Abstract
The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.
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References
Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96
Atanassov K (1999) Intuitionistic Fuzzy sets: theory and applications. Physica-Verlag, Heidelberg
Atanassov K, Gargov G (1989) Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31: 343–349
Atanassov K, Pasi G, Yager RR (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36: 859–868
Bustince H, Burillo P (1996) Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst 79: 403–405
Chen SM, Tan JM (1994) Handling multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 67: 163–172
Deschrijver G, Kerre EE (2003) On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst 136: 333–361
Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23: 610–614
Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114: 103–113
Li DF (2005) Multiple attribute decision making models and methods using intuitionistic fuzzy sets. J Comput Syst Sci 70: 73–85
Lin L, Yuan XH, Xia ZQ (2007) Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comp Syst Sci 73: 84–88
Kacprzyk J (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst 18: 105–118
Ngwenyama O, Bryson N (1999) Eliciting and mapping qualitative preferences to numeric rankings in group decision making. Eur J Oper Res 116: 487–497
Szmidt E, Kacprzyk J (2002a) Using intuitionistic fuzzy sets in group decision making. Control Cybern 31: 1037–1053
Szmidt E, Kacprzyk J (2002b) Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst 114: 505–518
Szmidt E, Kacprzyk J (2004) A concept of similarity for intuitionistic fuzzy sets and its use in group decision making. In: Proceedings of international joint conference on neural networks & IEEE international conference on Fuzzy Systems, Budapest, Hungary, pp. 25–29
Xu ZS (2004) Uncertain multiple attribute decision making: methods and applications. Tsinghua University Press, Beijing
Xu ZS (2005) An overview of methods for determining OWA weights. Int J Intell Syst 20: 843–865
Xu ZS (2007a) Intuitionistic preference relations and their application in group decision making. Inf Sci 177: 2363–2379
Xu ZS (2007b) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15: 1179–1187
Xu ZS, Chen J (2007) An approach to group decision making based on interval valued intuitionistic judgment matrices. Syst Eng Theory Pract 27(4): 126–133
Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans Syst Man Cybern 18: 183–190
Zadeh LA (1965) Fuzzy sets. Inf Control 8: 338–353
Zeleny M (1982) Multiple criteria decision making. McGraw-Hill, New York
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Xu, Z. A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making. Group Decis Negot 19, 57–76 (2010). https://doi.org/10.1007/s10726-009-9164-z
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DOI: https://doi.org/10.1007/s10726-009-9164-z