Abstract
The methodology of managing hesitancy situations is improving step by step with new basics and tools which have their specific characteristics. As a rule, aggregation operators can undoubtedly deal with the data in a definite way. Employing hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), the adaptability in creating assessment data under uncertainty can be accomplished to a bigger degree than either intuitionistic linguistic sets or hesitant fuzzy linguistic term sets do. In this view, this paper provides a multi-criteria group decision-making (MCGDM) method based on new aggregation operators for HIFLTSs and the proposed modified VIKOR method. Besides, some operational laws for HIFLTSs are studied with their important properties, which is followed by the definitions of some aggregation operators, including the hesitant intuitionistic fuzzy linguistic weighted averaging (HIFLWA) operator and the hesitant intuitionistic fuzzy linguistic weighted geometric (HIFLWG) operator. The hesitant intuitionistic fuzzy linguistic individual regret (HIFLIR) measure and hesitant intuitionistic fuzzy linguistic compromise (HIFLC) measure are established with the help of hesitant intuitionistic fuzzy group utility measure. After that, by using the proposed aggregation operators, we develop a modified VIKOR method in the context of HIFLTSs. The outcome of this research is ranking and selecting of best alternative with the help of modified VIKOR method based on aggregation operators for HIFLTSs. A numerical problem is provided to verify the proposed approach, and its accuracy and effectiveness have been demonstrated through the comparative analysis of the modified VIKOR method with the TOPSIS method for the selection of the best alternative. This research study showed that the proposed approach can describe the fuzziness and uncertainty of experts more relevantly and the ranking results calculated with the modified VIKOR method are effective and reliable.
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Beg I, Rashid T (2013) TOPSIS for hesitant fuzzy linguistic term sets. Int J Intell Syst 28:1162–1171. https://doi.org/10.1002/int.21623
Beg I, Rashid T (2014) Hesitant intuitionistic fuzzy linguistic term set, Notes on Intuitionistic Fuzzy Sets, 20(3):53-64, http://hdl.handle.net/123456789/1434
Büyüközkan G, Feyzioğlu O, Havle CA (2019) Analysis of success factors in aviation 4.0 using integrated intuitionistic fuzzy MCDM methods, International Conference on Intelligent and Fuzzy Systems, 598-606, https://doi.org/10.1007/978-3-030-23756-1-73.
Delgado M, Verdegay JL, Vila MA (1992) Linguistic decision making models. Int J Intell Syst 7:479–492
Dev S, Aherwar A, Patnaik A (2020) Material selection for automotive piston component using entropy VIKOR method. SILICON 12:155–169. https://doi.org/10.1007/s12633-019-00110-y
Faizi S, Rashid T, Zafar S (2017) An outranking method for multi-criteria group decision making using hesitant intuitionistic fuzzy linguistic term sets. J Intell Fuzzy Syst 32(3):2153–2164. https://doi.org/10.3233/JIFS-161976
Faizi S, Rashid T, Xu Z, Zafar S (2018) Distance measures for hesitant intuitionistic fuzzy linguistic term sets based on a risk factor parameter. Int J Comput Appl 41(6):418–435. https://doi.org/10.1080/1206212X.2018.1465653
Güler M, Mukul E, Büyüközkan G (2019) Analysis of e-government strategies with hesitant fuzzy linguistic multi-criteria decision making techniques, International Conference on Intelligent and Fuzzy Systems, 1068-1075, https://doi.org/10.1007/978-3-030-23756-1-126.
Gou X, Xu Z (2016) Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets. Inf Sci 372:407–427. https://doi.org/10.1016/j.ins.2016.08.034
Garg H, Arora R (2020) Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set, Journal of Ambient Intelligence and Humanized. Computing 11:375–410. https://doi.org/10.1007/s12652-019-01238-w
Geng X, Qiu H, Gong X (2017) An extended 2-tuple linguistic DEA for solving MAGDM problems considering the influence relationships among attributes. Comput Ind Eng 112:135–146. https://doi.org/10.1016/j.cie.2017.07.040
Gündoğdu FK, Kahraman C, Karaşan A (2019) Spherical fuzzy VIKOR method and its application to waste management. International Conference on Intelligent and Fuzzy Systems, 997-1005, https://doi.org/10.1007/978-3-030-23756-1-118
Herrera F, Herrera-Viedma E, Verdegay JL (1996) A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst 78(1):73–87. https://doi.org/10.1016/0165-0114(95)00107-7
Liao HC, Xu ZS (2013) A VIKOR based method for hesitant fuzzy multi-criteria decision making. Fuzzy Optim Decis Making 12:373–392. https://doi.org/10.1007/s10700-013-9162-0
Liao H, Xu Z, Zeng XJ (2014) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23:1343–1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Liao H, Xu Z, Zeng XJ (2015) Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets. Knowl Based Syst 76:127–138. https://doi.org/10.1016/j.knosys.2014.12.009
Lee HC, Chang CT (2018) Comparative analysis of MCDM methods for ranking renewable energy sources in Taiwan. Renew Sustain Energy Rev 92:883–896. https://doi.org/10.1016/j.rser.2018.05.007
Liu HB, Rodríguez RM (2014) A fuzzy envelope of hesitant fuzzy linguistic term set and its application to multi-criteria decision making. Inf Sci 258:220–238. https://doi.org/10.1016/j.ins.2013.07.027
Mahboob A, Rashid T, Sindhu MS (2021) An optimization preference based approach with hesitant intuitionistic linguistic distribution in group decision making. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2021.115965
Montserrat-Adell J, Xu Z, Gou X, Agell N (2019) Free double hierarchy hesitant fuzzy linguistic term sets, an application on ranking alternatives in GDM. Information Fusion 47:45–59. https://doi.org/10.1016/j.inffus.2018.07.002
Opricovic S (1998) Multicriteria optimization of civil engineering systems. Faculty Civil Eng, Belgrade 2:5–21
Opricovic S, Tzeng GH (2002) Multicriteria planning of post-earthquake sustainable reconstruction, Computer Aided Civil and Infrastructure. Engineering 17:211–220. https://doi.org/10.1111/1467-8667.00269
Opricovic S, Tzeng GH (2004) Compromise solution by MCDM methods, a comparative analysis of VIKOR and TOPSIS. Eur J Oper Res 156:445–455. https://doi.org/10.1016/S0377-2217(03)00020-1
Rodríguez RM, Martínez L, Herrera F (2011) Hesitant fuzzy linguistic term sets. Found Intell Syst 122:287–295
Rodríguez RM, Martínez L, Herrera F (2011) Hesitant fuzzy linguistic terms sets for decision making. IEEE Trans Fuzzy Syst 20:109–119. https://doi.org/10.1109/TFUZZ.2011.2170076
Rodríguez RM, Martínez L, Herrera F (2013) A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term set. Inf Sci 241:28–42. https://doi.org/10.1016/j.ins.2013.04.006
Rashid T, Faizi S, Xu Z (2018) ELECTRE based outranking method for multi-criteria decision making using hesitant intuitionistic fuzzy linguistic term sets. Int J Fuzzy Syst 20(1):78–92. https://doi.org/10.1007/s40815-017-0297-y
Stojčić M, Zavadskas EK, Pamučar D, Stević Ž, Mardani A (2019) Application of MCDM methods in sustainability engineering, a literature review 2008–2018. Symmetry 11:350. https://doi.org/10.3390/sym11030350
Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems, Studies in Fuzziness and Soft. Computing 238:1–159
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25(6):529–539. https://doi.org/10.1002/int.20418
