tailieunhanh - Multi-criteria Group Decision Making with Picture Linguistic Numbers
In 2013, Cuong and Kreinovich defined picture fuzzy set (PFS) which is a direct extension of fuzzy set (FS) and intuitionistic fuzzy set (IFS). Wang et al. (2014) proposed intuitionistic linguistic number (ILN) as a combination of IFS and linguistic approach. Motivated by PFS and linguistic approach, this paper introduces the concept of picture linguistic number (PLN), which constitutes a generalization of ILN for picture circumstances. | VNU Journal of Science: Comp. Science & Com. Eng., Vol. 32, No. 3 (2016) 39–52 Multi-criteria Group Decision Making with Picture Linguistic Numbers Pham Hong Phong1,∗, Bui Cong Cuong2 1 Faculty of Information Technology, National University of Civil Engineering, 55 Giai Phong Road, Hanoi, Vietnam 2 Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet Road, Building A5, Cau Giay, Hanoi, Vietnam Abstract In 2013, Cuong and Kreinovich defined picture fuzzy set (PFS) which is a direct extension of fuzzy set (FS) and intuitionistic fuzzy set (IFS). Wang et al. (2014) proposed intuitionistic linguistic number (ILN) as a combination of IFS and linguistic approach. Motivated by PFS and linguistic approach, this paper introduces the concept of picture linguistic number (PLN), which constitutes a generalization of ILN for picture circumstances. For multi-criteria group decision making (MCGDM) problems with picture linguistic information, we define a score index and two accuracy indexes of PLNs, and propose an approach to the comparison between two PLNs. Simultaneously, some operation laws for PLNs are defined and the related properties are studied. Further, some aggregation operations are developed: picture linguistic arithmetic averaging (PLAA), picture linguistic weighted arithmetic averaging (PLWAA), picture linguistic ordered weighted averaging (PLOWA) and picture linguistic hybrid averaging (PLHA) operators. Finally, based on the PLWAA and PLHA operators, we propose an approach to handle MCGDM under PLN environment. Received 18 March 2016, Revised 07 October 2016, Accepted 18 October 2016 Keywords: Picture fuzzy set, linguistic aggregation operator, multi-criteria group decision making, linguistic group decision making. 1. Introduction types: “yes”, “abstain”, “no” and “refusal”. Voting can be a good example of such situation as the voters may be divided into four groups: “vote for”, “abstain”, “vote against” and “refusal of .
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