Initial value problems in Type-2 fuzzy environment

Abstract

In real-world problems, uncertainty may not be ignored. Because in the actual scenario, the parameters involved may vary depending on a variety of factors. Accordingly, fuzzy numbers rather than crisp parameters may be used to deal with these uncertainties. It may be noted that the use of Type-2 fuzzy numbers (T2FN) over Type-1 fuzzy numbers (T1FN) is advantageous as the value of the membership function varies from observer to observer. There are several practical problems whose governing equations are initial value problems. The main goal of this investigation is to solve ordinary differential equations with type-2 fuzzy uncertain initial conditions in order to deal with such situations. This article presents an analytical method for solving type-2 fuzzy differential equations using Triangular Perfect Quasi Type-2 Fuzzy Numbers (TPQT2FN). A newly defined triple parametric form of the type-2 fuzzy number is used in this case. Finally, the proposed method is demonstrated using a few numerical examples and application problems.