Abstract
The majority of real-life decision-making problems often require the analysis and evaluation of multiple factors. The nested probabilistic linguistic term set is a good tool for describing multidimensional uncertain information because it contains a collection of inner-layer and outer-layer terms and expresses both ordinal and nominal terminologies. In order to avoid losing information in the process of converting linguistic terms into numerical values, this paper proposes a series of new equivalent transformation functions for nested probabilistic linguistic term sets and defines the corresponding comparison rules. The criteria importance through inter-criteria correlation (CRITIC) method is conducted to calculate the objective weights of attributes. Using equivalent transformation functions and the weighting approach with the nested probabilistic linguistic information, this paper combines the weighted MULTIMOORA method with dominance-directed graph to solve the doctor–patient shared decision-making problem. In addition, the results of comparative analysis show that the proposed method is reasonable and effective, and it is applicable to other decision-making scenarios.
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References
Altuntas S, Dereli T, Yilmaz MK (2015) Evaluation of excavator technologies: application of data fusion based MULTIMOORA methods. J Civ Eng Manag 21(8):977–997. https://doi.org/10.3846/13923730.2015.1064468
Barfod KW, Holmich P (2022) Acute Achilles’ tendon rupture—surgery or no surgery. N Engl J Med 386(15):1465–1466. https://doi.org/10.1056/NEJMe2202696
Brauers WKM, Zavadskas EK (2010) Project management by MULTIMOORA as an instrument for transition economies. Technol Econ Dev Econ 16(1):5–24. https://doi.org/10.3846/tede.2010.01
Buyukozkan G, Mukul E, Kongar E (2021) Health tourism strategy selection via SWOT analysis and integrated hesitant fuzzy linguistic AHP-MABAC approach. Socio-Economic Plan Sci 74:100929. https://doi.org/10.1016/j.seps.2020.100929
Celikbilek Y, Tuysuz F (2020) An in-depth review of theory of the TOPSIS method: an experimental analysis. J Manage Anal 7(2):281–300. https://doi.org/10.1080/23270012.2020.1748528
Deng SL, Sun ZY, Zhang CH, Chen G, Li J (2017) Surgical treatment versus conservative management for acute achilles tendon rupture: a systematic review and meta-analysis of randomized controlled trials. J Foot Ankle Surg 56(6):1236–1243. https://doi.org/10.1053/j.jfas.2017.05.036
Deng Y, Wang X, Min C (2020) Optimization-based TOPSIS method with incomplete weight information under nested probabilistic-numerical linguistic environment. Math Probl Eng 2020:1–14. https://doi.org/10.1155/2020/5092531
Diakoulaki D, Mavrotas G, Papayannakis L (1995) Determining objective weights in multiple criteria problems: the critic method. Comput Oper Res 22(7):763–770. https://doi.org/10.1016/0305-0548(94)00059-h
Divsalar M, Ahmadi M, Nemati Y (2022) A SCOR-based model to evaluate LARG supply chain performance using a hybrid MADM method. IEEE Trans Eng Manage 69(4):1101–1120. https://doi.org/10.1109/tem.2020.2974030
Fu C, Zhou KL, Xue M (2018) Fair framework for multiple criteria decision making. Comput Ind Eng 124:379–392. https://doi.org/10.1016/j.cie.2018.07.039
Gou XJ, Liao HC, Xu ZS, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: a case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34. https://doi.org/10.1016/j.inffus.2017.02.008
Hafezalkotob A, Hafezalkotob A, Liao HC, Herrera F (2019) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fusion 51:145–177. https://doi.org/10.1016/j.inffus.2018.12.002
Huang J, Liu HC, Duan CY, Song MS (2022) An Improved reliability model for fmea using probabilistic linguistic term sets and todim method. Ann Oper Res 312(1):235–258. https://doi.org/10.1007/s10479-019-03447-0
Khunkhun V, Pacheco C, Burns L, Gershen S, Mai TA, Scheeringa MS (2022) Patient preferences for shared decision making in Mental Health Care. Patient Educ Couns 105(4):1048–1049. https://doi.org/10.1016/j.pec.2021.07.026
