Developing Constrained Interval Operators for Fuzzy Logic with Interval Values

A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correc...

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Bibliographic Details
Published inAxioms Vol. 12; no. 12; p. 1115
Main Authors Pinheiro, Jocivania, Santiago, Regivan H. N., Bedregal, Benjamin, Bergamaschi, Flaulles
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2023
Subjects
Algebra
Comparative studies
Fuzzy algorithms
fuzzy implications
Fuzzy logic
Fuzzy systems
interval mathematics
interval-valued fuzzy logic
Mathematical analysis
Mathematical research
Operator theory
Operators
Brazil
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Summary:A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨⊆g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12121115