The unbalanced linguistic terms set (ULTS) is a special linguistic term set which can describe the vagueness assessment that is non-uniform and non-symmetrical distributed. So, it is effective to describe the uncertainty information existed in some special real decision making problems by ULTS. As a special prioritized operator, the scaled prioritized (SP) operator has the advantage of taking the priority among different criteria into account by detailed priority labels in known case and unknown case. In this paper, we combine the merits of SP operators and ULTS for dealing with some special multi-criteria decision making (MCDM) problems where there is a priority relationship between criteria under ULTS evaluation information. We present the unbalanced 2-tuple linguistic scaled prioritized averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric averaging operator, which can handle the issues of the detailed priority relationship among different categories of MCDM problems in knowable case. Further, we propose the unbalanced 2-tuple linguistic scaled prioritized weighted averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric weighted averaging operator, which can deal with the case when the detailed priority relationship among different categories of different criteria is unknowable. Then, we discussed several characteristics of the proposed operators, such as boundedness, monotonicity, and idempotency. Besides, we presented an approach for the MCDM problems according to the proposed operators. In the last, we provide an example to explain the calculating steps and effectiveness of these methods.
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Bartczuk Ł, Dziwiński P, Starczewski JT (2012) A new method for dealing with unbalanced linguistic term set. In: International conference on artificial intelligence and soft computing, vol 2012. Springer, Berlin, pp 207–212
Chen TY, Chang CH, Lu JR (2013) The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making. Eur J Oper Res 226(3):615–625
Churchman CW, Ackoff RL, Arnoff EL (1957) Introduction to operations research. Wiley, New York
Dong YC, Li CC, Xu YF, Gu X (2015a) Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations. Group Decis Negot 24(2):217–242
Dong YC, Wu YZ, Zhang HJ, Zhang GQ (2015b) Multi-granular unbalanced linguistic distribution assessments with interval symbolic proportions. Knowl Based Syst 82:139–151
Dong YC, Li CC, Herrera F (2016) Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information. Inf Sci 367:259–278
Fu ZG, Liao HC (2019) Unbalanced double hierarchy linguistic term set: the TOPSIS method for multi-expert qualitative decision making involving green mine selection. Inf Fusion 51:271–286
Garg H, Arora R (2018) Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making. Eng Appl Artif Intell 71:100–112
Han B, Chen HY, Zhu JM, Liu JP (2018) An approach to linguistic multiple attribute decision-making based on unbalanced linguistic generalized heronian mean aggregation operator. Comput Intell Neurosci. https://doi.org/10.1155/2018/1404067
He YD, Chen HY, He Z, Zhou LG (2016a) Scaled prioritized aggregation operators and their applications to decision making. Soft Comput 20(3):1021–1039
He YD, He Z, Shi LX (2016b) Multiple attributes decision making based on scaled prioritized intuitionistic fuzzy interaction aggregation operators. Int J Fuzzy Syst 18(5):924–938
He YD, He Z, Zhou PP, Deng YJ (2016c) Scaled prioritized geometric aggregation operators and their applications to decision making. Int J Uncertain Fuzziness Knowl Based Syst 24(1):13–45
Herrera F, Martinez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8:746–752
Herrera F, Martínez L (2001) A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making. IEEE Trans Syst Man Cybern B Cybern 31(2):227–234
Herrera F, Herrera-Viedma E, Martinez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16(2):354–370
Jiang L, Liu HB, Cai JF (2015) The power average operator for unbalanced linguistic term sets. Inf Fusion 22:85–94
Kang BY, Deng Y, Hewage K, Sadiq R (2019) A method of measuring uncertainty for Z-number. IEEE Trans Fuzzy Syst 27(4):731–738
Li DF (2005) Multi-attribute decision making models and methods using intuitionistic fuzzy sets. J Comput Syst Sci 70(1):73–85
Liu PD (2018) Two-dimensional uncertain linguistic generalized normalized weighted geometric Bonferroni mean and its application to multiple-attribute decision making. Sci Iran E 25(1):450–465
Liu PD, Chen SM (2018) Multiattribute group decision making based on intuitionistic 2-tuple linguistic information. Inf Sci 430:599–619
