Fuzzy-Valued Functions Calculus Through Midpoint Representation

In this paper, we are concerned with the calculus for fuzzy-valued functions of a single real variable when the adopted representation is the midpoint-radius; in particular, we extend the well-known LU-order to the more general case of the so-called γ-order based on the generalized Hukuhara difference and we show that the new index includes the commonly used order relations proposed in literature and it satisfies seven properties which play a crucial role in the justification of the main theorem based on the possibility to represent the efficient region through fuzzy-valued functions deeply related to the same region. Some graphical examples strengthen the innovative approach as a result of a generalization.