Affiliation:
1. Federal Research Center for Information and Computational Technologies, Novosibirsk, Russia
2. Novosibirsk State University, Novosibirsk, Russia
Abstract
We study systems of relations of the form [Formula: see text], where [Formula: see text] is a vector of binary relations with the components “[Formula: see text]”, “[Formula: see text]”, and “[Formula: see text]”, while the parameters (elements of the matrix [Formula: see text] and right-hand side vector [Formula: see text]) are uncertain and can take values from prescribed intervals. What is considered to be the set of its solutions depends on which logical quantifier is associated with each interval-valued parameter and what is the order of the quantifier prefixes for specific parameters. For solution sets that correspond to the quantifier prefix of a general form, we present equivalent quantifier-free analytical descriptions in the classical interval arithmetic, in Kaucher complete interval arithmetic and in the usual real arithmetic.
Publisher
World Scientific Pub Co Pte Ltd