Type-2 fuzzy numbers and operations by F-transform

The fuzzy transform setting (F-transform) is proposed as a tool for representation and approximation of type-2 fuzzy numbers; a type-2 fuzzy number is represented as a particular fuzzy-valued function and it is expressed in terms of a two-dimensional F-transform where the first dimension represents the universe domain and the second dimension represents the membership domain. Operators on two dimensional F-transform are then proposed to approximate arithmetic operations with type-2 fuzzy numbers.