Torra V (1997) The weighted OWA operator. Int J Intell Syst 12:53–156
Tzeng GH, Lin CW, Opricovic S (2005) Multi-criteria analysis of alternative fuel buses for public transportation. Energy Policy 33:1373–1383. https://doi.org/10.1016/j.enpol.2003.12.014
Wang L, Wang Y, Pedrycz W (2019) Hesitant 2-tuple linguistic Bonferroni operators and their utilization in group decision making. Appl Soft Comput 77:653–664. https://doi.org/10.1016/j.asoc.2019.01.038
Wei CP, Zhao N, Tang XJ (2014) Operators and comparisons of hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 22(3):575–585. https://doi.org/10.1109/TFUZZ.2013.2269144
Wu Z, Xu J, Jiang X, Zhong L (2019) Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions, VIKOR and TOPSIS. Inf Sci 473:101–120. https://doi.org/10.1016/j.ins.2018.09.038
Xu Z (2000) On consistency of the weighted geometric mean complex judgement matrix in AHP. Eur J Oper Res 126(3):683–687. https://doi.org/10.1016/S0377-2217(99)00082-X
Xu Z (2005) Deviation measures of linguistic preference relations in group decision making. Omega 33:249–254. https://doi.org/10.1016/j.omega.2004.04.008
Xia M, Xu Z (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu ZS (2004) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166:19–30. https://doi.org/10.1016/j.ins.2003.10.006
Xu ZS (2008) Group decision making based on multiple types of linguistic preference relations. Inf Sci 178:452–467. https://doi.org/10.1016/j.ins.2007.05.018
Xu ZS (2004) Uncertain multiple attribute decision making, methods and applications. Tsinghua University Press, Beijing
Yalcin N, Bayrakdaroglu A, Kahraman C (2012) Application of fuzzy multi-criteria decision making methods for financial performance evaluation of turkish manufacturing industries. Expert Syst Appl 39:350–364. https://doi.org/10.1016/j.eswa.2011.07.024
Yeh TM, Pai FY, Liao CW (2014) Using a hybrid MCDM methodology to identify critical factors in new product development. Neural Comput Appl 24:957–971. https://doi.org/10.1007/s00521-012-1314-6
Yager RR (1998) Fusion of ordinal information using weighted median aggregation. Int J Approx Reason 18:35–52. https://doi.org/10.1016/S0888-613X(97)10003-2
Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183–190. https://doi.org/10.1109/21.87068
Yang YPO, Shieh HM, Leu JD, Tzeng GH (2009) A VIKOR-based multiple criteria decision method for improving information security risk. Int J Inf Technol Decis Making 8(2):267–287. https://doi.org/10.1142/S0219622009003375
Zhou L, Chen H (2012) A generalization of the power aggregation operators for linguistic environment and its application in group decision making, Knowledge Based Systems, 216–224, https://doi.org/10.1016/j.knosys.2011.08.004
Zhou L, Chen H, Liu J (2012) Generalized power aggregation operators and their applications in group decision making. Comput Ind Eng 62(4):989–999. https://doi.org/10.1016/j.cie.2011.12.025
Zhou H, Wang J, Li XE, Wang JQ (2016) Intuitionistic hesitant linguistic sets and their application in multi-criteria decision making problems. Oper Res Int J 16:131–160. https://doi.org/10.1007/s12351-015-0199-4
Zhou W, Xu Z, Chen M (2015) Preference relations based on hesitant intuitionistic fuzzy information and their application in group decision making. Comput Ind Eng 87:163–175. https://doi.org/10.1016/j.cie.2015.04.020
Zhu C, Zhu L, Zhang X (2016) Linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision-making. Information Sciences. https://doi.org/10.1016/j.ins.2016.07.011
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Faizi, S., Shah, M. & Rashid, T. A modified VIKOR method for group decision-making based on aggregation operators for hesitant intuitionistic fuzzy linguistic term sets. Soft Comput 26, 2375–2390 (2022). https://doi.org/10.1007/s00500-021-06547-x
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DOI: https://doi.org/10.1007/s00500-021-06547-x