Some Interval-Valued Intuitionistic Fuzzy Zhenyuan Aggregation Operators and Their Application to Multi-Attribute Decision Making

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Abstract
This paper develops some new decision making methods for multi-attribute decision making (MADM) problems, in which the attribute weights take the form of crisp numbers, and attribute values take the form of interval-valued intuitionistic fuzzy information. First, based on the Zhenyuan integral, an interval-valued intuitionistic fuzzy Zhenyuan averaging (IVIFZA) operator and an interval-valued intuitionistic fuzzy Zhenyuan geometric (IVIFZG) operator are introduced to facilitate aggregation of interval-valued intuitionistic fuzzy information. The proposed operators allow one to fully consider the importance of different combinations of attributes and, therefore, are highly suitable to handle problems involving inter-dependent or interactive attributes. We further proceed by exploring some desirable properties of the IVIFZA and IVIVZG operators. By employing the proposed operators, a MADM approach based on intervalvalued intuitionistic fuzzy information is proposed. Finally, an illustrative example is presented to verify the developed approach and to demonstrate its practicality and effectiveness.

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