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.

The q-rung orthopair sets (q-ROFSs) is an extended version of conventional orthopair fuzzy sets, such as intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The most appealing feature of q-ROFSs is that they provide a wider range of reasonable membership grades and offer decision makers (DMs) more leeway in expressing their legitimate perceptions. The q-rung orthopair fuzzy numbers (q-ROFNs) play a vital role in computational intelligence, machine learning, neural network, and artificial intelligence. We develop numerous generalized aggregation operators (AOs) for information fusion of q-ROFNs to address some drawbacks of existing AOs. For this objective, we enhance the existing AOs by adding pairs of hesitation within the membership functions, and as a result, we introduce new operational rules for q-ROFNs utilizing Einstein norm operations. Based on suggested operational laws, we introduce new AOs namely “q-rung orthopair fuzzy Einstein interactive weighted geometric operator,” “q-rung orthopair fuzzy Einstein interactive ordered weighted geometric operator,” “generalized q-rung orthopair fuzzy Einstein interactive weighted geometric operator,” “generalized q-rung orthopair fuzzy Einstein interactive ordered weighted geometric operator,” and “generalized q-rung orthopair fuzzy Einstein interactive hybrid geometric operator.” Then, certain special cases of proposed AOs are explored and their some essential characteristics are described. A new multicriteria decision-making (MCDM) approach is devised with the help of suggested AOs for modeling uncertainties in the real-life problems. Additionally, a practical application of proposed MCDM approach is presented. Moreover, the comparison analysis, sensitivity analysis and authenticity analysis of proposed MCDM approach with existing approaches is also presented to discuss the feasibility, authenticity, and superiority of the proposed method.