Hesitant fuzzy multi-attribute decision-making based on the minimum deviation method
 作者： Hua Zhao,  Zeshui Xu,  Hai Wang,  Shousheng Liu 作者单位： 1PLA University of Science and Technology2Sichuan University3Southeast University 刊名： Soft Computing, 2017, Vol.21 (12), pp.3439-3459 来源数据库： Springer Journal DOI： 10.1007/s00500-015-2020-y 关键词： Hesitant fuzzy set;  Multi-attribute decision-making;  Minimum deviation;  Weight; 英文摘要： As a powerful and efficient tool in expressing the indeterminate and fuzzy information, the hesitant fuzzy set (HFS) has shown its increasing importance. It was first proposed by Torra and Narukawa, permitting the membership degree of an element to a set of several possible values. In this paper, based on the idea of minimum deviation between the subjective and the objective preferences, we first develop two methods to determine the attribute weights under the hesitant fuzzy environment. To do so, we present the concept of hesitant fuzzy expected value and then establish several optimization models to gain the attribute weights. After that, we use the information aggregation techniques to integrate the hesitant fuzzy attribute values or their expected values, and then sort the... alternatives by the overall values. Moreover, we generalize these two methods to interval-valued HFSs, and a numerical example is utilized to show the detailed implementation procedure and effectiveness of our methods in solving multi-attribute decision-making problems with hesitant fuzzy or interval-valued hesitant fuzzy information. 原始语种摘要： As a powerful and efficient tool in expressing the indeterminate and fuzzy information, the hesitant fuzzy set (HFS) has shown its increasing importance. It was first proposed by Torra and Narukawa, permitting the membership degree of an element to a set of several possible values. In this paper, based on the idea of minimum deviation between the subjective and the objective preferences, we first develop two methods to determine the attribute weights under the hesitant fuzzy environment. To do so, we present the concept of hesitant fuzzy expected value and then establish several optimization models to gain the attribute weights. After that, we use the information aggregation techniques to integrate the hesitant fuzzy attribute values or their expected values, and then sort the... alternatives by the overall values. Moreover, we generalize these two methods to interval-valued HFSs, and a numerical example is utilized to show the detailed implementation procedure and effectiveness of our methods in solving multi-attribute decision-making problems with hesitant fuzzy or interval-valued hesitant fuzzy information.

• fuzzy　模糊的
• decision　决定
• deviation　偏差
• making　制定
• attribute　属性
• minimum　极小
• expected　预期
• weights　法码
• hesitant　犹豫
• information　报告