Abstract
For problems in multi-criteria group decision-making (MCGDM), this paper defines intuitionistic interval numbers, and the operational laws and comparison method of it. Some intuitionistic interval information aggregation operators are proposed, such as intuitionistic interval weighted arithmetic averaging operator, intuitionistic interval weighted geometric averaging operator, intuitionistic interval ordered weighted averaging operator, intuitionistic interval heavy averaging operator and intuitionistic interval aggregating operator. Then, based on intuitionistic interval fuzzy information, a method is developed to handle the problems in MCGDM. In this method, by applying the knowledge level of the experts to the decision making problem, the model of maximizing comprehensive membership coefficient is constructed to determine the weights of decision makers. By calculating the distances to the ideal and negative ideal solutions, the comprehensive attribute values and the rank of the alternatives can be obtained. Finally, an example is provided to demonstrate the feasibility and effectiveness of the proposed method.
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References
Altuzarra A, Moreno-Jiménez JM et al (2010) Consensus building in AHP-group decision making: a Bayesian approach. Oper Res 58(6): 1755–1773
Arbel A, Vargas LG (1990) The analytic hierarchy process with interval judgments. In: Proceedings of the IX international conference on MCMD. Fairfax, VA
Arbel A, Vargas LG (1993) Preference programming and preference simulation: robustness issues in the AHP. Eur J Oper Res 69(2): 200–209
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1): 87–96
Atanassov K, Cargo G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31(3): 343–349
Bustine H, Burillo P (1996) Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 79: 403–405
Contreras I (2012) Ordered weighted disagreement functions. Group Decis Negotiat 21(3): 345–361
Ertugrul I (2011) Fuzzy group decision making for the selection of facility location. Group Decis Negotiat 20(6): 725–740
Fatih EB, Serkan G (2009) Mustafa Kurt and Diyar Akay. A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36: 11363–11368
Feng X, Qian G (2010) The method of grey related analysis to multiple attribute decision making problems with intuitionistic fuzzy sets. International conference on E-Business and E-Government, pp 1588–1591
Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23: 610–614
Kuo MS, Liang GS et al (2006) Extensions of the multicriteria analysis with pairwise comparison under a fuzzy environment. Int J Approx Reason 43: 268–285
Li DF (2010) A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput Math Appl 60(6): 1557–1570
Lin L, Yuan XH et al (2007) Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comput Syst Sci 73(1): 84–88
Liu F, Yuan XH (2007) Fuzzy number intuitionistic fuzzy set. Fuzzy Syst Math 21(1): 88–91 (in Chinese)
Moore R, Lodwick W (2003) Interval analysis and fuzzy set theory. Fuzzy Sets Syst 135(1): 5–9
Moreno-Jiménez JM, Vargas LG (1993) A probabilistic study of preference structures in the analytic hierarchy process with interval judgments. Math Comput Model 17(4–5): 73–81
Nayagam VLG, Sivaraman G (2011) Ranking of interval-valued intuitionistic fuzzy sets. Appl Soft Comput 11: 3368–3372
Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32(1): 107–117
Senguta A, Pal TK (2000) On comparing interval numbers. Eur J Oper Res 27(1): 28–43
Shu MH, Cheng CH et al (2006) Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron Reliab 46(12): 2139–2148
Wan SP (2009) Method of attitude index for interval multi-attribute decision-making. Control Decis 24(1): 35–38 (in Chinese)
Wang JQ (2008) Overview on fuzzy multi-criteria decision-making approach. Control Decis 23(6):601–606, 612. (in Chinese)
Wang JQ, Li JJ (2011) Multi-criteria fuzzy decision-making method based on cross entropy and score functions. Expert Syst Appl 38: 1032–1038
Wei GW (2008) Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting. Knowl Based Syst 21: 833–836
Wu JZ, Zhang Q (2011) Multicriteria decision making method based on intuitionistic fuzzy weighted entropy. Expert Syst Appl 38: 916–922
Xu Z (2005) On method for uncertain multiple attribute decision making problems with uncertain multiplicative preference information on alternatives. Fuzzy Optim Decis Making 4: 131–139
Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15(6): 1–10
Xu ZS, Cai XQ (2012) Uncertain power average operators for aggregating interval fuzzy preference relations. Group Decis Negotiat 21(3): 381–397
Ye J (2010) Multicriteria fuzzy decision-making method using entropy weights-based correlation coefficients of interval-valued intuitionistic fuzzy sets. Appl Math Model 34: 3864–3870
Yue Z (2011) An extended TOPSIS for determining weights of decision makers with interval numbers. Knowl Based Syst 24: 146–153
Zhang XF, Guan ER et al (2001) Interval-valued fuzzy comprehensive evaluation and its application. Syst Eng Theory Pract 21(12): 81–84 (in Chinese)
Zhang J, Wu D et al (2005) The method of grey related analysis to multiple attribute decision making problems with interval numbers. Math Comput Model 42: 991–998
Zhang QS, Jiang SY et al (2010) Some information measures for interval-valued intuitionistic fuzzy sets. Inf Sci 180: 5130–5145
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Wang, Jq., Han, Zq. & Zhang, Hy. Multi-criteria Group Decision-Making Method Based on Intuitionistic Interval Fuzzy Information. Group Decis Negot 23, 715–733 (2014). https://doi.org/10.1007/s10726-012-9316-4
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DOI: https://doi.org/10.1007/s10726-012-9316-4