Kim JH, Ahn BS (2019) Extended VIKOR method using incomplete criteria weights. Expert Syst Appl 126:124–132. https://doi.org/10.1016/j.eswa.2019.02.019
Kosiol J, Keiler A, Loizides A, Gruber H, Henninger B, Bolderl A, Gruber L (2022) Operative versus conservative treatment of acute Achilles tendon ruptures: preliminary results of clinical outcome, kinematic MRI and contrast-enhanced ultrasound. Arch Orthop Trauma Surg. https://doi.org/10.1007/s00402-022-04457-7
Li Y, Zhang YX, Xu ZS (2020) A decision-making model under probabilistic linguistic circumstances with unknown criteria weights for online customer reviews. Int J Fuzzy Syst 22(3):777–789. https://doi.org/10.1007/s40815-020-00812-1
Liao HC, Xu ZS, Zeng XJ (2015) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355. https://doi.org/10.1109/tfuzz.2014.2360556
Liao HC, Qin R, Gao CY, Wu XL, Hafezalkotob A, Herrera F (2019) Score-Hedlisf: a score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: an application to unbalanced hesitant fuzzy linguistic MULTIMOORA. Inf Fusion 48:39–54. https://doi.org/10.1016/j.inffus.2018.08.006
Lin CY, Renwick L, Lovell K (2022) Health professionals’ perspectives on shared decision-making in secondary mental healthcare: a qualitative study. J Ment Health 31(5):709–715. https://doi.org/10.1080/09638237.2021.2022608
Liu HC, Wang JH, Zhang L, Zhang QZ (2022) New success likelihood index model for large group human reliability analysis considering noncooperative behaviors and social network. Reliabil Eng Syst Safety 228:108817. https://doi.org/10.1016/j.ress.2022.108817
Liu PD, Li Y (2019) An extended MULTIMOORA method for probabilistic linguistic multi-criteria group decision-making based on prospect theory. Comput Ind Eng 136:528–545. https://doi.org/10.1016/j.cie.2019.07.052
Luo L, Zhang C, Liao HC (2019) Distance-based intuitionistic multiplicative MULTIMOORA method integrating a novel weight-determining method for multiple criteria group decision making. Comput Ind Eng 131:82–98. https://doi.org/10.1016/j.cie.2019.03.038
Morrison T, Foster E, Dougherty J, Barton J (2022) Shared decision making in rheumatology: a scoping review. Semin Arthritis Rheumat 56:152041. https://doi.org/10.1016/j.semarthrit.2022.152041
Ocampo L, Aro JL, Evangelista SS, Maturan F, Casinillo L, Yamagishi K, Selerio E (2022) Composite ecotourism potential index based on an integrated stochastic CRITIC-weighted sum method. Curr Issue Tour. https://doi.org/10.1080/13683500.2022.2090906
Pang Q, Wang H, Xu ZS (2016) Probabilistic linguistic linguistic term sets in multi-attribute group decision making. Inf Sci 369:128–143. https://doi.org/10.1016/j.ins.2016.06.021
Paramanik AR, Sarkar S, Sarkar B (2022) Oswmi: An objective-subjective weighted method for minimizing inconsistency in multi-criteria decision making. Comput Ind Eng 169:108138. https://doi.org/10.1016/j.cie.2022.108138
Park SH, Lee HS, Young KW, Seo SG (2020) Treatment of acute Achilles tendon rupture. Clin Orthop Surg 12(1):1–8. https://doi.org/10.4055/cios.2020.12.1.1
Park CH, Yan H, Park J, Chang MC (2021) Mini-open repair for acute achilles tendon rupture: Ring forceps vs the achillon device. Am J Sports Med 49(13):3613–3619. https://doi.org/10.1177/03635465211044464
Peng XD, Zhang X, Luo ZG (2020) Pythagorean fuzzy MADM method based on CoCoSo and CRITIC with score function for 5G industry evaluation. Artif Intell Rev 53(5):3813–3847. https://doi.org/10.1007/s10462-019-09780-x
Pramanik S, Mallick R (2020) MULTIMOORA strategy for solving multi-attribute group decision making (MAGDM) in trapezoidal neutrosophic number environment. Caai Trans Intell Technol 5(3):150–156. https://doi.org/10.1049/trit.2019.0101
Qi XL, Yu XH, Wang L, Liao XL, Zhang SJ (2019) Promethee for prioritized criteria. Soft Comput 23(22):11419–11432. https://doi.org/10.1007/s00500-019-04109-w
Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119. https://doi.org/10.1109/tfuzz.2011.2170076
