In this paper we show that the classes of MV-algebras and MV-semirings\ud
are isomorphic as categories. This approach allows one to keep the inspiration and\ud
use new tools from semiring theory to analyze the class of MV-algebras. We present\ud
a representation ofMV-semirings byMV-semirings of continuous sections in a sheaf\ud
of commutative semirings whose stalks are localizations of MV-semirings over prime\ud
ideals. Using the categorical equivalence, we obtain a representation of MV-algebras
In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein, we develop an approach to sheaf
representations of MV-algebras which combines two techniques for the representation of MV-algebras devised
by Filipoiu and Georgescu and by Dubuc and Poveda .
Following Davey approach, we use a
subdirect representation of MV-algebras that is based on local MV-algebras. This allowed us to obtain:
(a) a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on the spectruum of its prime ideals;
(b) a representation of MV-algebras, having the space of minimal prime ideals compact, as MV-algebra of all global sections of a Hausdorff sheaf of MV-chains on the space of minimal prime ideals, which is a Stone
space;
(c) an adjunction between the category of all MV-algebras and the category of MV-algebraic spaces, where an MV-algebraic space is a pair (X; F), where X is a compact topological space and F is a sheaf of MValgebras with stalks that are local
Formal Concept Analysis (FCA) and its fuzzy extension have been widely used to arrange data into a lattice that is an effective data structure useful to address several aims, such as: data mining, ontology learning and merging, and so on. In literature it is possible to distinguish two main approaches to address fuzzy FCA implementation: The one-sided threshold and the fuzzy closure one. This work focuses on a specific definition of one-sided threshold algorithm and fuzzy closure one. Specifically, it shows that these methods can be unified, since the onesided threshold approach can be seen as a specialization of the fuzzy closure. The lattice generated using onesided fuzzy threshold approach is a substructure of the lattice generated using the fuzzy closure approach. In addition, an experimentation has been performed on both implementations of the fuzzy FCA, one-sided threshold and fuzzy closure. In particular, the results are compared in terms of running time and number of extracted fuzzy concepts by varying the t-norm function Łukasiewicz, Gödel, and Product
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