On the existence of states on MTL-algebras

Authors:
Lianzhen Liu
Affiliations:
School of Science, Jiangnan University, 214122 Wuxi, China
Venue:
Information Sciences: an International Journal
Year:
2013

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Abstract

The aim of this paper is to investigate the existence of Bosbach states and Riecan states on MTL-algebras. We prove that an MTL-algebra L has Bosbach states if and only if L has an MV-filter. We also establish that L has a state-morphism if and only if L has a maximal MV-filter. Furthermore, we obtain the necessary and sufficient condition for an MTL-chain having Riecan states.