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    Interval-valued algebras and fuzzy logics

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    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

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    Let O\mathcal{O} be a complete discrete valuation ring, K\mathcal{K} its quotient field, and let AA be the symmetric Kronecker algebra over O\mathcal{O}. We consider the full subcategory of the category of AA-lattices whose objects are AA-lattices MM such that M⊗OKM\otimes_{\mathcal{O}}\mathcal{K} is projective A⊗OKA\otimes_{\mathcal{O}}\mathcal{K}-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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