Fuzzy-Valued Functions Calculus Through Midpoint Representation

Laerte Sorini, Maria Letizia Guerra (), Benedetta Amicizia, Mina Shahidi and Luciano Stefanini
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Laerte Sorini: Department of Economics, Society and Politics, University of Urbino, 61029 Urbino, Italy
Maria Letizia Guerra: Department of Statistical Sciences “Paolo Fortunati”, University of Bologna, 40126 Bologna, Italy
Benedetta Amicizia: Department of Statistical Sciences “Paolo Fortunati”, University of Bologna, 40126 Bologna, Italy
Mina Shahidi: Department of Mathematics, Statistic and Scientific Computing, Unicamp, Campinas 13083-859, Brazil
Luciano Stefanini: Department of Economics, Society and Politics, University of Urbino, 61029 Urbino, Italy

Mathematics, 2025, vol. 13, issue 16, 1-22

Abstract: 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.

Keywords: fuzzy-valued function; midpoint representation; convexity of fuzzy function; extrema of fuzzy function; gH-differentiability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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