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.
Research supported by Ministry of Education, Science and Technological Development, Republic of Serbia, Grant No. 174013.
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Bleblou, O.S.A., Šešelja, B., Tepavčević, A. (2019). Generalized Boolean Algebras and Applications. In: Cornejo, M., Kóczy, L., Medina, J., De Barros Ruano, A. (eds) Trends in Mathematics and Computational Intelligence. Studies in Computational Intelligence, vol 796. Springer, Cham. https://doi.org/10.1007/978-3-030-00485-9_16
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DOI: https://doi.org/10.1007/978-3-030-00485-9_16
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