Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

Yuqin Du; Xiangjun Du; Yuanyuan Li; Jian-Xin Cui; Fujun Hou

doi:10.1007/s00500-022-07465-2

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

Soft comput. 2022;26(22):11973-12008. doi: 10.1007/s00500-022-07465-2. Epub 2022 Sep 19.

Authors

Yuqin Du¹, Xiangjun Du², Yuanyuan Li³, Jian-Xin Cui⁴, Fujun Hou⁵

Affiliations

¹ School of Economics, University of Chinese Academy of Social Sciences, Beijing, 102488 People's Republic of China.
² School of Mechanical Engineering, Tiangong University, Tianjin, 300387 People's Republic of China.
³ Department of Finance, Nankai University Binhai College, Binhai, 300270 People's Republic of China.
⁴ China Railway Investment Group Limited, Beijing, 100039 People's Republic of China.
⁵ School of Management and Economics, Beijing Institute of Technology, Beijing, 100081 People's Republic of China.

Abstract

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.

Keywords: Aggregation operators; Complex q-rung orthopair fuzzy set; Frank operator; Multi-attribute decision making.

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