Advanced Investment Analysis Using Butcher’s Seventh Order RK Methods and ITFS in MAGDM for Indian Banks

Abstract

MAGDM (Multi-Attribute Group Decision Making) proves to be the most effective solution when compared to other decision-making methods. The data set used in this analysis is extracted from Intuitionistic Triangular Fuzzy Number (ITFNs) matrices, where the values are calculated according to specific orders of Runge-Kutta methods, a widely recognized numerical technique for solving differential equations. In this context, decision-making involves applying the Intuitionistic Triangular Fuzzy Weighted Geometric Operator (ITFWG) and the Intuitionistic Triangular Hybrid Geometric Operator (ITFHG). These operators help handle the uncertainty and imprecision inherent in the decision-making process, providing a more robust evaluation of alternatives. To rank the alternatives, an extended version of the Normalized Hamming Distance formula is employed. This formula measures the dissimilarity between different alternatives, providing a more accurate and comprehensive ranking based on the fuzzy data. The methodology ensures that each alternative is evaluated not only for its individual attributes but also for the interactions and trade-offs among those attributes in the decision-making process. The paper further illustrates the application of this approach through a numerical example, highlighting the elasticity and effectiveness of the proposed methodology. The numerical results demonstrate how the use of Intuitionistic Triangular Fuzzy Numbers, coupled with Runge-Kutta methods, enhances the precision and reliability of the decision-making process, making it an effective tool for complex real-world problems. MAGDM is the best solution that comes into play, compared to other solutions. From Intuitionistic triangular fuzzy number matrices, the data set is taken. The values shall be determined in accordance with some order of Runge Kutta methods. By using decision making, we have used Intuitionistic Triangular Fuzzy Weighted Geometric Operator and Intuitionistic Triangular Hybrid Geometric operator solutions. The values shall be determined in accordance with some order of Runge Kutta methods. By using decision making, we have used Intuitionistic Triangular Fuzzy Weighted Geometric Operator and Intuitionistic Triangular Hybrid Geometric operator solutions. For ranking alternatives, a new extended Normalized Hamming Distance formula is used. This paper presents the numerical illustration of elasticity and effectiveness.