Lexicographic MV-algebras and lexicographic states

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• 作者：Denisa Diaconescu^a ; ^{ddiaconescu@fmi.unibuc.ro" class="auth_mail} ; Tommaso Flaminio^b ; ^{tommaso.flaminio@uninsubria.it" class="auth_mail} ; Ioana Leu艧tean^a ; ^{ioana@fmi.unibuc.ro" class="auth_mail}
• 关键词：MV-algebras ; Lexicographic product ; 鈩?/em>-Groups ; States
• 刊名：Fuzzy Sets and Systems
• 出版年：1 June, 2014
• 年：2014
• 卷：244
• 期：Complete
• 页码：63-85
• 全文大小：439 K

文摘

In this paper we introduce lexicographic MV-algebras and prove that they are the counterpart of unital abelian lattice-ordered groups defined via lexicographic products. The Di Nola-Lettieri categorical equivalence between perfect MV-algebras and abelian lattice-ordered groups is extended to lexicographic MV-algebras. We also investigate lexicographic states of lexicographic MV-algebras. These are additive and normalized maps from any lexicographic MV-algebra into an ad hoc defined MV-subalgebra of a non-principal ultraproduct of the real unit interval . For lexicographic states we prove a representation theorem which can be regarded as the measure-theoretical analog of the representation theorem for lexicographic MV-algebras. We also provide necessary and sufficient conditions for a lexicographic state to be faithful.