued q-rung orthopair fuzzy interactive Dubois–Prade operator and its application in group decision-making. Granul. Comput. 8, 1799–1818 (2023). https://doi.org/10.1007/s41066-023-00395-w
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41066-023-00395-w