|Authors:||Bleblou, Omalkhear Salem Almabruk
|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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