Abstract
Post-acute care (PAC) is an interdisciplinary healthcare service used to assist in returning patients to their community after they receive acute medical services. To establish a fully developed PAC service model, the National Health Insurance Administration in Taiwan attempts to recruit professional medical service institutions (consisting of medical centers and regional and district hospitals) in a trial program for improving the rehabilitation quality of patients with cerebrovascular diseases (CVDs) and to reduce the re-hospitalization rate. The evaluation and selection of adequate medical service institutions are critical in the program for enhancing the effectiveness of hospital-based PAC in acute stroke management. However, because of the complexity of the national health insurance system and the healthcare system in Taiwan, the determination of pilot hospitals is a highly complicated and ambiguous multiple criteria decision analysis (MCDA) problem. Focusing on the requirement of generating a set of pilot hospitals for the PAC program and tackling imprecise and uncertain information associated with a complex medical circumstance, the purpose of this paper is to develop a novel compromising decision-making method based on the interval-valued Pythagorean fuzzy (IVPF) set theory and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methodology to address the multiple criteria selection problem of pilot hospitals in assisting the establishment of a hospital-based PAC model. Considering the powerfulness of IVPF sets when handling vagueness and complex uncertainty in practical problems, this paper proposes a useful IVPF VIKOR method that is significantly different from the existing VIKOR methodology. The proposed methodology represents a comprehensive integration of high-order uncertainties within a decision environment into the basic VIKOR structure that is designed to lead to both better description and better applicability of MCDA. This paper presents some novel concepts such as remoteness indices and remoteness-based multiple criteria ranking indices and investigates their desirable properties in detail. With the theoretical support of these new concepts, this paper establishes useful remoteness-based group utility indices, individual regret indices, and compromise indices for the assessment of acceptable advantage and acceptable stability. Unlike the current VIKOR-based ranking process, this paper provides a systematic ranking procedure that is capable of improving the efficiency of determining ultimate compromise solutions. Overall, the present study provides several significant contributions, such as structuring the selection problem for hospital-based PAC, extending the IVPF theory and VIKOR to the medical and healthcare fields, simplifying the manipulation procedure in handling IVPF information, constructing valuable concepts of remoteness-based indices, and developing an effective IVPF VIKOR ranking procedure. A real-world example of selecting pilot hospitals in the PAC program for CVDs is provided to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. Furthermore, other valuable MCDA applications with a comparative analysis are conducted to validate the advantages of the proposed method in a variety of fields.
Similar content being viewed by others
References
Akram M, Shahzadi S (2016) Novel intuitionistic fuzzy soft multiple-attribute decision-making methods. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2543-x
Bagheri M, Shojaei P, Tayebi Khorami M (2018) A comparative survey of the condition of tourism infrastructure in Iranian provinces using VIKOR and TOPSIS. Decis Sci Lett 7(1):87–102
Banaeian N, Mobli H, Fahimnia B, Nielsen IE, Omid M (2018) Green supplier selection using fuzzy group decision making methods: a case study from the agri-food industry. Comput Oper Res 89:337–347
Bai Z-Y (2013) An interval-valued intuitionistic fuzzy TOPSIS method based on an improved score function, Sci World J 2013(2013):879089. https://doi.org/10.1155/2013/879089
Bausys R, Zavadskas E-K (2015) Multicriteria decision making approach by VIKOR under interval neutrosophic set environment. Econ Comput Econ Cybern Stud Res 49(4):33–48
Chang T-H (2014) Fuzzy VIKOR method: a case study of the hospital service evaluation in Taiwan. Inf Sci 271:196–212
Chen T-Y (2015) An interval type-2 fuzzy LINMAP method with approximate ideal solutions for multiple criteria decision analysis. Inf Sci 297:50–79
