International Journal of Fuzzy Systems, Vol. 16, No. 2, June 2014 © 2014 TFSA 184 A Generalized Multiple Attributes Group Decision Making Approach Based on Intuitionistic Fuzzy Sets Zhifu Tao, Huayou Chen, Ligang Zhou, and Jinpei Liu Abstract 1 The aim of this paper is to investigate an intuition- istic fuzzy sets based generalized multiple attributes group decision making (GMAGDM) adapting to the situation that the attribute sets considered by a group of experts are not the same and the decision informa- tion are provided with intuitionistic fuzzy numbers (IFNs). Firstly, we develop three general procedures to handle different intuitionistic fuzzy sets based GMAGDM issues with diverse weight information: completely known, partly known and completely un- known. Then, a novel procedure on the basis of in- formation collection and transformation is put for- ward. Therein the transformation relation between the IFN and the interval-valued hesitant fuzzy ele- ment (IVHFE) is utilized. Finally, an investment se- lection problem is illustrated to show the reasonabil- ity and efficiency of the proposed algorithms. Keywords: Multi-attributes group decision making, generalized multi-attributes group decision making, intuitionistic fuzzy sets, interval-valued hesitant fuzzy element, information transformation. 1. Introduction Decision making problem is widespread in real life, and the most discussed decision situation is the multi-attributes group decision making (MAGDM) is- sues. A MAGDM problem is to find the best from possi- ble alternative sets 1 2 { , , , } m X x x x   via the decision in- formation about attributes A={a 1 , a 2 , , a n } and evalua- tion values given by a group of experts E={e 1 , e 2 , , e l }. Especially, a MAGDM problem will degenerated to be a MADM problem while the number of experts l=1. Corresponding Author: H.Y. Chen is with the School of Mathematical Science, Anhui University, 230601, China. E-mail: huayouc@126.com Z. F. Tao is with the School of Mathematical Science, Anhui Univer- sity, Hefei Anhui, E-mail: zhifut_0514@163.com. L.G. Zhou is with the School of Mathematical Science, Anhui Uni- versity. J. P. Liu is with the School of Business, Anhui University. Manuscript received 26 Nov. 2013; revised 7 April 2014; accepted 27 April 2014. When dealing with group decision making, it’s neces- sary to consider the diverse types of uncertainty. Fuzzy set theory and its natural ability to deal with uncertainty could provide the needed flexibility to handle the uncer- tainty factors in decision making. Thus, it’s of practical meaning to study such a kind of MAGDM problem un- der fuzzy environment. Intuitionistic fuzzy set (IFS) was presented by Atanassov [1] based on Zadeh’s fuzzy set [2], which has been proofed to be a very useful tool. The interval-valued fuzzy set (IVFS) [3] and the hesitant fuzzy set (HFS) [4-5] are also two generalizations of the fuzzy set. But in nature, IFS and IVFS, IVFS and HFS are equivalent, respectively [4-6]. The application of IFS in MAGDM problem is a hot topic in recent years [4, 7-13], among which the decision information provided with IFSs and intuitionistic fuzzy preference relations are two main fields. A fuzzy con- sensus discussion on the basis of the distance was given by Szmidt and Kacprzyk [7]. Xu [8] discussed some types of intuitionistic preference relations and their properties, then provided an application of such informa- tion in the MAGDM issue. Wang [9] derived the in- tuitionistic fuzzy weights from intuitionistic fuzzy pref- erence relations by building some linear goal program- ming models. Atanassov, Pasi and Yager [10] investi- gated an IFS based interpretations of a kind of complex decision making. Zhang [11] developed some general- ized power geometric operators, which are novel tools to aggregate intuitionistic fuzzy information. While in Ref. [12-13], two objective decision technologies were put forward: the TOPSIS method and kinds of objective ways to obtain the associated weighting vector. It’s worth noting that the information aggregation processes and the approaches to get the weights have attracted many authors’ interests [14-17, 30, 32, 38]. Wu and Cao [14] proposed several geometric operators to aggregate intuitionistic trapezoidal fuzzy numbers. Chen [15] pro- posed the induced generalized continuous ordered weighted averaging operator and discussed its applica- tion. Zhou and Chen [16] developed some generalized power aggregation operators. However, although the fuzzy information has been investigated in decision models and has also been widely studied, MAGDM is still a difficult process because of the complexity of real problems. The traditional decision theories are mainly pay attention on the situation that all