Interval uncertainties are very common in group decision making (GDM), especially with the increasing complexity of decision-making systems. The aggregation approach is a widely used method for integrating interval uncertain information in a single interval output that is the basis for ranking alternatives. The ranking results are usually presented in absolute form, that is, an alternative has a 100% probability of being superior to the alternative immediately behind it. However, it seems inadequate and unreasonable to deduce this type of absolute ranking solely since overlap is common among interval outputs, that is an alternative is not always absolutely superior (or inferior) to another one. To this problem, this paper tries to explore other types of outputs for interval GDM problems using stochastic simulation, including ranking of alternatives with probabilities, competition for each ordered position, pairwise priority comparison of alternatives, and overall advantage of alternatives. All of these outputs provide us with more information to form a complete understanding of alternatives from different aspects. Finally, a numerical example regarding the policy selection about a company expanding into a new market is introduced to illustrate the obtainment of these possible outputs.
Decision analysis Group decision making Simulation Ranking with probabilities Pairwise priority matrix
This is a preview of subscription content, log in to check access.
The authors are very grateful to the Managing Editor and the anonymous reviewers for their insightful and constructive comments and suggestions that have led to an improved version of this paper.
This study was funded by the National Natural Science Foundation of China (Grant Nos. 71671031, 71701040, 71803073), the Humanities and Social Sciences Foundation of Chinese Ministry of Education (Grant Nos. 17YJC630067, 18YJC790211).
Compliance with ethical standards
Conflict of interest
All authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Beg I, Rashid T (2014) Aggregation operators of interval-valued 2-tuple linguistic information. Int J Intell Syst 29(7):634–667CrossRefGoogle Scholar
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, BerlinzbMATHGoogle Scholar
Bustince H, Fernandez J, Kolesárová A, Mesiar R (2013) Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 220(1):69–77MathSciNetzbMATHCrossRefGoogle Scholar
Chen SM, Huang ZC (2017) Multiattribute decision making based on interval-valued intuitionistic fuzzy values and particle swarm optimization techniques. Inf Sci 397–398:206–218CrossRefGoogle Scholar
Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl Based Syst 37:528–540CrossRefGoogle Scholar
Chen SM, Cheng SH, Tsai WH (2016) Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values. Inf Sci 367–368:418–442CrossRefGoogle Scholar
Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3(2):236–240CrossRefGoogle Scholar
Gou XJ, Xu ZS (2017) Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making. Fuzzy Optim Decis Mak 16(2):183–204MathSciNetzbMATHCrossRefGoogle Scholar
He YD, He Z, Huang H (2017) Decision making with the generalized intuitionistic fuzzy power interaction averaging operators. Soft Comput 21(5):1129–1144zbMATHCrossRefGoogle Scholar
Joshi D, Kumar S (2016) Interval-valued intuitionstic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. Eur J Oper Res 248(1):183–191zbMATHCrossRefGoogle Scholar
Labreuche C, Grabisch M (2003) The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets Syst 137(1):11–26MathSciNetzbMATHCrossRefGoogle Scholar
Liu PD (2011) A weighted aggregation operators multi-attribute group decision-making method based on interval-valued trapezoidal fuzzy numbers. Expert Syst Appl 38(1):1053–1060MathSciNetCrossRefGoogle Scholar
Liu PD, Jin F (2012) A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers. Appl Math Model 36(6):2498–2509MathSciNetzbMATHCrossRefGoogle Scholar
Liu PD, Shi LL (2017) Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making. Neural Comput Appl 28(5):1079–1093CrossRefGoogle Scholar
