According to United Nations forecasts, India is now expected to pass China as the most populous country in the world in 2023. This is due to the fact that in 2022, China saw its first population decline in over 60 years. In order to keep pace with the rapid rise in its population, India will need to significantly raise food production in the future. Specific soil selection can help in achieving expected food production. In this article, we use Laplacian energy and regression coefficient measurements to face decision-making issues based on intuitionistic fuzzy preference relations (IFPRs). We present a novel statistical measure for evaluating the appropriate position weights of authority by computing the fuzzy evidence of IFPRs and the specific similarity grade among one distinct intuitionistic preference connection to the others. This new way of thinking bases decisions on evidence from both external and internal authorities. We evolved a statistical (regression coefficient measure) approach to determine the importance of alternatives and the best of the alternatives after integrating the weights of authority into IFPRs. This statistical analysis can be put to good use to choose the best soil for different crops to provide food for India's rapidly growing population in the future. To show how useful and realistic the suggested statistical measure is, a good example from real life is given. Additionally, we discovered how correlation and regression coefficient measurements are related to one another in intuitionistic fuzzy graphs.

A new cosine similarity measure between hesitancy fuzzy graphs, which have been shown to have greater discriminating capacity than certain current ones in group decision making problems by example verification. This study proposes a novel method for estimating expert-certified repute scores by determining the ambiguous information of hesitancy fuzzy preference relations as well as the regular cosine similarity grades from one separable hesitancy fuzzy preference relation to some others. The new approach considers both "objective" and "subjective" information given by experts. We construct working procedures for assessing the eligible reputational scores of the experts by applying hesitancy fuzzy preference relations. In an evaluation in which multiple conflicting factors are taken into consideration, this can be applied to increase or reduce the relevancy of specified criteria. Applying the two effective methods, the newly developed cosine similarity measure, the energy of hesitancy fuzzy graph, and we provide a solution to a decisional issue. Finally, the two working procedures and examples are given to verify the practicality and dominance of the proposed techniques.