Chen T-Y (2015) An interval type-2 fuzzy technique for order preference by similarity to ideal solutions using a likelihood-based comparison approach for multiple criteria decision analysis. Comput Ind Eng 85:57–72
Chen T-Y (2016) An inclusion comparison approach for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. Technol Econ Dev Econ 22(3):357–392
Chen T-Y (2018) Remoteness index-based Pythagorean fuzzy VIKOR methods with a generalized distance measure for multiple criteria decision analysis. Inf Fusion 41:129–150
Chen S-M, Yang M-W, Yang S-W, Sheu T-W, Liau C-J (2012) Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets. Expert Syst Appl 39(15):12085–12091
Ding R-Y, Lin YCS, Huang K-H, Chen Y-F, Kao M-J (2016) Cost-effectiveness analysis of post-acute rehabilitation program in patients with hip fracture. Taipei City Med J 13(3):63–73 (in Chinese)
Garg H (2016) A novel accuracy function under interval-valued Pythagorean fuzzy environment for solving multicriteria decision making problem. J Intell Fuzzy Syst 31(1):529–540
Gou X, Xu Z, Liao H (2016) Alternative queuing method for multiple criteria decision making with hybrid fuzzy and ranking information. Inf Sci 357:144–160
Gou X, Xu Z, Ren P (2016) The properties of continuous Pythagorean fuzzy information. Int J Intell Syst 31(5):401–424
Gul M, Celik E, Aydin N, Taskin Gumus A, Guneri AF (2016) A state of the art literature review of VIKOR and its fuzzy extensions on applications. Appl Soft Comput 46:60–89
Gupta P, Mehlawat MK, Grover N (2016) Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method. Inf Sci 370–371:184–203
Hafezalkotob A, Hafezalkotob A (2017) Interval target-based VIKOR method supported on interval distance and preference degree for machine selection. Eng Appl Artif Intell 57:184–196
Hajiagha SHR, Hashemi SS, Mohammadi Y, Zavadskas EK (2016) Fuzzy belief structure based VIKOR method: an application for ranking delay causes of Tehran metro system by FMEA criteria. Transport 31(1):108–118
Hall CJ, Peel NM, Comans TA, Gray LC, Scuffham PA (2012) Can post-acute care programmes for older people reduce overall costs in the health system? A case study using the Australian Transition Care Programme. Health Soc Care Commun 20(1):97–102
Han D-S (2015) The demonstration on improving the quality of post-acute care in Taiwan national health insurance. New Taipei J Nurs 17(2):1–9 (in Chinese)
Jiang Y, Liang X, Liang H (2017) An I-TODIM method for multi-attribute decision making with interval numbers. Soft Comput 21(18):5489–5506
Kaliszewski I, Podkopaev D (2016) Simple additive weighting—a metamodel for multiple criteria decision analysis methods. Expert Syst Appl 54:155–161
Keshavarz Ghorabaee MG (2016) Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robot Comput Integr Manufactur 37:221–232
Lee W-J, Chou M-Y, Peng L-N, Liang C-K, Liu L-K, Liu C-L, Chen L-K, Wu Y-H, VAIC Study Group (2014) Predicting clinical instability of older patients in post-acute care units: a nationwide cohort study. Geriatr Gerontol Int 14(2):267–272
Liang W, Zhang X, Liu M (2015) The maximizing deviation method based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc. https://doi.org/10.1155/2015/746572
Liao H, Xu Z (2013) A VIKOR-based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Mak 12(4):373–392
Liu H-C, Wu J, Li P (2013) Assessment of health-care waste disposal methods using a VIKOR-based fuzzy multi-criteria decision making method. Waste Manag 33(12):2744–2751
Liu P, Zhang L (2017) An extended multiple criteria decision making method based on neutrosophic hesitant fuzzy information. J Intell Fuzzy Syst 32(6):4403–4413
Lu M-T, Lin S-W, Tzeng G-H (2013) Improving RFID adoption in Taiwan’s healthcare industry based on a DEMATEL technique with a hybrid MCDM model. Decis Support Syst 56(1):259–269
Mechanic R (2014) Post-acute care—the next frontier for controlling medicare spending. N Engl J Med 370:692–694
Mohanty RK, Sooraj TR, Tripathy BK (2017) IVIFS and decision-making. Adv Intell Syst Comput 468:319–330
Mohsen O, Fereshteh N (2017) An extended VIKOR method based on entropy measure for the failure modes risk assessment—a case study of the geothermal power plant (GPP). Saf Sci 92:160–172
Opricovic S (1998) Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade
Opricovic S, Tzeng G-H (2002) Multicriteria planning of post-earthquake sustainable reconstruction. Comput Aided Civ Infrastruct Eng 17(3):211–220
Opricovic S, Tzeng G-H (2004) Compromise solution by MCDM methods: a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156(2):445–455
