Abstract
Double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is one of the successful extensions of the hesitant fuzzy linguistic term set used for describing the uncertain information in a more prominent manner for solving the group decision-making problems. In DHHFLTS, the membership functions are represented in terms of linguistic membership degrees which are a flexible structure for preference elicitation and enrich the ability for rational decision-making with complex linguistic expressions. Driven by the flexibility of DHHFLTS, in this paper, a new decision framework is developed for solving decision-making problems, which provides scientific and rational decisions based on the preference information. For it, initially, a new aggregation operator is proposed for aggregating decision-makers’ preferences. Later, the importance of the attribute weights in the problems is determined by formulating a mathematical model and the COPRAS method is extended to the DHHFLTS context for prioritizing alternatives. The applicability of the presented approach is demonstrated through a numeric example related to green supplier selection. A comparative analysis with existing studies is also administered to test the effectiveness and verify the method.
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Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci (NY) 8:199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inf Sci (NY) 239:223–239
Tehrim ST, Riaz M (2019) A novel extension of TOPSIS to MCGDM with bipolar neutrosophic soft topology. J Intell Fuzzy Syst 37:5531–5549. https://doi.org/10.3233/JIFS-190668
Riaz M, Hashmi MR (2019) MAGDM for agribusiness in the environment of various cubic m-polar fuzzy averaging aggregation operators. J Intell Fuzzy Syst 37:3671–3691. https://doi.org/10.3233/JIFS-182809
Zare A, Feylizadeh MR, Mahmoudi A, Liu S (2018) Suitable computerized maintenance management system selection using grey group TOPSIS and fuzzy group VIKOR: a case study. Decis Sci Lett 7:341–358. https://doi.org/10.5267/j.dsl.2018.3.002
Rodriguez RM, Martinez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20:109–119. https://doi.org/10.1109/TFUZZ.2011.2170076
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539. https://doi.org/10.1002/int
Tüysüz F, Şimşek B (2017) A hesitant fuzzy linguistic term sets-based AHP approach for analyzing the performance evaluation factors: an application to cargo sector. Complex Intell Syst 3:167–175. https://doi.org/10.1007/s40747-017-0044-x
Zhu B, Xu Z (2014) Consistency measures for hesitant fuzzy linguistic preference relations. IEEE Trans Fuzzy Syst 22:35–45. https://doi.org/10.1109/TFUZZ.2013.2245136
Liao H, Xu Z, Zeng XJ, Merigó JM (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
Deepak D, Mathew B, John SJ, Garg H (2019) A topological structure involving hesitant fuzzy sets. J Intell Fuzzy Syst 36(6):6401–6412
Liao H, Xu Z, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci (NY) 271:125–142. https://doi.org/10.1016/j.ins.2014.02.125
Liao H, Wu D, Huang Y, Ren P, Xu Z, Verma M (2018) Green logistic provider selection with a hesitant fuzzy linguistic thermodynamic method integrating cumulative prospect theory and PROMETHEE. Sustainability 10:1–16. https://doi.org/10.3390/su10041291
Wang H (2015) Extended hesitant fuzzy linguistic term sets and their aggregation in group decision making. Int J Comput Intell Syst 8:14–33. https://doi.org/10.1080/18756891.2014.964010
Wei G, Alsaadi FE, Hayat T, Alsaedi A (2016) Hesitant fuzzy linguistic arithmetic aggregation operators in multiple attribute decision making. Iran J Fuzzy Syst 13:1–16
Liao H, Xu Z, Herrera-Viedma E, Herrera F (2017) Hesitant fuzzy linguistic term set and its application in decision making: a state-of-the-art survey. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-017-0432-9
Gou X, Liao H, Xu Z, 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
