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Ideals and Bosbach States on Residuated Lattices

Author

Listed:
  • Francis Woumfo

    (Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon)

  • Blaise B. Koguep Njionou

    (Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon)

  • Etienne R. Temgoua Alomo

    (Department of Mathematics, École Normale Supérieure de Yaoundé, University of Yaoundé 1, P.O. Box 47, Yaoundé, Cameroon)

  • Celestin Lele

    (Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon)

Abstract

In random experiments, the fact that the sets of events has a structure of a Boolean algebra, i.e. it follows the rules of classical logic, is the main hypothesis of classical probability theory. Bosbach states have been introduced on commutative and non-commutative algebras of fuzzy logics as a way of probabilistically evaluating the formulas. In this paper, we focus on the relationship between some properties of ideals and Bosbach states in the framework of commutative residuated lattices. In particular, we introduce the concept of co-kernel of a Bosbach state which is an ideal and we establish the relationship between the notion of co-kernel and the kernel. Moreover, we define and characterize maximal ideals and maximal MV-ideals in residuated lattices.

Suggested Citation

  • Francis Woumfo & Blaise B. Koguep Njionou & Etienne R. Temgoua Alomo & Celestin Lele, 2021. "Ideals and Bosbach States on Residuated Lattices," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 281-302, July.
    • Handle: RePEc:wsi:nmncxx:v:17:y:2021:i:02:n:s1793005721500150
    DOI: 10.1142/S1793005721500150
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