Intuitionistic Fuzzy Aggregation Operators and Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets

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Intuitionistic Fuzzy Aggregation Operators and Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets

2.1 Introduction How to aggregate information and preference is an important problem in real management and decision process [1–7]. Due to the complexity of management environments and decision problems themselves, decision makers may provide their ratings or judgments to some certain degree, but it is possible that they are not so sure about their judgments. Namely, there may exist some hesitancy degree, which is a very important factor to be taken into account when trying to construct really adequate models and solutions of decision problems. Such a kind of hesitancy degrees is suitably expressed with intuitionistic fuzzy sets rather than exact numerical values. Thus, how to aggregate intuitionistic fuzzy information becomes an important part of multiattribute decision-making with intuitionistic fuzzy sets [8–13]. The classical weighted aggregation is usually known in the literature by the linear (or simple additive) weighted averaging method [14–16]. Another important aggregation operator within the class of weighted averaging operators is the ordered weighted averaging (OWA) operator introduced by Yager [4], which has been used in many management applications. In 2004, Yager [5] further introduced the generalized ordered weighted averaging (GOWA) operator, which is a generalization of the OWA operator and the generalized mean operator through adding an additional parameter as the power of the OWA operator. This chapter mainly discusses extension forms of these aggregation operators with intuitionistic fuzzy sets, including the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy OWA operator, intuitionistic fuzzy hybrid weighted averaging operator, intuitionistic fuzzy GOWA operator, intuitionistic fuzzy generalized hybrid weighted averaging operator and their applications to multiatribute decision-making with intuitionistic fuzzy sets [9–13].

D.-F. Li, Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing 308, DOI: 10.1007/978-3-642-40712-3_2,  Springer-Verlag Berlin Heidelberg 2014

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2 Intuitionistic Fuzzy Aggregation Operators and Multiattribute Decision-Making

2.2 Intuitionistic Fuzzy Aggregation Operators and Properties ~¼ For the sake of convenience, as stated earlier, if an intuitionistic fuzzy set A   hxj ; lA~ ðxj Þ; tA~ ðxj Þi j xj 2 X on the finite universal set X ¼ fx1 ; x2 ; . . .; xn g has ~ ¼ 1, then usually A ~ is denoted by Aj ¼ hlj ; tj i only one element, i.e., jAj 1 ðj ¼ 1; 2; . . .; nÞ for short, where lj ¼ lA~ ðxj Þ and tj ¼ tA~ ðxj Þ satisfy the conditions: lj 2 ½0; 1, tj 2 ½0; 1, and 0  lj þ tj  1. The set of these singleton intuitionistic fuzzy sets is denoted by F.2 In the sequent, to investigate on aggregation problems of imprecise and uncertain information in decision-making with intuitionistic fuzzy sets, we discuss several commonly-used aggregation operators such as the intui