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Mathematics
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New Perspectives in Interval Analysis and Fuzzy-Valued Functions
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New Perspectives in Interval Analysis and Fuzzy-Valued Functions

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 2763

Editor

Prof. Laerte Sorini

E-Mail Website
Guest Editor
Department of Economics, Society, Politics, University of Urbino Carlo Bo, 61029 Urbino, Italy
Interests: fuzzy numbers; optimization models; computational mathematics; interval analysis
Special Issues, Collections and Topics in MDPI journals

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

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

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

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Published Papers (3 papers)

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Research

26 pages, 1395 KB  
Article
Polar Orders on Lattices of Real Intervals
by Benedetta Amicizia, Maria Letizia Guerra and Luciano Stefanini
Mathematics 2026, 14(14), 2612; https://doi.org/10.3390/math14142612 - 18 Jul 2026
Viewed by 273
Abstract
Two classes of partial orders are considered and analyzed for the space KC of compact real intervals. The first generalizes the well-known Lower-Upper (LU) partial order, based on the relative position of the intervals’ elements on the real line; the second extends [...] Read more.
Two classes of partial orders are considered and analyzed for the space KC of compact real intervals. The first generalizes the well-known Lower-Upper (LU) partial order, based on the relative position of the intervals’ elements on the real line; the second extends the standard partial order induced by set inclusion. Using mid-point representation, non-empty intervals are associated to points in the ordinary upper half-plane; the two classes of order relations are characterized in terms of two real parameters, appropriately combined to linearly partition the half-plane into four disjoint sliced subsets, which separate comparable from incomparable intervals. We show that pairs of order relations obtained with the same parameters (denote these orders by ⪷ and ⫅, respectively) have an interesting polarity property which allows one to formalize a general setting for analyzing questions of Interval Analysis related to different forms of comparability. In particular, the obtained lattice structures (KC,⪷), (KC,⫅) are detailed and the polarity property is proved for them: if two intervals are incomparable with respect to ⪷ (or ⫅), they are necessarily comparable with respect to ⫅ (or ⪷, respectively). Finally, for any pair of orders (⪷,⫅) with the polarity property, we prove that two total (linear) orders ⪷T and ⫅T are (uniquely) constructed in KC which completely remove incomparable cases. The presentation is supported by several illustrative pictures and some examples. Full article
(This article belongs to the Special Issue New Perspectives in Interval Analysis and Fuzzy-Valued Functions)
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22 pages, 2467 KB  
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 1092
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 KB  
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
Cited by 1 | Viewed by 717
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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