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

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.

Decision-making for solar panel selection using Sugeno-Weber triangular norm-based on q-rung orthopair fuzzy information

“…frontiersin.org moderate aggregation model, allowing the decision-maker to investigate optimal options during decision-making. In order to verify the applicability of the proposed approaches, we applied existing approaches developed by different mathematicians such as Jana et al (2019), Wang et al (2019), Darko and Liang (2020), Du et al (2022), Khan et al (2022), Seikh andMandal (2022), and. The Hamacher aggregation tools with some realistic properties were generalized by Darko and Liang (2020), and a list of new approaches based on the q-rung orthopair fuzzy environments was developed.…”

“…Properties of Aczel-Alsina aggregation tools were explored by Farid and Riaz (2023) to develop a list of new approaches, namely, q-ROF Aczel-Alsina weighted average (q-ROFAAWA) operator, and Khan et al (2022) introduced AOs of the q-ROF Aczel-Alsina weighted geometric (q-ROFAAWG) operator. Wang et al (2019) extended the theory of q-ROFS in the form of complex q-ROF environments, and Du et al (2022) utilized the concepts of Frank aggregation tools based on complex q-ROF systems. After the aggregation process, the results are computed using existing methodologies as listed in Table 8.…”

Multi-attribute decision-making method based on complex T-spherical fuzzy frank prioritized aggregation operators

“…Xu et al [ 49 ] introduced the group decision-making technique for complex fuzzy data using frank laws. Yuqin Du [ 50 ]. developed the complex q-ROFS frank AOs and their application.…”

Advanced Linguistic Complex T-Spherical Fuzzy Dombi-Weighted Power-Partitioned Heronian Mean Operator and Its Application for Emergency Information Quality Assessment

“…As the main mark to distinguish fuzzy sets, the phase term plays a crucial role in constructing the CFS model. Subsequent scholars proposed a complex intuitionistic fuzzy set [20] (CIFS), complex Pythagorean fuzzy set [21] (CPyFS), complex q-rung orthopair fuzzy set [22] (CqROFS), complex picture fuzzy set [23] (CPFS), and complex spherical fuzzy set [24] (CSFS). Nasir et al [25] finally introduced the complex T-spherical fuzzy set (CT-SFS), which greatly improves the research's flexibility, applicability, and effectiveness of the research, and facilitates the subsequent research in the field of fuzzy decision-making.…”