New Perspectives in Interval Analysis and Fuzzy-Valued Functions

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 31 January 2026 | Viewed by 471

Special Issue Editor


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Guest Editor
Department of Economics, Society, Politics, University of Urbino Carlo Bo, 61029 Urbino, Italy
Interests: fuzzy numbers; optimization models; computational mathematics; interval analysis
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Special Issue Information

Dear Colleagues,

The purpose of the present Special Issue is to collect contributions reflecting new perspectives in mathematical models for uncertainty, including interval analysis, fuzzy numbers, fuzzy-valued functions, and all possible implications in optimization and statistics applied in economics, management, and finance.

A potential list of topics includes the following:

  • Fuzzy calculus
  • Interval analysis
  • Smoothing techniques
  • Time series analysis
  • Forecasting techniques
  • Risk management

Prof. Laerte Sorini
Guest Editor

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Keywords

  • interval analysis
  • fuzzy numbers
  • fuzzy-valued functions
  • ordering of intervals
  • ordering of fuzzy numbers

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Published Papers (2 papers)

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Research

22 pages, 2467 KiB  
Article
Fuzzy-Valued Functions Calculus Through Midpoint Representation
by Laerte Sorini, Maria Letizia Guerra, Benedetta Amicizia, Mina Shahidi and Luciano Stefanini
Mathematics 2025, 13(16), 2543; https://doi.org/10.3390/math13162543 - 8 Aug 2025
Viewed by 128
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue New Perspectives in Interval Analysis and Fuzzy-Valued Functions)
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27 pages, 338 KiB  
Article
Bernstein Approximations for Fuzzy-Valued Functions
by Hsien-Chung Wu
Mathematics 2025, 13(15), 2424; https://doi.org/10.3390/math13152424 - 28 Jul 2025
Viewed by 175
Abstract
Studying the Bernstein approximations for fuzzy functions is a new attempt. With the help of considering the support functions of fuzzy sets in which the weak* topology for the normed dual space is involved, we are able to approximate continuous fuzzy functions by [...] Read more.
Studying the Bernstein approximations for fuzzy functions is a new attempt. With the help of considering the support functions of fuzzy sets in which the weak* topology for the normed dual space is involved, we are able to approximate continuous fuzzy functions by considering the Bernstein polynomials for fuzzy functions. We first study the Bernstein approximations for the support functions of fuzzy sets. Using the concept of isometry between the metric spaces of fuzzy sets and the normed spaces of support functions of fuzzy sets, the Bernstein approximations for the support functions of fuzzy sets can naturally lead to the Bernstein approximations for continuous fuzzy functions. Full article
(This article belongs to the Special Issue New Perspectives in Interval Analysis and Fuzzy-Valued Functions)
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