Extremal states on bounded residuated l-monoids with general comparability

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dc.contributor.author Rachůnek, Jiří
dc.contributor.author Šalounová, Dana
dc.date.accessioned 2011-03-16T09:52:27Z
dc.date.available 2011-03-16T09:52:27Z
dc.date.issued 2011
dc.identifier.citation Soft computing. 2011, vol. 15, no. 1, p. 199-203. en
dc.identifier.issn 1432-7643
dc.identifier.issn 1433-7479
dc.identifier.uri http://hdl.handle.net/10084/84364
dc.description.abstract Bounded residuated lattice ordered monoids (RlR-monoids) are a common generalization of pseudo-BLBL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. We investigate bounded RlR-monoids satisfying the general comparability condition in connection with their states (analogues of probability measures). It is shown that if an extremal state on Boolean elements fulfils a simple condition, then it can be uniquely extended to an extremal state on the RlR-monoid, and that if every extremal state satisfies this condition, then the RlR-monoid is a pseudo-BLBL-algebra. en
dc.language.iso en en
dc.relation.ispartofseries Soft computing en
dc.relation.uri http://dx.doi.org/10.1007/s00500-010-0545-7 en
dc.subject bounded residuated l-monoid en
dc.subject pseudo-BLBL-algebra en
dc.subject heyting algebra en
dc.subject pseudo-MV-algebra en
dc.subject filter en
dc.subject normal filter en
dc.subject general comparability property en
dc.subject Boolean element en
dc.subject state en
dc.subject extremal state en
dc.title Extremal states on bounded residuated l-monoids with general comparability en
dc.type Article en
dc.identifier.location Není ve fondu ÚK en
dc.identifier.doi 10.1007/s00500-010-0545-7
dc.identifier.wos 000286197800020

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