Du Yuqin, Du Xiangjun, Li Yuanyuan, Cui Jian-Xin, Hou Fujun
School of Economics, University of Chinese Academy of Social Sciences, Beijing, 102488 People's Republic of China.
School of Mechanical Engineering, Tiangong University, Tianjin, 300387 People's Republic of China.
Soft comput. 2022;26(22):11973-12008. doi: 10.1007/s00500-022-07465-2. Epub 2022 Sep 19.
The complex q-rung orthopair fuzzy sets (Cq-ROFSs) can serve as a generalization of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets FS (CFSs). Cq-ROFSs provide more freedom for people handling uncertainty and vagueness by the truth and falsity grades on the condition that the sum of the q-powers of the real part and imaginary part is within the unit interval. Further, Frank operational laws are an extended form of Archimedes' T mode and Archimedes' S mode and Frank aggregation operators have a certain parameter which makes them more flexible and more generalized than many other aggregation operators in the process of information fusion. The objectives of this paper are to extend the Frank operations to the complex q-rung orthopair fuzzy environment and to introduce their score function and accuracy function. Meanwhile, some complex q-rung fuzzy Frank aggregation operators are developed, such as the complex q-rung orthopair fuzzy Frank weighted averaging (Cq-ROFFWA) operator, the complex q-rung orthopair fuzzy Frank weighted geometric (Cq-ROFFWG) operator, and the complex q-rung orthopair fuzzy Frank ordered weighted averaging (Cq-ROFFOWA) operator, and their special cases are discussed. In addition, an innovative MADM method is introduced according to the propounded operators to deal with multi-attribute decision-making problems under the complex q-rung orthopair fuzzy environment. Consequently, the practicability and effectiveness of the created methods are proposed by parameter exploration and comparative analysis.
复q阶正交对模糊集（Cq - ROFSs）可以作为q阶正交对模糊集（q - ROFSs）和复模糊集（CFSs）的推广。在实部和虚部的q次幂之和在单位区间内的条件下，Cq - ROFSs通过真值和假值等级为人们处理不确定性和模糊性提供了更多的自由度。此外，Frank运算定律是阿基米德T模和阿基米德S模的扩展形式，Frank聚合算子有一个特定的参数，这使得它们在信息融合过程中比许多其他聚合算子更灵活、更具一般性。本文的目的是将Frank运算扩展到复q阶正交对模糊环境，并引入它们的得分函数和准确性函数。同时，开发了一些复q阶模糊Frank聚合算子，如复q阶正交对模糊Frank加权平均（Cq - ROFFWA）算子、复q阶正交对模糊Frank加权几何（Cq - ROFFWG）算子和复q阶正交对模糊Frank有序加权平均（Cq - ROFFOWA）算子，并讨论了它们的特殊情况。此外，根据所提出的算子引入了一种创新的多属性决策方法，以处理复q阶正交对模糊环境下的多属性决策问题。因此，通过参数探索和比较分析，验证了所提出方法的实用性和有效性。
