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Generalized Boolean Algebras and Applications

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Trends in Mathematics and Computational Intelligence

Part of the book series: Studies in Computational Intelligence ((SCI,volume 796))

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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Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia

    O. S. A. Bleblou, B. Šešelja & A. Tepavčević

Authors
  1. O. S. A. Bleblou
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  2. B. Šešelja
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  3. A. Tepavčević
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Corresponding author

Correspondence to A. Tepavčević .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Faculty of Engineering, University of Cádiz, Puerto Real, Cádiz, Spain

    María Eugenia Cornejo

  2. Faculty of Engineering Sciences, Széchenyi István University, Gyõr, Hungary

    László T. Kóczy

  3. Department of Mathematics, Science Faculty, University of Cádiz, Puerto Real, Cádiz, Spain

    Jesús Medina

  4. Faculty of Science and Technology, University of Algarve, Faro, Portugal

    Antonio Eduardo De Barros Ruano

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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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