Natural trapezoidal approximations of fuzzy numbers

Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is considered. New operators that fulfill additional requirements for the core and support of the fuzzy number are suggested. These supplementary conditions guarantee the proper interpretation of the solution even for very skew input fuzzy numbers. Moreover, the trapezoidal approximation without expected interval invariance is also examined and the relationship between these two approximations is discussed.