Opricovic S, Tzeng G-H (2007) Extended VIKOR method in comparison with outranking methods. Eur J Oper Res 178(2):514–529
Pamučar D, Petrović I, Ćirović G (2018) Modification of the best-worst and MABAC methods: a novel approach based on interval-valued fuzzy-rough numbers. Expert Syst Appl 91:89–106
Peng X, Yang Y (2016) Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators. Int J Intell Syst 31(5):444–487
Prvu Bettger JA, Stineman MG (2007) Effectiveness of multidisciplinary rehabilitation services in postacute care: state-of-the-science. A review. Arch Phys Med Rehabil 88(11):1526–1534
Rao C, Xiao X, Xie M, Goh M, Zheng J (2017) Low carbon supplier selection under multi-source and multi-attribute procurement. J Intell Fuzzy Syst 32(6):4009–4022
Ren P, Xu Z, Gou X (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259
Ren Z, Xu Z, Wang H (2017) Dual hesitant fuzzy VIKOR method for multi-criteria group decision making based on fuzzy measure and new comparison method. Inf Sci 388–389:1–16
Shahriari MR (2017) Soft computing based on a modified MCDM approach under intuitionistic fuzzy sets. Iran J Fuzzy Syst 14(1):23–41
Soner O, Celik E, Akyuz E (2017) Application of AHP and VIKOR methods under interval type 2 fuzzy environment in maritime transportation. Ocean Eng 129:107–116
Szmidt E (2014) Distances and similarities in intuitionistic fuzzy sets. Stud Fuzziness Soft Comput. https://doi.org/10.1007/978-3-319-01640-5
Tsao C-Y, Chen T-Y (2016) A projection-based compromising method for multiple criteria decision analysis with interval-valued intuitionistic fuzzy information. Appl Soft Comput 45:207–223
Wan S-P, Wang F, Dong J-Y (2016) A preference degree for intuitionistic fuzzy values and application to multi-attribute group decision making. Inf Sci 370–371:127–146
Wang X, Cai J (2017) A group decision-making model based on distance-based VIKOR with incomplete heterogeneous information and its application to emergency supplier selection. Kybernetes 46(3):501–529
Wang J-C, Chen T-Y (2014) A closeness coefficient-based multiple criteria decision-making method using interval type-2 fuzzy sets and its application to watershed site selection. J Ind Prod Eng 31(1):1–16
Wu K-Y, Wu S-C, Hung Y-N, Wu C-C, Lin L-C, Hu H-H (2012) The need for post-acute care for stroke patients in Taiwan. Taiwan J Public Health 31(3):251–262 (in Chinese)
Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting, Edmonton, Canada, June 24–28, pp 57–61
Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965
Yager RR (2016) Properties and applications of Pythagorean fuzzy sets. In: Angelov P, Sotirov S (eds) Imprecision and uncertainty in information representation and processing. Studies in Fuzziness and Soft Computing 332. Springer, Dordrecht, pp 119–136
Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28(5):436–452
Yang W, Pang Y, Shi J, Wang C (2016) Linguistic hesitant intuitionistic fuzzy decision-making method based on VIKOR. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2526-y
Yang W, Shi J, Pang Y, Zheng X (2016) Linear assignment method for interval neutrosophic sets. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2575-2
Ye J (2009) Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment. Expert Syst Appl 36(3):6899–6902
Zeng Q-L, Li D-D, Yang Y-B (2013) VIKOR method with enhanced accuracy for multiple criteria decision making in healthcare management. J Med Syst 37:1–9
Zhang X (2016) Multicriteria Pythagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods. Inf Sci 330:104–124
Zhang X, Xu Z (2014) Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078
Acknowledgements
The author acknowledges the assistance of the respected editor and the anonymous referees for their insightful and constructive comments, which helped to improve the overall quality of the paper. The author is grateful for grant funding support from the Taiwan Ministry of Science and Technology (MOST 105-2410-H-182-007-MY3) and Chang Gung Memorial Hospital (BMRP 574 and CMRPD2F0202) during the study completion.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that there is no conflict of interest regarding the publication of this paper.
Rights and permissions
About this article
Cite this article
Chen, TY. A novel VIKOR method with an application to multiple criteria decision analysis for hospital-based post-acute care within a highly complex uncertain environment. Neural Comput & Applic 31, 3969–3999 (2019). https://doi.org/10.1007/s00521-017-3326-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-017-3326-8