| 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 <i>constrained interval operators</i>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>g</mi><mo>¨</mo></mover></semantics></math></inline-formula> and the best interval representation: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>g</mi><mo stretchy="false">^</mo></mover></semantics></math></inline-formula>. Although <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>g</mi><mo>¨</mo></mover><mo>⊆</mo><mover accent="true"><mi>g</mi><mo stretchy="false">^</mo></mover></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>g</mi><mo>¨</mo></mover></semantics></math></inline-formula> 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.
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