کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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389761 | 661174 | 2014 | 23 صفحه PDF | دانلود رایگان |

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 [⁎0,1] of the real unit interval [0,1][0,1]. 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.
Journal: Fuzzy Sets and Systems - Volume 244, 1 June 2014, Pages 63–85