Regression coefficient measure of intuitionistic fuzzy graphs with application to soil selection for the best paddy crop

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.