کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
390287 661238 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
States on semi-divisible generalized residuated lattices reduce to states on MV-algebras
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
States on semi-divisible generalized residuated lattices reduce to states on MV-algebras
چکیده انگلیسی

A semi-divisible residuated lattice is a residuated lattice L satisfying an additional condition weaker than that of divisibility. Such structures are related to mathematical fuzzy logic as well as to extended probability theory by the fact that the subset of complemented elements induces an MV-algebra. We define generalized residuated lattices by omitting commutativity of the corresponding monoidal operation and study semi-divisibility in such structures. We show that, given a good generalized residuated lattice L, the set of complemented elements of L, denoted by MV(L), forms a pseudo-MV-algebra if and only if L is semi-divisible. Maximal filters on a semi-divisible generalized residuated lattice L are in one-to-one correspondence with maximal filters on MV(L). We study states on semi-divisible generalized residuated lattices. Riečan states on a semi-divisible generalized residuated lattice L are determined by Riečan states on MV(L). The same holds true for Bosbach states whenever L is a good divisible generalized residuated lattice. Extremal Riečan states on a semi-divisible generalized residuated lattice L are in one-to-one correspondence with maximal and semi-normal filters on L.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Fuzzy Sets and Systems - Volume 159, Issue 22, 16 November 2008, Pages 3051-3064