Approximate Solution of Intuitionistic Fuzzy Volterra Integral Equation of Separable-Type Kernel Using Elzaki Adomian Decomposition Method

An intuitionistic fuzzy number, which incorporates both membership and nonmembership functions at a same time, allows for a more accurate representation of uncertainty. This work presents an approximate solution to the Volterra integral equation that involves both membership and nonmembership degrees of uncertainty named as intuitionistic fuzzy Volterra integral equations. To solve these equations, a hybrid approach is developed by linking the Elzaki transform method, a mathematical method used to simplify differential and integral equations with the Adomian decomposition method, making the Elzaki Adomian decomposition method. The process begins by parametrically modeling the fuzzy-valued function, transforming the original Volterra integral equation into four separate intuitionistic fuzzy Volterra integral equations. The Elzaki Adomian decomposition method generates an approximate result through the infinite series expansion, which enables the finding of an accurate solution for the unknown functions. The efficiency of the result is also shown by both tabular and graphical analyses. The method also provides upper and lower error bounds, which guarantees mathematical consistency. After carefully examining the results for all cases, the report concludes with a brief summary of the study and potential future research directions. This work presents an opportunity to apply the method to more complex fuzzy models and nonlinear kernels.