| 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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