Abstract
In this paper, a set of Dombi power partitioned Heronian mean operators of q-rung orthopair fuzzy numbers (qROFNs) are presented, and a multiple attribute group decision making (MAGDM) method based on these operators is proposed. First, the operational rules of qROFNs based on the Dombi t-conorm and t-norm are introduced. A q-rung orthopair fuzzy Dombi partitioned Heronian mean (qROFDPHM) operator and its weighted form are then established in accordance with these rules. To reduce the negative effect of unreasonable attribute values on the aggregation results of these operators, a q-rung orthopair fuzzy Dombi power partitioned Heronian mean operator and its weighted form are constructed by combining qROFDPHM operator with the power average operator. A method to solve MAGDM problems based on qROFNs and the constructed operators is designed. Finally, a practical example is described, and experiments and comparisons are performed to demonstrate the feasibility and effectiveness of the proposed method. The demonstration results show that the method is feasible, effective, and flexible; has satisfying expressiveness; and can consider all the interrelationships among different attributes and reduce the negative influence of biased attribute values.
Highlights
Data Availability Statement: All procedure code files are available from the protocols.io database
The problem is always coupled with a q-rung orthopair fuzzy decision matrix Mk = 1⁄2Ykij m;n, where i = 1, 2, . . ., m, j = 1, 2,. . .,n and Ykij 1⁄4 ðmkij; vkijÞ (k = 1, 2,. . .,t) is a q-rung orthopair fuzzy numbers (qROFNs) that stands for the evaluation value of alternative Ai with respect to attribute Cj given by decision maker Dk
Taking each of the columns of the collective information decision matrix and the weight set as input, the collective information of each alternative can be computed by the proposed qROFDWPPHM operator, which is shown as follows: Yi 1⁄4 qROFDWPPHMa;bðYi1; Yi2; . . . ; YinÞ
Summary
The recently proposed Dombi t-conorm and Dombi t-norm (DTT) [41], which are special types of the Archimedean t-norm and t-conorm (ATT), are powerful tools for information aggregation and have been applied to the aggregation of IFSs [42], hesitant fuzzy sets [43], and single-valued neutrosophic information [44]. They have not yet been applied to the aggregation of qROFSs. It is interesting to extend the operational rules of qROFNs based on the DTT.
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