<abstract><p>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.</p></abstract>

Group decision-making is a technique wherein professionals rank and select the most acceptable ones based on recognised criteria. The objective of the present study was to establish a strategy for solving issues with Laplacian energy and association coefficient measures of intuitionistic fuzzy graphs through group decision-making. Initially, making use of Laplacian energy, the load of each criterion is determined, and the entire criterion load vector is then computed by averaging the determined loads. The substitutes are then ranked using the association coefficient measure linked to every criterion. Finally, we used the proposed technique wherein professionals rank and select the most acceptable based on recognised criteria with real-time application.

Intuitionistic fuzzy graphs are extensions of fuzzy graphs that preserve the dualism characteristics of fuzzy graphs and have a stronger capacity to describe ambiguity in actual decision-making issues than fuzzy graphs. In this research paper, the Laplacian energy and correlation coefficient of intuitionistic fuzzy graphs are computed for finding group decision-making problems that are supported by intuitionistic fuzzy preference relations. We propose a novel method for calculating establishments' comparative position loads by manipulating the undecided corroboration of IFPR and the correlation coefficient of one personality IFPR to the other items. As a result, we comprehend a large number of establishments in the detailed IFPR and devise a correlation coefficient process to investigate the significance of alternatives and the best of the alternatives. Finally, we present a collaborative decision-making technique in a money-investing scheme, and that idea may be devised in disparate beneficial investing schemes.