Abstract
The q-rung orthopair fuzzy set (q-ROFS), which is the extension of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), satisfies the sum of q-th power of membership degree and nonmembership degree is limited 1. Evidently, the q-ROFS can depict more fuzzy assessment information and consider decision-maker’s (DM’s) hesitance. Thus, the concept of a dual hesitant q-rung orthopair fuzzy set (DHq-ROFS) is developed in this paper. Then, based on Hamacher operation laws, weighting average (WA) operator and weighting geometric (WG) operator, some dual hesitant q-rung orthopair fuzzy Hamacher aggregation operators are developed, such as the dual hesitant q-rung orthopair fuzzy Hamacher weighting average (DHq-ROFHWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher weighting geometric (DHq-ROFHWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighted average (DHq-ROFHOWA) operator, the dual hesitant q-rung orthopair fuzzy Hamacher ordered weighting geometric (DHq-ROFHOWG) operator, the dual hesitant q-rung orthopair fuzzy Hamacher hybrid average (DHq-ROFHHA) operator, and the dual hesitant q-rung orthopair fuzzy Hamacher hybrid geometric (DHq-ROFHHG) operator. The precious merits and some particular cases of above mentioned aggregation operators are briefly introduced. In the end, an actual application for scheme selection of construction project is provided to testify the proposed operators and deliver a comparative analysis.
Highlights
In real-life decision-making problems, how to select the most desirable alternative from a given alternative set is very important
On account of the PFSs [17,55] and dual hesitant fuzzy sets (DHFSs) [27,28], Xu and Wei [56] further defined the dual hesitant Pythagorean fuzzy sets (DHPFSs), based on Hamacher operation laws weighting average (WA) operator and weighting geometric (WG) operator, some new aggregation operators under dual hesitant Pythagorean fuzzy environment were developed for multiple attribute decision-making (MADM) problems
When γ = 2, the DHq-ROFHOWG operator is going to degrade into the dual hesitant q-rung orthopair fuzzy Einstein ordered weighting geometric (DHq-ROEOWG) operator, presented as w j n
Summary
In real-life decision-making problems, how to select the most desirable alternative from a given alternative set is very important. (1) The DHq-ROFS can extend the scope of the assessment operators to aggregate the dual hesitant q-rung orthopair fuzzy information. These information to depict more fuzzy information, and consider the human’s hesitance, it is more operators have the following advantages. (2) The Hamacher operations can consider the assessment information to depict more fuzzy information, and consider the human’s hesitance, relationship between fused arguments, obviously, Hamacher operations are more suitable for handling it is more useful and reasonable to derive decision-making results. It is of great significance to propose some new operators based on operations can consider the relationship between fused arguments, obviously, Hamacher operations the dual hesitant q-rung orthopair fuzzy information and Hamacher operations.
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