Midpoint Representation of Fuzzy-Valued Functions and Applications

We present new results in the calculus for fuzzy-valued functions of a single real variable. We adopt extensively the midpoint-radius representation of intervals in the real half-plane and show its usefulness in fuzzy calculus. Concepts related to convergence and limits, continuity, level-wise gH-differentiability have interesting and useful midpoint expressions. Partial orders for fuzzy numbers and extremal points (min and max) for fuzzy functions associated to a partial order are discussed and analysed in detail. Graphical examples and pictures accompany the presentation.