Journal
INFORMATION SCIENCES
Volume 388, Issue -, Pages 247-273Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2017.01.023
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In rough set theory (RST), and more generally in granular computing on information tables (GRC-IT), a central tool is the Pawlak's indiscernibility relation between objects of a universe set with respect to a fixed attribute subset. Let us observe that Pawlak's relation induces in a natural way an equivalence relation on the attribute power set that identifies two attribute subsets yielding the same indiscernibility partition. We call indistinguishability relation of a given information table I the equivalence relation that can be considered as a kind of global indiscernibility. In this paper we investigate the mathematical foundations of indistinguishability relation through the introduction of two new structures that are, respectively, a complete lattice and an abstract simplicial complex. We show that these structures can be studied at both a micro granular and a macro granular level and that are naturally related to the core and the reducts of I. We first discuss the role of these structures in GrC-IT by providing some interpretations, then we prove several mathematical results concerning the fundamental properties of such structures. (C) 2017 Elsevier Inc. All rights reserved.
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