Contra-hormonic generalized fuzzy numerical scheme for solving mechanical engineering problems

Abstract

Differential equations are employed in a variety of engineering and applied mathematics fields, including mechanics, thermodynamics, and general relativity. It is occasionally necessary to deal with multi-index, uncertainty, or restriction dynamics in addition to imprecise, confusing, or insufficient situational information while modelling a wide range of real-world events. For this reason, compared to fuzzy set models, trapezoidal or triangular fuzzy set models, intuitionistic fuzzy set models are far more useful and flexible for handling this type of data. The differential equations in a generalized trapezoidal intuitionistic fuzzy environment were studied in this work. Contra-harmonic mean approaches are used in a fuzzy environment to solve the generalized trapezoidal intuitionistic fuzzy initial value problems (FIVPs). The generalized numerical technique is employed in many higher-order generalized intuitionistic fuzzy FIVPs, as well as circuit evaluation, mass-spring systems, steam supply management sliding value, and other practical applications in science. By comparing the numerical test application results to those obtained using exact and analytical procedures, we established that our generalized fuzzy numerical method is more efficient, consistent, and stable than existing analytical and numerical methods.