The Impact of Fuzzy Logic on Differential Equation Solutions in Dynamic Systems

This research examines how fuzzy logic represents uncertainty in system parameters and how it affects differential equation solutions in dynamic systems. Fuzzy logic may better describe uncertainty in real-world systems than traditional differential equations. The purpose is to investigate how adding fuzziness to differential equations might enhance dynamic system knowledge and forecast accuracy under uncertainty. The fuzzy Runge-Kutta technique and fuzzy differential inclusions are used to solve dynamic systems with fuzzy parameters. Three example studies fuzzy population dynamics, mechanical system, and economic growth use these methodologies. Each time, fuzzy numbers are used to simulate system characteristics like growth rate, damping coefficient, and inflation rate to account for system uncertainty in the differential equations. The answers are examined using fuzzy sets and systems theory. The findings show that fuzzy logic enhances uncertainty modeling in dynamic systems. Fuzzy differential equation solutions show many effects, indicating machine behavior under uncertainty. The variety of acceptable machine actions extends as parameter uncertainty increases, showing how fuzzy good judgment provides a more flexible and comprehensible portrayal of complex systems than typical models that use crisp values. This method enhances dynamic machine analysis's resilience and prediction accuracy, especially in real-world situations. Adding fuzzy good judgment to differential equations enhances dynamic system modeling and analysis by accounting for uncertainty. Fuzzy differential equations give more complete and comprehensible system behavior information, especially for real-world systems with unknown parameter values. This method allows for more accurate and adaptable system modeling, notably in population dynamics, mechanical systems, and economics. Fuzzy optimization and fuzzy manipulation are advised to make fuzzy differential equations more applicable to complicated systems. Future research may integrate fuzzy logic with machine learning and AI to improve system prediction and choice-making in dynamic contexts.