Multicriteria decision-making with proportional distribution based spherical fuzzy fairly aggregation operators

Spherical fuzzy sets (SFSs) are strong models for modeling uncertain information in the computational intelligence and decision-making analysis. The key features of SFSs include the sum of the squares of membership grades (positive, neutral, and negative) lies in the unit closed interval [0, 1]. These models outperform other conventional fuzzy structures. The goal of this article is to develop some novel operational laws and “aggregation operators” (AOs) in a spherical fuzzy environment. For this goal, we define new neutral or fairly operational laws that incorporate the concept of proportional distribution to achieve a neutral or fair remedy of three indexes of spherical fuzzy numbers. Subsequently, we propose new “spherical fuzzy fairly weighted average operator” and “spherical fuzzy fairly ordered weighted averaging operator” based on suggested operational laws. The suggested AOs provide more generalized, reliable, and accurate information than other fuzzy techniques. Furthermore, a fairly multicriteria decision-making algorithm is developed using proposed fairly AOs with multiple decision-makers evaluations and partial weight information under SFSs. Moreover, a robust application of suggested algorithm is given to demonstrate the hierarchical medical treatment systems.