Ideals and Bosbach States on Residuated Lattices

Francis Woumfo (), Blaise B. Koguep Njionou, Etienne R. Temgoua Alomo () and Celestin Lele ()
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Francis Woumfo: Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
Blaise B. Koguep Njionou: Department of Mathematics and Computer Science, Faculty of 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, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon

New Mathematics and Natural Computation (NMNC), 2020, vol. 16, issue 03, 551-571

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.

Keywords: Bosbach state; ideal; maximal ideal; residuated lattice; state-morphism (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S1793005720500337

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