Abstract
Interval-valued picture fuzzy linguistic variable concept is introduced in this article, in which we consider principal component and proposed a generalized interval-valued picture fuzzy linguistic induced hybrid aggregation (GIVPLIHA) operator with entropic order-inducing variable and TOPSIS method. Then, we discussed some basic properties of the GIVPLIHA operator. We also discussed an algorithm for linguistic group decision-making based on GIVPLIHA operator and TOPSIS technique. To prove the validity and applicability of the developed method, finally, we solved a decision-making problem of a company to make a policy for the selection of the best investment strategy. We conclude from the comparison and sensitive analysis that the proposed decision-making method is more effective and reliable than other existing models.
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17 March 2021
A Correction to this paper has been published: https://doi.org/10.1007/s00500-021-05720-6
References
Ashraf S, Abdullah S, Qadir A (2018) Novel concept of cubic picture fuzzy sets. J New Theory 24:59–72
Ashraf S, Mahmood T, Abdullah S, Khan Q (2019) Different approaches to multi-criteria group decision making problems for picture fuzzy environment. Bull Braz Math Soc New Ser 50(2):373–397
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20(1):87–96
Atanassov KT (1999) Interval valued intuitionistic fuzzy sets. Intuitionistic fuzzy sets. Physica, Heidelberg, pp 139–177
Bo C, Zhang X (2017) New operations of picture fuzzy relations and fuzzy comprehensive evaluation. Symmetry 9(11):268
Bordogna G, Fedrizzi M, Pasi G (1997) A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans Syst Man Cybern Part A Syst Hum 27(1):126–133
Chen Z, Liu P, Pei Z (2015) An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int J Comput Intell Syst 8(4):747–760
Cuong BC, Kreinovich V (2013) Picture fuzzy sets—a new concept for computational intelligence problems. In: 2013 third world congress on information and communication technologies (WICT 2013). IEEE, pp 1–6
Cuong BC, Kreinovich V (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420
Dutta P (2017) Medical diagnosis via distance measures on picture fuzzy sets. AMSE J Ser Adv A 54(2):657–672
Garg H (2017) Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. Arab J Sci Eng 42(12):5275–5290
Garg H, Kumar K (2018) Group decision making approach based on possibility degree measures and the linguistic intuitionistic fuzzy aggregation operators using Einstein norm operations. J Mult Valued Log Soft Comput 31:175–209
Herrera F, Herrera-Viedma E (1997) Aggregation operators for linguistic weighted information. IEEE Trans Syst Man Cybern Part A Syst Hum 27(5):646–656
Herrera F, Herrera-Viedma E (2000) Linguistic decision analysis: steps for solving decision problems under linguistic information. Fuzzy Sets Syst 115(1):67–82
Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8(6):746–752
HHerrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making. IEEE Trans Syst Man Cybern Part B (Cybern) 31(2):227–234
Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Int J Inf 80:1–17
Herrera F, Herrera-Viedma E, Verdegay JL (1996) Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst 79(2):175–190
Herrera F, Herrera-Viedma E, Martínez L (2000) A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst 114(1):43–58
Joshi DK, Bisht K, Kumar S (2018) Interval-valued intuitionistic uncertain linguistic information-based TOPSIS method for multi-criteria group decision-making problems. Ambient communications and computer systems. Springer, Singapore, pp 305–315
Liao X, Li Y, Lu B (2007) A model for selecting an ERP system based on linguistic information processing. Inf Syst 32(7):1005–1017
Martı L, Herrera F (2012) An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges. Inf Sci 207:1–18
Peng X, Dai J (2017) Algorithm for picture fuzzy multiple attribute decision-making based on new distance measure. Int J Uncertain Quantif 7(2):177–187
Peng HG, Wang JQ, Cheng PF (2018) A linguistic intuitionistic multi-criteria decision-making method based on the Frank Heronian mean operator and its application in evaluating coal mine safety. Int J Mach Learn Cybernet 9(6):1053–1068
Phong PH, Cuong BC (2016) Multi-criteria group decision making with picture linguistic numbers. VNU J Sci Comput Sci Commun Eng 32(3)
Phuong PTM, Thong PH (2018) Theoretical analysis of picture fuzzy clustering: convergence and property. J Comput Sci Cybern 34(1):17–32
