A generalized vertex method for computing with fuzzy intervals

We introduce a new method for computing functions of fuzzy intervals under various monotonicity assumptions on the concerned functions. Our method makes exact computation for all possibility degrees, without resorting to α-cuts. We formally present the notion of left and right profiles of fuzzy intervals as a tool for fuzzy interval computation. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end point of intervals are changed into left and right profiles. Our approach is illustrated by numerous simple examples all along the paper, and a special section is devoted to the application of these concepts to different known problems.