24,369 research outputs found
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
On periodic stable Auslander-Reiten components containing Heller lattices over the symmetric Kronecker algebra
Let be a complete discrete valuation ring, its
quotient field, and let be the symmetric Kronecker algebra over
. We consider the full subcategory of the category of -lattices
whose objects are -lattices such that
is projective
-modules. In this paper, we study Heller
lattices of indecomposable periodic modules over the symmetric Kronecker
algebra. As a main result, we determine the shapes of stable Auslander-Reiten
components containing Heller lattices of indecomposable periodic modules over
the symmetric Kronecker algebra.Comment: 35 pages (v1), correct several errors (v2
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