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International Journal for Uncertainty Quantification
Hesitant trapezoidal fuzzy aggregation operators based on Archimedean t-norm and t-conorm and their application in MADM with completely unknown weight information
In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant trapezoidal fuzzy elements (HTFEs). The existing t-norms and t-conorms, including the Algebraic, Einstein, Frank and Hamacher t-norms and t-conorms, can be regarded as special cases of Archimedean t-norm and t-conorm. Firstly, we develop some new operational laws for HTFEs based on the Archimedean t-norm and t-conorm. Then, based on the operational laws, we define some hesitant trapezoidal fuzzy aggregation operators and their generalizations are also introduced, and some desirable properties and the relationships of these operators are discussed in detail. Meanwhile, we present two objective weight determination methods. Inspired by the idea of dependent aggregation, we propose some dependent hesitant trapezoidal fuzzy aggregation operators: the dependent hesitant trapezoidal fuzzy Frank ordered weighted average (DHTFFOWA) operator and the dependent hesitant trapezoidal fuzzy Frank ordered weighted geometric (DHTFFOWG) operator. Furthermore, we develop an approach to MADM under hesitant trapezoidal fuzzy environment. Finally, an illustrative example for software development project selection is given to verify the developed method and to demonstrate its applicability and validity.
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