Power Aggregation Operators Based on t-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making

Abstract

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises.

Prioritized Aggregation Operators for Intuitionistic Fuzzy Information Based on Aczel–Alsina T-Norm and T-Conorm and Their Applications in Group Decision-Making

“…The proposed work has its limitations when the information expressing uncertainty has more characteristics and can be extended to the environment of interval-valued IFSs [45]. We also aim to extend this work to the frame of complex IFSs [46], complex Pythagorean fuzzy sets [47], complex q-rung orthopedic fuzzy sets [48], and T-spherical fuzzy sets (TSFSs) [49]. The proposed Aczel-Alsina AOs can also be associated with Maclaurin symmetric mean operators [24] and Bonferroni mean operators [50].…”

Development of p,q− quasirung orthopair fuzzy hamacher aggregation operators and its application in decision-making problems

“…Abdullah et al [ 31 ] established cubic Pythagorean fuzzy AOs through the utilization of Hamacher t-norm and t-conorm, while also outlining their essential properties. Ali et al [ 32 ] introduced power AOs that leverage Hamacher t-norm and t-conorm within the context of complex Intuitionistic fuzzy numbers. Gayen et al [ 33 ] employed Hamacher t-norm and t-conorm to establish core operational laws for q-rung orthopair trapezoidal fuzzy numbers, introducing a series of tailored AOs.…”

An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws

“…On the basis of these operational laws, several academics introduced the AOs. Examples include Ali et al (2021b) who used the t-norm (TRM) and t-conorm (TCRM) in power AOs, Seikh and Mandal (2021) who used the Dombi TRM and TCRM, Huang (2014) who used the Hamacher TRM, and Wang and Liu (2012) and Zhao and Wei (2013). Using Hamacher TRM and TCRM, Akram et al (2021) presented the AOs for the complex IFS.…”