Abstract
We investigate the multiple criteria decision making (MCDM) problem concerns on the selection of shale gas areas with interval-valued hesitant fuzzy information. First, some Hamacher operations of interval-valued hesitant fuzzy information are introduced, which generalize and extend the existing ones. Then some interval-valued hesitant fuzzy Hamacher weighted aggregation operators, especially, the interval-valued hesitant fuzzy Hamacher synergetic weighted averaging (IVHFHSWA) operators and their geometric version (IVHFHSWG) operators that weight simultaneously the argument variables themselves and their position orders and thus generalize the ideas of the weighted averaging and the ordered weighted averaging, are proposed. The distinct advantages of these operators are that they can provide more choices for the decision makers and considerably enhance or deteriorate the performance of aggregation. The essential properties of these operators are studied and their specific cases are discussed. Based on the IVHFHSWA operator, we propose a practical approach to shale gas areas selection with interval-valued hesitant fuzzy information. Finally, an illustrative example for selecting the shale gas areas is used to demonstrate the practicality and effectiveness of the proposed approach and a comparative analysis is performed with other approaches to highlight the distinctive advantages of the proposed operators.
Highlights
We investigate the multiple criteria decision making (MCDM) problem concerns on the selection of shale gas areas with intervalvalued hesitant fuzzy information
Based on the IVHFHSWA operator, we propose a practical approach to shale gas areas selection with interval-valued hesitant fuzzy information
Unlike the other generalizations of fuzzy sets, hesitant fuzzy sets (HFSs), which permit the membership degree of an element to a set to be represented as several possible values between 0 and 1, are quite suited for describing the situation where we have a set of possible values, rather than a margin of error or some possibility distribution on the possible values, and HFSs are very useful in dealing with the practical decision making situations where people hesitate among several values to express their opinions [3,4,5] or their opinions with incongruity [6,7,8], especially, the group decision making with anonymity [9,10,11,12]
Summary
As a novel generalization of fuzzy sets, hesitant fuzzy sets (HFSs) [1, 2] introduced by Torra and Narukawa have been successfully used in the decision making field as a powerful tool for processing with uncertain and vague information. Torra and Narukawa [1, 2] proposed some set theoretic operations such as union, intersection, and complement on HFSs. Subsequently, Xia and Xu [6] defined some new operations on HFSs based on the interconnection between HFSs and the IFSs and made an intensive study of hesitant fuzzy information aggregation techniques and their applications in decision making. Given the advantages of the Hamacher t-norms, in this paper, we will investigate the interval-valued hesitant fuzzy aggregation operators based on the Hamacher t-norms and apply them to the multiple criteria decision making.
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