A probabilistic approach to the arithmetics of fuzzy numbers
An alternative look on fuzzy numbers based on two random variables and their summation and multiplication is introduced. This approach to summation covers the standard Zadeh's extension principle and triangular norm-based approach, however, it is more general. We illustrate it on some examples. Moreover, copula-based summation preserving the class of triangular (trapezoidal) fuzzy numbers is discussed.
fuzzy number copula fuzzy arithmetics triangle function triangular norm