Liu PD, Liu WQ (2018) Scaled prioritized operators based on the linguistic intuitionistic fuzzy numbers and their applications to multi-attribute decision making. Int J Fuzzy Syst 20(5):1539–1550
Liu PD, Wang P (2019) Multiple-attribute decision making based on archimedean Bonferroni operators of q-rung orthopair fuzzy numbers. IEEE Trans Fuzzy Syst 27(5):834–848
Merigó JM, Gil-Lafuente AM (2013) Induced 2-tuple linguistic generalized aggregation operators and their application in decision-making. Inf Sci 236:1–16
Morente-Molinera JA, Al-Hmouz R, Morfeq A, Balamash AS, Herrera-Viedma E (2016) A decision support system for decision making in changeable and multi-granular fuzzy linguistic contexts. J Multiple Valued Log Soft Comput 26(3-5): 485–514
Morente-Molinera JA, Kou G, Samuylov K, Ureña R, Herrera-Viedma E (2019) Carrying out consensual group decision making processes under social networks using sentiment analysis over comparative expressions. Knowl Based Syst 165:335–345
Qin JD, Liu XW (2016) 2-Tuple linguistic Muirhead mean operators for multiple attribute group decision making and its application to supplier selection. Kybernetes 45(1):2–29
Tao ZF, Han B, Zhou LG, Chen HY (2018) The novel computational model of unbalanced linguistic variables based on archimedean copula. Int J Uncertain Fuzziness Knowl Based Syst 26(4):601–631
Teng F, Liu PD, Zhang L, Zhao J (2019) Multiple attribute decision making methods with unbalanced linguistic variables based on Maclaurin symmetric mean operators. Int J Inf Technol Decis Mak 18(1):105–146
Tian ZP, Wang J, Wang JQ, Zhang HY (2017) Simplified neutrosophic linguistic multi-criteria group decision-making approach to green product development. Group Decis Negot 26(3):597–627
Tian ZP, Nie RX, Wang JQ, Zhang HY (2019) Signed distance-based ORESTE for multicriteria group decision-making with multigranular unbalanced hesitant fuzzy linguistic information. Expert Syst 36(1):e12350
Torra V (1996) Negation functions based semantics for ordered linguistic labels. Int J Intell Syst 11(11):975–988
Torra V (2001) Aggregation of linguistic labels when semantics is based on antonyms. Int J Intell Syst 16(4):513–524
Wang BL, Liang JY, Qian YH, Dang CY (2015) A normalized numerical scaling method for the unbalanced multi-granular linguistic sets. Int J Uncertain Fuzziness Knowl Based Syst 23(2):221–243
Wang CQ, Fu XG, Meng SS, He YD (2017) Multi-attribute decision-making based on the SPIFGIA operators. Granul Comput 2(4):321–331
Wei CP, Rodríguez RM, Martínez L (2018) Uncertainty measures of extended hesitant fuzzy linguistic term sets. IEEE Trans Fuzzy Syst 26(3):1763–1768
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
Xu ZS (2004) A method based on linguistic aggregation operators for group decision making under linguistic preference relations. Inf Sci 166(1–4):19–30
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433
Yager RR (2004) Modeling prioritized multicriteria decision making. IEEE Trans Syst Man Cybern Part B 34:2396–2404
Yager RR (2008) Prioritized aggregation operators. Int J Approx Reason 48:263–274
Yu DJ, Wu YY (2012) Interval-valued intuitionistic fuzzy Heronian mean operators and their application in multi-criteria decision making. Afr J Bus Manag 6(11):4158–4168
Yu XH, Xu ZS (2013) Prioritized intuitionistic fuzzy aggregation operators. Inf Fusion 14:108–116
Yu XH, Xu ZS, Liu SS (2013) Prioritized multi-criteria decision making based on preference relations. Comput Ind Eng 66:104–115
Zadeh LA (1965) Fuzzy collections. Inf Control 8:338–356
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8(3):199–249
Zhang HM (2014) Linguistic Intuitionistic fuzzy sets and application in MAGDM. J Appl Math 1:1–11
Zhang HJ, Dong YC, Chiclana F, Yu S (2019) Consensus efficiency in group decision making: a comprehensive comparative study and its optimal design. Eur J Oper Res 275(2):580–598
Zou L, Pei Z, Karimi HR, Shi P (2012) The unbalanced linguistic aggregation operator in group decision making. Math Probl Eng 2012:1–12
This paper is supported by the National Natural Science Foundation of China (Nos. 71771140 and 71471172), 文化名家暨“四个一批”人才项目 (Project of cultural masters and “the four kinds of a batch” talents), the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045).
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Liu, P., Liu, W. Multiple-criteria decision making method based on the scaled prioritized operators with unbalanced linguistic information. Artif Intell Rev (2020). https://doi.org/10.1007/s10462-020-09812-x
- Scaled prioritized operator
- Unbalanced linguistic terms set
- Multi-criteria decision making