Rodriguez RM, Martinez L, Herrera F (2011) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Singh P (2015) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 28(2):591–604
Son LH (2015) A novel kernel fuzzy clustering algorithm for geo-demographic analysis. Inf Sci Inform Comput Sci Intell Syst Appl Int J 317(C):202–223
Thong PH (2015a) A new approach to multi-variable fuzzy forecasting using picture fuzzy clustering and picture fuzzy rule interpolation method. Knowledge and systems engineering. Springer, Cham, pp 679–690
Thong NT (2015b) HIFCF: an effective hybrid model between picture fuzzy clustering and intuitionistic fuzzy recommender systems for medical diagnosis. Expert Syst Appl 42(7):3682–3701
Thong PH, Fujita H (2016) Interpolative picture fuzzy rules: a novel forecast method for weather nowcasting. In: 2016 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 86–93
Van Viet P, Chau HTM, Van Hai P (2015) Some extensions of membership graphs for picture inference systems. In: 2015 seventh international conference on knowledge and systems engineering (KSE). IEEE, pp 192–197
Wang JQ, Li JJ (2009) The multi-criteria group decision making method based on multi-granularity intuitionistic two semantics. Sci Technol Inf 33(1):8–9
Wang P, Xu X, Wang J, Cai C (2017) Interval-valued intuitionistic linguistic multi-criteria group decision-making method based on the interval 2-tuple linguistic information. J Intell Fuzzy Syst 33(2):985–994
Wei G (2016) Picture fuzzy cross-entropy for multiple attribute decision making problems. J Bus Econ Manag 17(4):491–502
Wei G, Alsaadi FE, Hayat T, Alsaedi A (2018) Projection models for multiple attribute decision making with picture fuzzy information. Int J Mach Learn Cybern 9(4):713–719
Wu SJ, Wei GW (2017) Picture uncertain linguistic aggregation operators and their application to multiple attribute decision making. Int J Knowl Based Intell Eng Syst 21(4):243–256
Wu Z, Xu J (2015) Possibility distribution-based approach for MAGDM with hesitant fuzzy linguistic information. IEEE Trans Cybern 46(3):694–705
Xian S (2012) Fuzzy linguistic induced ordered weighted averaging operator and its application. J Appl Math 2012:210392. https://doi.org/10.1155/2012/210392
Xian S, Sun W (2014) Fuzzy linguistic induced Euclidean OWA distance operator and its application in group linguistic decision making. Int J Intell Syst 29(5):478–491
Xian S, Dong Y, Liu Y, Jing N (2018) A novel approach for linguistic group decision making based on generalized interval-valued intuitionistic fuzzy linguistic induced hybrid operator and TOPSIS. Int J Intell Syst 33(2):288–314
Xu Z (2004a) A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf Sci 166(1–4):19–30
Xu Z (2004b) Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf Sci 168(1–4):171–184
Xu Z (2005) An approach to pure linguistic multiple attribute decision making under uncertainty. Int J Inf Technol Decis Making 4(02):197–206
Xu Z (2005) An approach based on similarity measure to multiple attribute decision making with trapezoid fuzzy linguistic variables. International conference on fuzzy systems and knowledge discovery. Springer, Berlin, Heidelberg, pp 110–117
Xu Z (2006a) An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decis Support Syst 41(2):488–499
Xu Z (2006b) A direct approach to group decision making with uncertain additive linguistic preference relations. Fuzzy Optim Decis Making 5(1):21–32
Xu Z (2009) An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis Negot 18(2):119–145
Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219
Yang Y, Liang C, Ji S, Liu T (2015) Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making. J Intell Fuzzy Syst 29(4):1711–1722
Zadeh LA (1965) Fuzzy sets. Inf. Control 8(3):338–353
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning–II. Inf Sci 8(4):301–357
Zhang H (2014) Linguistic intuitionistic fuzzy sets and application in MAGDM. J Appl Math 2014:432092. https://doi.org/10.1155/2014/432092
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The authors Yasser D. Al-Otaibi, Muhammad Aslam extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha 61413, Saudi Arabia for funding this work through research groups programs under Grant Number R.G.P.1/23/42.
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Qiyas, M., Abdullah, S., Al-Otaibi, Y.D. et al. Generalized interval-valued picture fuzzy linguistic induced hybrid operator and TOPSIS method for linguistic group decision-making. Soft Comput 25, 5037–5054 (2021). https://doi.org/10.1007/s00500-020-05508-0
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DOI: https://doi.org/10.1007/s00500-020-05508-0