The Fourth Industrial Revolution, also known as Industry 4.0, is attracting a significant amount of attention because it has the potential to revolutionize a variety of industries by developing a production system that is fully automated and digitally integrated. The implementation of this transformation, however, calls for a significant investment of resources and may present difficulties in the process of adapting existing technology to new endeavors. Researchers have proposed integrating the Analytic Hierarchy Process (AHP) with extensions of fuzzy rough sets, such as the three-dimensional q-spherical fuzzy rough set (q-SFRS), which is effective in handling uncertainty and quantifying expert judgments, to prioritize projects related to Industry 4.0. This would allow the projects to be ranked in order of importance. In this article, a novel framework is presented that combines AHP with q-SFRS. To calculate aggregated values, the new framework uses a new formula called the q-spherical fuzzy rough arithmetic mean, when applied to a problem involving the selection of a project with five criteria for evaluation and four possible alternatives, the suggested framework produces results that are robust and competitive in comparison to those produced by other multi-criteria decision-making approaches.

This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.

q-Rung orthopair fuzzy soft set handles the uncertainties and vagueness by membership and non-membership degree with attributes, here is no information about the neutral degree so to cover this gap and get a generalized structure, we present hybrid of picture fuzzy set and q-rung orthopair fuzzy soft set and initiate the notion of q-rung orthopair picture fuzzy soft set, which is characterized by positive, neutral and negative membership degree with attributes. The main contribution of this article is to investigate the basic operations and some averaging aggregation operators like q-rung orthopair picture fuzzy soft weighted averaging operator and q-rung orthopair picture fuzzy soft order weighted averaging operator under the environment of q-rung orthopair picture fuzzy soft set. Moreover, some fundamental properties and results of these aggregation operators are studied, and based on these proposed operators we presented a stepwise algorithm for MADM by taking the problem related to medical diagnosis under the environment of q-rung orthopair picture fuzzy soft set and finally, for the superiority we presented comparison analysis of proposed operators with existing operators.

Green supplier selection has been an important technique for environmental sustainability and reducing the harm of ecosystems. In the current climate, green supply chain management (GSCM) is imperative for maintaining environmental compliance and commercial growth. To handle the change related to environmental concern and how the company manages and operates, they are integrated the GSCM into traditional supplier selection process. The main aims of this study were to outline both traditional and environmental criteria for selecting suppliers, providing a comprehensive framework to assist decision-maker in prioritizing green supplier effectively. In order to address issue to simulate decision-making problems and manage inaccurate data. A useful technique of fuzzy set was proposed to handle uncertainty in various real-life problems, but all types of data could not be handled such as incomplete and indeterminate. However, several extensions of fuzzy set were considered, such as intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and q-rung orthopair fuzzy soft set considering membership and nonmember ship grade to handle the uncertainty problem. However, there was a lack of information about the neutral degree and parameterization axioms lifted by existing approaches, so to fill this gap and overcome the difficulties Ali et al. proposed a generalized structure by combining the structure of picture fuzzy set and q-rung orthopair fuzzy soft set, known as q-rung orthopair picture fuzzy soft sets, characterized by positive, neutral and negative membership degree with parameterization tools and aggregation operator to solve the multi criteria group decision-making problem. Additionally, the TOPSIS method is a widely utilized to assist individuals and organizations in selecting the most appropriate option from a range of choices, taking into account various criteria. Finally, we demonstrate an illustrative example related to GSCM to enhance competitiveness, based on criteria both in general and with a focus on environmental consideration, accompanied by an algorithm and flow chart.