Authors: Bleblou, Omalkhear Salem Almabruk
Šešelja, Branimir
Tepavčević, Andreja 
Title: Generalized boolean algebras and applications
Journal: Trends in Mathematics and Computational Intelligence
Series/Report no.: Studies in Computational Intelligence
Volume: 796
First page: 139
Last page: 145
Issue Date: 1-Jan-2019
ISBN: 978-3-030-00484-2
ISSN: 1860-949X
DOI: 10.1007/978-3-030-00485-9_16
Abstract: 
A new notion of a lattice valued Boolean algebra is introduced. It is based on an algebra with two binary, a unary and two nullary operations, which is not a crisp Boolean algebra in general. The classical equality is replaced by a lattice valued equivalence so that the Boolean algebra identities are correspondingly satisfied. Main properties of the new introduced notion are proved, and a connection with the notion of a generalized lattice valued lattice is provided. As an application, the paper contains basic structures for developing generalized Boolean functions.
Publisher: Springer Link
Project: Development of methods of computation and information processing: theory and applications 

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