Affiliation:
1. Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, Cubo 30B, 87036 Arcavacata di Rende (CS), Italy
Abstract
In this paper, we investigate Pawlak’s rough set theory from a categorical point of view, by introducing specific categories of lower and upper operators in order to analyze in a generalized setting the usual approximant operators of rough set theory. We determine several embeddings and isomorphisms between these categories and suitable categories of finitary matroids, set partitions and equivalence relations, some of which already investigated in recent papers. Using the aforementioned isomorphic categories, we exhibit several categorical properties of lower and upper operators. In addition, as one of the main applications of rough set theory concerns Pawlak’s information systems and Granular Computing, in the last part of the paper we translate in categorical terms the occurrence of rough sets in Granular Computing and, to this end, we need to work with a category [Formula: see text] of pairings (i.e. generalizations of Pawlak’s information systems) and pairing homomorphisms. More specifically, we exhibit several categorical properties of pairings, such as balancedness, completeness, exactness, [Formula: see text]-[Formula: see text]-factorizability and prove that [Formula: see text] is Heyting but, in general, it does not admit coproducts.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
1 articles.
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