Some new Shapley dual hesitant fuzzy Choquet aggregation operators and their applications to multiple attribute group decision making-based TOPSIS

An extension of TOPSIS, a multi-criteria dual hesitant fuzzy decision making technique, to a group decision environment is investigated, where the importance of combinations or their ordered positions is not only globally considered, but also overall focus on the correlations among combinations or their ordered positions. Firstly, to get a broad view of the techniques used, some operational laws on dual hesitant fuzzy numbers are introduced. Based on these operational laws, motivated by the ideas of Choquet integral and Shapley index, two dual hesitant fuzzy aggregation operators called the Shapley dual hesitant fuzzy Choquet averaging operator (SDHFCA) and Shapley dual hesitant fuzzy Choquet geometric operator (SDHFCG) are proposed. Then, some desirable properties of the two operators are discussed, such as idempotency, monotonicity, boundary and commutativity. Secondly, the Shapley Choquet integral-based Hamming distance between any dual hesitant fuzzy numbers is defined. Combining the SDHFCA operator and the SDHFCG operator with Shapley Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria dual hesitant fuzzy group decision making problems. Finally, a green chain supplier selection example is used to illustrate the developed procedures.