Titlebook: Algebraic Methods in General Rough Sets; A. Mani,Gianpiero Cattaneo,Ivo Düntsch Book 2018 Springer Nature Switzerland AG 2018 granular rou

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Three Lessons on the Topological and Algebraic Hidden Core of Rough Set Theory,ology and algebraic logic..Many algebraic aspects of Rough Set Theory, are known nowadays. Other are less known, although they are important, for instance because they unveil the “epistemological meaning” of some “unexplained” mathematical features of well-known algebraic structures..We shall wrap e

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Irredundant Coverings, Tolerances, and Related Algebras,scourse. We consider especially tolerances induced by irredundant coverings of the universe .. This is natural in view of Pawlak’s original theory of rough sets defined by equivalence relations: any equivalence . on . is induced by the partition .∕. of . into equivalence classes, and .∕. is a specia

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Algebraic Representation, Dualities and Beyond,d, new proofs have been proposed, open problems are specified and new directions are suggested. Some recent duality results in the literature are also adapted for use in rough contexts. New results are also proved on granular connections between generalized rough and L-fuzzy sets by the present auth

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Rough Objects in Monoidal Closed Categories, manipulation in general can be enriched by extending constructions to work similarly over monoidal closed categories embracing both algebraic as well as order structures. The chapter will also show how the rough information model in this monoidal closed category extension connects with other inform

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S-Approximation Spaces, decider mappings . is considered, i.e. combining S-approximation spaces .. = (.., .., .., ..) for . = 1, …, .. Moreover, the problem of preserving the corresponding properties of the lower and upper approximation operators as well as the three regions of the 3WD in the combination of different S-ap

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2297-0215 other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value..978-3-030-01162-8Series ISSN 2297-0215 Series E-ISSN 2297-024X

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Getting Started with Terraform,s called respectively, from the more general to the stronger one, as Tarski, Kuratowski and Halmos closures. A characterization of this last is given in terms of Brouwer Zadeh lattice structure..Part III provides an interpretation of the pairs of internal-closure operators in terms of pairs of neces

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Neutron emission in heavy ion reactions,f approximations in general (that is, not confined to particular kind of relations). Indeed, these tools lead to pairs of operators fulfilling ., whose combinations, in turn, provide pre-topological and topological operators, which, in some cases, turn into approximation operators..Once one has appr