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.
CITATION STYLE
Bleblou, O. S. A., Šešelja, B., & Tepavčević, A. (2019). Generalized boolean algebras and applications. In Studies in Computational Intelligence (Vol. 796, pp. 139–145). Springer Verlag. https://doi.org/10.1007/978-3-030-00485-9_16
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