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This paper presents a thorough review of our state-of-the-art technique for enhancing dynamic grid partitioning and scheduling in multi-energy source systems. We use a hybrid approach to T-spherical fuzzy sets, combining the alternative ranking order method accounting for the two-step normalization (AROMAN) method for alternating ranking order to enable two-step normalisation with the method based on removal effects of criteria (MEREC) for eliminating criteria effects. This enables us to obtain the highest level of accuracy from our findings. To ascertain the relative importance of these criteria, we use MEREC to perform a rigorous examination of the influence that each evaluation criterion has on the outcomes of the decision-making process. In addition, we use AROMAN to provide a strong foundation for assessing potential solutions by accounting for spherical fuzzy sets to account for any ambiguity. We illustrate how our approach successfully considers several factors, such as social acceptability, technical feasibility, environmental sustainability, and economic feasibility, through the analysis of an extensive case study. Our approach provides decision-makers (DMs) with a rigorous and rational framework for assessing and choosing the best grid division and scheduling options. This is done in an effort to support the administration and design of resilient and sustainable multi-energy systems. This research contributes to the growing body of knowledge in this area by offering insights that help to direct policy, planning, and investment decisions in the shift towards more sustainable energy infrastructures. Moreover, it adds to the growing body of information on multi-criteria decision-making (MCDM) in energy system optimization.

To find the correspondence between every number of attributes, the Bonferroni mean (BM) operator is most widely used and proven to be a flexible approach. To express uncertain information, the frame of the interval-valued T-spherical fuzzy set (IVTSFS) is a recent development in fuzzy settings which discusses four aspects of uncertain information using closed sub-intervals of [0,1] and hence reduces the information loss greatly. In this research study, we introduced the principle of BM operators with IVTSFS to develop the principle of the inter-valued T-spherical fuzzy (IVTSF) BM (IVTSFBM) operator, the IVTSF-weighted BM (IVTSFWBM) operator, the IVTSF geometric BM (IVTSFGBM) operator, and the IVTSF-weighted geometric BM (IVTSFWGBM) operator. To see the significance of the proposed BM operators, we applied these BM operators to evaluate the performance of solar cells that play an important role in the field of energy storage. To do so, we developed a multi-attribute group decision-making (MAGDM) procedure based on IVTSF information and applied it to the problem of solar cells to evaluate their performance under uncertainty, where four aspects of opinion about solar cells were taken into consideration. We studied the results obtained using BM operators with some previous operators to see the significance of the proposed IVTSF BM operators.

The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches.