Ideals and Bosbach States on Residuated Lattices

Author:

Woumfo Francis1,Koguep Njionou Blaise B.1,Temgoua Alomo Etienne R.2,Lele Celestin1

Affiliation:

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

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

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Theory and Mathematics,Computational Mathematics,Computer Science Applications,Human-Computer Interaction

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