Abstract
Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.
Highlights
Fuzzy sets (FSs) [1] originally put forward by Zadeh are a very useful tool and have achieved a great success in various fields
In order to compare among the different interval-valued hesitant fuzzy elements (IVHFEs), we first give the properties of interval numbers
Suppose that the decision makers are required to provide the information that the alternative Xi satisfies the attribute Cj with anonymity, and the information expressed by interval-valued values; these values can be considered as an IVHFE αij
Summary
Fuzzy sets (FSs) [1] originally put forward by Zadeh are a very useful tool and have achieved a great success in various fields. We extend the Hamacher t-conorm and t-norm to interval-valued hesitant fuzzy environment and investigate some improved intervalvalued hesitant fuzzy Hamacher operators that allow DMs to have more choice in MAGDM problems. More and more decision making methods and theories have been developed on the basis of IVHFSs. On the one hand, just as the HFSs, introducing the axiomatic definition of entropy and investigating some entropy formulas for IVHFSs are the important issues. The axiomatic definition of entropy and an entropy formula for IVHFEs are investigated, and some new improved Hamacher aggregation operators are proposed to aggregate interval-valued hesitant fuzzy information.
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