Saleem A, Khan IA, Crouser NJ, Martin KD (2022) Utilizing a percutaneous versus open achilles tendon repair technique for treating acute Achilles tendon ruptures in physically active adults: a critically appraised topic. J Sport Rehabil 31(7):943–949. https://doi.org/10.1123/jsr.2021-0330
Santrock RD, Friedmann AJ, Hanselman AE (2017) Acute rupture open repair techniques. Clin Podiatr Med Surg 34(2):245–250. https://doi.org/10.1016/j.cpm.2016.10.010
Sharkasi N, Rezakhah S (2022) A modified CRITIC with a reference point based on fuzzy logic and hamming distance. Knowl Based Syst 255:109768. https://doi.org/10.1016/j.knosys.2022.109768
Su WH, Luo DD, Zhang CH, Zeng SZ (2022) Evaluation of online learning platforms based on probabilistic linguistic term sets with self-confidence multiple attribute group decision making method. Expert Syst Appl 208:118153. https://doi.org/10.1016/j.eswa.2022.118153
Tian Y, Kang BY (2020) A modified method of generating Z-number based on OWA weights and maximum entropy. Soft Comput 24(20):15841–15852. https://doi.org/10.1007/s00500-020-04914-8
Wang XX, Xu ZS, Gou XJ (2019) Nested probabilistic-numerical linguistic term sets in two-stage multi-attribute group decision making. Appl Intell 49(7):2582–2603. https://doi.org/10.1007/s10489-018-1392-y
Wang XX, Xu ZS, Wen Q, Li HH (2021) A multidimensional decision with nested probabilistic linguistic term sets and its application in corporate investment. Economic Research-Ekonomska Istraživanja 34(1):3382–3400. https://doi.org/10.1080/1331677x.2021.1875255
Wang XX, Li YY, Xu ZS, Luo YY (2022) Nested information representation of multi-dimensional decision: an improved PROMETHEE method based on NPLTSs. Inf Sci 607:1224–1244. https://doi.org/10.1016/j.ins.2022.06.053
Wu XL, Liao HC (2018) An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Information Fusion 43:13–26. https://doi.org/10.1016/j.inffus.2017.11.008
Wu XL, Liao HC, Xu ZS, Hafezalkotob A, Herrera F (2018) Probabilistic linguistic MULTIMOORA: a multicriteria decision making method based on the probabilistic linguistic expectation function and the improved Borda Rule. IEEE Trans Fuzzy Syst 26(6):3688–3702. https://doi.org/10.1109/tfuzz.2018.2843330
Yang B, Liu Y, Kan SL, Zhang D, Xu H, Liu FF, Ning GZ, Feng SQ (2017) Outcomes and complications of percutaneous versus open repair of acute Achilles tendon rupture: a meta-analysis. Int J Surg 40:178–186. https://doi.org/10.1016/j.ijsu.2017.03.021
Yang X, Meng H, Quan Q, Peng J, Lu S, Wang A (2018) Management of acute Achilles tendon ruptures a review. Bone Joint Res 7(10):561–569. https://doi.org/10.1302/2046-3758.710.Bjr-2018-0004.R2
Zadeh LA (1975) Concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zhang CH, Chen C, Streimikiene D, Balezentis T (2019) Intuitionistic fuzzy MULTIMOORA approach for multi-criteria assessment of the energy storage technologies. Appl Soft Comput 79:410–423. https://doi.org/10.1016/j.asoc.2019.04.008
Zhao H, You JX, Liu HC (2017) Failure mode and effect analysis using MULTIMOORA method with continuous weighted entropy under interval-valued intuitionistic fuzzy environment. Soft Comput 21(18):5355–5367. https://doi.org/10.1007/s00500-016-2118-x
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant Nos. 72101168, 72071135; the National Natural Science Foundation of Sichuan Province under Grant No. 2022NSFSC0942; the Fundamental Research Funds for the Central Universities under Grant YJ202063; and China Postdoctoral Science Foundation under Grant No. 2021M692259.
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Xiao, J., Xu, Z. & Wang, X. An improved MULTIMOORA with CRITIC weights based on new equivalent transformation functions of nested probabilistic linguistic term sets. Soft Comput 27, 11629–11646 (2023). https://doi.org/10.1007/s00500-023-08218-5
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DOI: https://doi.org/10.1007/s00500-023-08218-5