Liu BS, Shen YH, Zhang W, Chen XH, Wang XQ (2015) An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making. Eur J Oper Res 245(1):209–225MathSciNetzbMATHCrossRefGoogle Scholar
Liu X, Tao ZF, Chen HY (2017) A new interval-valued 2-tuple linguistic bonferroni mean operator and its application to multiattribute group decision making. Int J Fuzzy Syst 19(1):86–108MathSciNetCrossRefGoogle Scholar
Lopez-Morales V, Suarez-Cansino J (2016) Reliable intervals method in decision-based support models for group decision-making. Int J Inf Technol Decis Mak 16(1):183–204CrossRefGoogle Scholar
Meng FY, Chen XH, Zhang Q (2014) Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making. Appl Math Model 38(9–10):2543–2557MathSciNetzbMATHCrossRefGoogle Scholar
Merigó JM, Casanovas M, Yang JB (2014) Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators. Eur J Oper Res 235(1):215–224MathSciNetzbMATHCrossRefGoogle Scholar
Park JH, Park Y, Kwun YC, Tan X (2011) Extension of TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment. Appl Math Model 35(5):2544–2556MathSciNetzbMATHCrossRefGoogle Scholar
Peng JJ, Wang JQ, Wang J, Chen XH (2014) Multicriteria decision making approach with hesitant interval-valued intuitionistic fuzzy sets. Sci World J 2014:1–22Google Scholar
Sahin R (2016) Fuzzy multicriteria decision making method based on the improved accuracy function for interval-valued intuitionistic fuzzy sets. Soft Comput 20(7):2557–2563zbMATHCrossRefGoogle Scholar
Song MX, Jiang W, Xie CH, Zhou DY (2017) A new interval numbers power average operator in multiple attribute decision making. Int J Intell Syst 32(6):631–644CrossRefGoogle Scholar
Tan CQ (2011) A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Syst Appl 38(4):3023–3033CrossRefGoogle Scholar
Wang SF (2017) Interval-valued intuitionistic fuzzy Choquet integral operators based on Archimedean t-norm and their calculations. J Comput Anal Appl 23(4):703–712MathSciNetGoogle Scholar
Wei GW (2016) Interval valued hesitant fuzzy uncertain linguistic aggregation operators in multiple attribute decision making. Int J Mach Learn Cybern 7(6):1093–1114CrossRefGoogle Scholar
Wei CP, Zhang YZ (2015) Entropy measures for interval-valued intuitionistic fuzzy sets and their application in group decision-making. Math Probl Eng 2015:1–13MathSciNetzbMATHGoogle Scholar
Wei G, Zhao X, Lin R (2013) Some hesitant interval-valued fuzzy aggregation operators and their applications in multiple attribute decision making. Knowl Based Syst 46:45–53CrossRefGoogle Scholar
Wu YN, Xu H, Xu CB, Chen KF (2016) Uncertain multi-attributes decision making method based on interval number with probability distribution weighted operators and stochastic dominance degree. Knowl Based Syst 113:199–209CrossRefGoogle Scholar
Xu DL, Yang JB, Wang YM (2006) The evidential reasoning approach for multi-attribute decision analysis under interval uncertainties. Eur J Oper Res 174(3):1914–1943zbMATHCrossRefGoogle Scholar
Xu XH, Cai CG, Chen XH (2015) A multi-attribute large group emergency decision making method based on group preference consistency of generalized interval-valued trapezoidal fuzzy numbers. J Syst Sci Syst Eng 24(2):211–228CrossRefGoogle Scholar
Yager RR (2001) The power average operator. IEEE Trans Syst Man Cybern Part A Syst Hum 31(6):724–731CrossRefGoogle Scholar
Ye J (2017) Multiple attribute group decision making based on interval neutrosophic uncertain linguistic variables. Int J Mach Learn Cybern 8(3):837–848CrossRefGoogle Scholar
Yue ZL (2013) Group decision making with multi-attribute interval data. Inf Fusion 14(4):551–561CrossRefGoogle Scholar
Yue ZL, Jia YY (2017) A direct projection-based group decision-making methodology with crisp values and interval data. Soft Comput 21(9):2395–2405zbMATHCrossRefGoogle Scholar
Zhang HM (2013a) Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making. Appl Math Model 37(6):4269–4282MathSciNetzbMATHCrossRefGoogle Scholar
Zhang Z (2013b) Interval-valued intuitionistic hesitant fuzzy aggregation operators and their application in group decision making. J Appl Math 2013:1–33Google Scholar