Pang Q, Wang H, Xu Z (2016) Probabilistic linguistic term sets in multi-attribute group decision making. Inf Sci (NY) 369:128–143. https://doi.org/10.1016/j.ins.2016.06.021
Gou X, Xu Z, Herrera F (2018) Consensus reaching process for large-scale group decision making with double hierarchy hesitant fuzzy linguistic preference relations. Knowl Based Syst 157:20–33. https://doi.org/10.1016/j.knosys.2018.05.008
Gou X, Xu Z, Liao H, Herrera F (2018) Multiple criteria decision making based on distance and similarity measures under double hierarchy hesitant fuzzy linguistic environment. Comput Ind Eng 126:516–530. https://doi.org/10.1016/j.cie.2018.10.020
Maclaurin C (1729) A fecond Letter to martin folkes, esq., concerning the roots of equations with demonstration of other roots of algebra. Philos Trans R Soc Lond Ser A 36:59–96
Zheng Y, Xu Z, He Y, Liao H (2018) Severity assessment of chronic obstructive pulmonary disease based on hesitant fuzzy linguistic COPRAS method. Appl Soft Comput J 69:60–71. https://doi.org/10.1016/j.asoc.2018.04.035
Riaz M, Tehrim ST (2019) Multi-attribute group decision making based on cubic bipolar fuzzy information using averaging aggregation operators. J Intell Fuzzy Syst 37:2473–2494. https://doi.org/10.3233/JIFS-182751
Riaz M, Tehrim ST (2019) Cubic bipolar fuzzy ordered weighted geometric aggregation operators and their application using internal and external cubic bipolar fuzzy data. Comput Appl Math 38:1–25. https://doi.org/10.1007/s40314-019-0843-3
Xu Z, Yager RR (2011) Intuitionistic fuzzy Bonferroni means. IEEE Trans Syst Man Cybern B Cybern 41:568–578. https://doi.org/10.1002/int.20515
Guan K, Guan R (2011) Some properties of a generalized Hamy symmetric function and its applications. J Math Anal Appl 376:494–505. https://doi.org/10.1016/j.jmaa.2010.10.014
Qin J, Liu X (2014) An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators. J Intell Fuzzy Syst 27:2177–2190. https://doi.org/10.3233/IFS-141182
Sharma HK, Roy J, Kar S, Prentkovskis O (2018) Multi criteria evaluation framework for prioritizing Indian railway stations using modified rough AHP-Mabac method. Transp Telecommun 19:113–127. https://doi.org/10.2478/ttj-2018-0010
Askarifar K, Motaffef Z, Aazaami S (2018) An investment development framework in Iran’s seashores using TOPSIS and best–worst multi-criteria decision making methods. Decis Sci Lett 7:55–64. https://doi.org/10.5267/j.dsl.2017.4.004
Zhang Y, Li P, Wang Y, Ma P, Su X (2013) Multiattribute decision making based on entropy under interval-valued intuitionistic fuzzy environment. Math Probl Eng 2013:1–8. https://doi.org/10.1016/j.eswa.2012.01.027
Shemshadi A, Shirazi H, Toreihi M, Tarokh MJ (2011) A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting. Expert Syst Appl 38:12160–12167. https://doi.org/10.1016/j.eswa.2011.03.027
Alimardani M, Zolfani SH, Aghdaie MH, Tamošaitienė J (2013) A novel hybrid SWARA and VIKOR methodology for supplier selection in an agile environment. Technol Econ Dev Econ 19:533–548. https://doi.org/10.3846/20294913.2013.814606
Zavadskas EK, Kaklauskas A, Turskis Z, Tamošaitiene J (2008) Selection of the effective dwelling house walls by applying attributes values determined at intervals. J Civ Eng Manag 14:85–93. https://doi.org/10.3846/1392-3730.2008.14.3
Zavadskas EK, Turskis Z, Kildienė S (2014) State of art surveys of overviews on MCDM/MADM methods. Technol Econ Dev Econ 20:165–179. https://doi.org/10.3846/20294913.2014.892037
Zavadskas EK, Turskis Z, Tamošaitiene J, Marina V (2008) Multicriteria selection of project managers by applying grey criteria. Technol Econ Dev Econ 14:462–477. https://doi.org/10.3846/1392-8619.2008.14.462-477
Zavadskas EK, Kaklauskas A, Turskis Z, Tamošaitienė J (2009) Multi-attribute decision-making model by applying grey numbers. Inst Math Inf Vilnius 20:305–320. https://doi.org/10.1016/s0377-2217(97)00147-1
Nguyen HT, Md Dawal SZ, Nukman Y, Aoyama H, Case K (2015) An integrated approach of fuzzy linguistic preference based AHP and fuzzy COPRAS for machine tool evaluation. PLoS ONE 10:1–24. https://doi.org/10.1371/journal.pone.0133599
