Induced generalized dual hesitant fuzzy Shapley hybrid operators and their application in multi-attributes decision making

In this study, two induced generalized dual hesitant fuzzy hybrid operators called the induced generalized dual hesitant fuzzy Shapley hybrid weighted averaging (IG-DHFSHWA) operator and the induced generalized dual hesitant fuzzy Shapley hybrid geometric mean (IG-DHFSHGM) operator are defined. These operators not only globally consider the importance of the elements and their ordered positions, but also overall reflect their correlations. Furthermore, when the weight information about attributes and ordered positions is partly known, using similarity measure analysis (SMA) method and the Shapley function models for the optimal fuzzy measures on an attribute set and on an ordered set are respectively established. Then, an approach to multi-attributes decision making with incomplete weight information and interactive conditions under dual-hesitant fuzzy environment is developed. Finally, a practical example for green supplier evaluation problem with dual hesitant fuzzy information is employed to verify the developed approach and to demonstrate its practically and effectiveness.