Approximation of Sets Based on Partial Covering

Csajbók, Zoltán Ernő

doi:10.1007/978-3-642-36505-8_9

Cited by 12 publications

(2 citation statements)

References 69 publications

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“…Furthermore, we deal with sequences of partial coverings. These are coverings that do not fully cover the universe, and they are suitable for describing situations in which some information is lost during the refinement process [36]. Refinement sequences of partial coverings are obtained starting from incomplete information tables, that are tables where a set of objects is described by a set of attributes, but some information is lost or not available [63].…”

Section: -Alan Turingmentioning

confidence: 99%

Sequences of Refinements of Rough Sets: Logical and Algebraic Aspects

Boffa

Gerla

2020

Lecture Notes in Computer Science

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In this thesis, a generalization of the classical Rough set theory [81] is developed considering the so-called sequences of orthopairs that we define in [16] as special sequences of rough sets.Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets (defined in [29]). Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property [28], and some classes of finite residuated lattices (more precisely, we consider Nelson algebras [86], Nelson lattices [21], IUML-algebras [69] and Kleene lattice with implication [24]) as sequences of orthopairs. I am deeply thankful to my family: my parents, my sister Rosa, my brother Angelo and his girlfriend Roberta, for their unconditional love and spiritual support in all my life. v vii "I magination is the Discovering Faculty, pre-eminently. It is that which penetrates into the unseen worlds around us, the worlds of Science. It is that which feels & discovers what is, the real which we see not, which exists not for our senses. Those who have learned to walk on the threshold of the unknown worlds, by means of what are commonly termed par excellence the exact sciences, may then with the fair white wings of Imagination hope to soar further into the unexplored amidst which we live.

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Section: -Alan Turingmentioning

confidence: 99%

Sequences of Refinements of Rough Sets: Logical and Algebraic Aspects

Boffa

Gerla

2020

Lecture Notes in Computer Science

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“…As a useful tool to deal with covering data, covering-based rough sets have been attracting more and more research interest [1,5,19,41], and in their returns these lead to many interesting and significant problems. For example, from the theoretical point of view, covering approximation models have been constructed [37,42], covering axiomatic systems have been established [17,39], covering reduction problems have been defined [10,21], and covering decision systems have been proposed [11,29].…”

Section: Introductionmentioning

confidence: 99%

Four matroidal structures of covering and their relationships with rough sets

Wang

Zhu

et al. 2013

International Journal of Approximate Reasoning

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Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids.

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From Vagueness to Rough Sets in Partial Approximation Spaces

Csajbók

Mihálydeák

2014

Rough Sets and Intelligent Systems Paradigms

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Approximation of Sets Based on Partial Covering

Cited by 12 publications

References 69 publications

Sequences of Refinements of Rough Sets: Logical and Algebraic Aspects

Sequences of Refinements of Rough Sets: Logical and Algebraic Aspects

Four matroidal structures of covering and their relationships with rough sets

From Vagueness to Rough Sets in Partial Approximation Spaces

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