کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
394839 665908 2009 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The pseudo-linear semantics of interval-valued fuzzy logics
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
پیش نمایش صفحه اول مقاله
The pseudo-linear semantics of interval-valued fuzzy logics
چکیده انگلیسی

Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called interval-valued residuated lattices (IVRLs). Triangle algebras have been used to construct triangle logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRLs.In this paper, we prove that the so-called pseudo-prelinear triangle algebras are subdirect products of pseudo-linear triangle algebras. This can be compared with MTL-algebras (prelinear residuated lattices) being subdirect products of linear residuated lattices.As a consequence, we are able to prove the pseudo-chain completeness of pseudo-linear triangle logic (PTL), an axiomatic extension of TL introduced in this paper. This kind of completeness is the analogue of the chain completeness of monoidal T-norm based logic (MTL).This result also provides a better insight in the structure of triangle algebras; it enables us, amongst others, to prove properties of pseudo-prelinear triangle algebras more easily. It is known that there is a one-to-one correspondence between triangle algebras and couples (L,α)(L,α), in which LL is a residuated lattice and αα an element in that residuated lattice. We give a schematic overview of some properties of pseudo-prelinear triangle algebras (and a number of others that can be imposed on a triangle algebra), and the according necessary and sufficient conditions on LL and αα.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Sciences - Volume 179, Issue 6, 1 March 2009, Pages 717–728
نویسندگان
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