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Fuzzy-Valued Functions Calculus Through Midpoint Representation

Author

Listed:
  • 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)

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.

Suggested Citation

  • Laerte Sorini & Maria Letizia Guerra & Benedetta Amicizia & Mina Shahidi & Luciano Stefanini, 2025. "Fuzzy-Valued Functions Calculus Through Midpoint Representation," Mathematics, MDPI, vol. 13(16), pages 1-22, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2543-:d:1720601
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