Micro and macro models of granular computing induced by the indiscernibility relation

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• 作者：Cinzia Bisi^a ; ^{bsicnz@unife.it} ; Giampiero Chiaselotti ; ^b ; ^{giampiero.chiaselotti@unical.it} ; Davide Ciucci^c ; ^{ciucci@disco.unimb.it} ; Tommaso Gentile^c ; ^{tommaso.gentile@unimb.it} ; Federico G. Infusino^b ; ^{f.infusino@mat.unical.it}
• 刊名：Information Sciences
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：388-389
• 期：Complete
• 页码：247-273
• 全文大小：1020 K
• 卷排序：388

文摘

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 II 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 II. 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.