Razavi Hajiagha SH, Hashemi SS, Zavadskas EK (2013) A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment. Technol Econ Dev Econ 19:22–37. https://doi.org/10.3846/20294913.2012.762953
Gorabe D, Pawar D, Pawar N (2014) Selection of industrial robots using complex proportional assessment method. Am Int J Res Sci Technol Eng Math Sci Technol Eng Math 5(2):2006–2009
Vahdani B, Mousavi SM, Tavakkoli-Moghaddam R, Ghodratnama a, Mohammadi M (2014) Robot selection by a multiple criteria complex proportional assessment method under an interval-valued fuzzy environment. Int J Adv Manuf Technol 73:687–697. https://doi.org/10.1007/s00170-014-5849-9
Mousavi-Nasab SH, Sotoudeh-Anvari A (2017) A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems. Mater Des 121:237–253. https://doi.org/10.1016/j.matdes.2017.02.041
Chatterjee P, Athawale VM, Chakraborty S (2011) Materials selection using complex proportional assessment and evaluation of mixed data methods. Mater Des 32:851–860. https://doi.org/10.1016/j.matdes.2010.07.010
Garg H, Nancy (2019) Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures. Measurement 138:278–290
Yazdani M, Chatterjee P, Zavadskas EK, Hashemkhani Zolfani S (2017) Integrated QFD-MCDM framework for green supplier selection. J Clean Prod 142:3728–3740. https://doi.org/10.1016/j.jclepro.2016.10.095
Chatterjee K, Kar S (2018) Supplier selection in Telecom supply chain management: a Fuzzy-Rasch based COPRAS-G method. Technol Econ Dev Econ 24:765–791. https://doi.org/10.3846/20294913.2017.1295289
Chatterjee K, Kar S (2018) A multi-criteria decision making for renewable energy selection using Z-numbers. Technol Econ Dev Econ 24:739–764. https://doi.org/10.3846/20294913.2016.1261375
Raghunath BV, Punnagaiarasi A, Rajarajan G, Irshad A, Elango A (2016) Impact of dairy effluent on environment—a review. Integrated Waste Management in India. Springer, Cham, pp 239–249
Lima Junior FR, Osiro L, Carpinetti LCR (2014) A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection. Appl Soft Comput J 21:194–209. https://doi.org/10.1016/j.asoc.2014.03.014
Spearman C (1904) The proof and measurement of association between two things. Am J Psychol 15:72–101
Garg H, Nancy (2019) Multiple criteria decision making based on Frank Choquet Heronian mean operator for single-valued neutrosophic sets. Appl Comput Math 18(2):163–188
Muirhead RF (1902) Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proc Edinb Math Soc 21:144–162. https://doi.org/10.1017/S001309150003460X
Moghaddampour J, Setalani FD, Ghasemi H, Eivazi MR (2018) Crafting decision options and alternatives for designing cultural observation system using general morphological modelling. Decis Sci Lett 7:359–380. https://doi.org/10.5267/j.dsl.2018.3.001
Riaz M, Caǧman N, Zareef I, Aslam M (2019) N-soft topology and its applications to multi-criteria group decision making. J Intell Fuzzy Syst 36:6521–6536
Riaz M, Smarandache F, Firdous A, Fakhar A (2019) On soft rough topology with multi-attribute group decision making. Mathematics 7:1–18. https://doi.org/10.3390/math7010067
Garg H, Kaur G (2020) Quantifying gesture information in brain hemorrhage patients using probabilistic dual hesitant fuzzy sets with unknown probability information. Comput Ind Eng 140:106211. https://doi.org/10.1016/j.cie.2019.106211
Riaz M, Davvaz B, Firdous A, Fakhar A (2019) Novel concepts of soft rough set topology with applications. J Intell Fuzzy Syst 36:3579–3590. https://doi.org/10.3233/JIFS-181648
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Krishankumar, R., Ravichandran, K.S., Shyam, V. et al. Multi-attribute group decision-making using double hierarchy hesitant fuzzy linguistic preference information. Neural Comput & Applic 32, 14031–14045 (2020). https://doi.org/10.1007/s00521-020-04802-0
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DOI: https://doi.org/10.1007/s00521-020-04802-0