An intuitionistic fuzzy weighted OWA operator and its application
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ORIGINAL ARTICLE
An intuitionistic fuzzy weighted OWA operator and its application Xia Liang • Cuiping Wei • Zhimin Chen
Received: 20 May 2012 / Accepted: 26 December 2012 Ó Springer-Verlag Berlin Heidelberg 2013
Abstract In this paper, we define a new operator, an intuitionistic fuzzy weighted OWA (IFWOWA) operator, to aggregate intuitionistic fuzzy information. The proposed operator combines the advantages of the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator. We then study its properties, compare it with the intuitionistic fuzzy hybrid averaging (IFHA) operator, and use it to solve multi-attribute group decision making problem with intuitionistic fuzzy information. Keywords Multi-attribute group decision making Intuitionistic fuzzy sets Intuitionistic fuzzy weighted OWA operator Averaging operator
1 Introduction As a generalized form of fuzzy sets (FSs) [26], intuitionistic fuzzy sets (IFSs) [1, 2] can depict the fuzziness and uncertainty of objective world more exquisitely than fuzzy sets. Gau and Buehrer [7] introduced the notion of vague sets. Bustince and Burillo [3] pointed out that the theory of vague sets is equivalent with that of IFSs. Now, IFSs have been applied in many fields, such as decision making
X. Liang School of Business Administration, Northeastern University, Shenyang 110004, Liaoning, China e-mail: [email protected] C. Wei (&) Z. Chen Institute of Operations Research, Qufu Normal University, Rizhao 276826, Shandong, China e-mail: [email protected]
[9, 10, 21, 22, 23], medical diagnosis [6] and pattern recognition [16, 17]. For multi-attribute decision making (MADM) problem with intuitionistic fuzzy information, an important research topic is to aggregate satisfactions of individual attributes, described by intuitionistic fuzzy numbers, to obtain an overall evaluation value for an alternative. The overall evaluation value is then used to help select alternatives. Xu and Yager [18, 20] defined some geometric aggregation operators and used them to multi-attribute group decision making with intuitionistic fuzzy information. In [19], Xu proposed the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator to aggregate intuitionistic fuzzy information. The IFWA operator weights intuitionistic fuzzy arguments themselves, while the IFOWA operator weights the ordered position of intuitionistic fuzzy arguments. Then Xu [19] defined the intuitionistic fuzzy hybrid averaging (IFHA) operator in order to combine the advantages of the IFWA operator and the IFOWA operator. The IFHA operator is a scoring operator which is monotonic. But it dose not remain between the minimum the maximum of the arguments or satisfy idempotency, that is, it is not an averaging operator defined by Yager in [25]. In this work, we define an intuitionistic fuzzy weighted OWA (IFWOWA) operator, which is an averaging operator and generalize the IFWA operato
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