Covering Rough Sets and Formal Topology – A Uniform Approach Through Intensional and Extensional Constructors

Pagliani, Piero

doi:10.1007/978-3-662-53611-7_4

Cited by 10 publications

(6 citation statements)

References 27 publications

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“…In the literature [10,16,19] one can find different measures that can be useful here. Selection of appropriate measure depends on the application.…”

Section: Esgi144mentioning

confidence: 99%

The Seismic Shock Prediction Algorithm based on the Rock Mass behaviour data

Moroń

Staruch

Tomaszewski

et al. 2021

Preprint

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KGHM S.A. exploits copper ore deposits in underground mining facilities. As a result of this operation the seismic activity of the rock mass is induced. One of the symptoms of seismic activity of the rock mass is the occurrence of high energy seismic shocks. These phenomena can lead to severe destructions in mine workings. Resulting from that is a threat to work safety in the area of seismic shock occurrence and risk of damage to mine's property. Particularly strong seismic shocks may also pose a threat to objects on the surface. The level of seismic activity of the rock mass depends on many factors that can be divided into factors related to the environment in which the operation is carried out and factors related to methods of conducting the operation. In the report authors propose an algorithm for prediction of the occurrence of seismic shocks with a given energy.

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“…In the literature [10,16,19] one can find different measures that can be useful here. Selection of appropriate measure depends on the application.…”

Section: Esgi144mentioning

confidence: 99%

The Seismic Shock Prediction Algorithm based on the Rock Mass behaviour data

Moroń

Staruch

Tomaszewski

et al. 2021

Preprint

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“…Such contexts were never intended to be captured through property systems or related basic constructors (see Düntsch and Gediga (2000); Pagliani and Chakraborty (2008); Yao and Yao (2012)). In particular, the examples of Pagliani (2016) are abstract and the possible problems with basic constructors (when viewed from the perspective of approximation properties satisfied) are issues relating to construction -empirical aspects are missed. Definition 2.4.…”

Section: Granular Operator Spaces and Property Systemsmentioning

confidence: 99%

“…• The view that dialectical negation cannot be reduced to classical negation (see Ioan (1998)). Indeed, in rough sets many kinds of negations and partial negations have been used in the literature (see for example, Banerjee and Chakraborty (1996); Cattaneo and Ciucci (2004); Mani (2005Mani ( , 2018a; Pagliani (1998Pagliani ( , 2000, Cattaneo and Ciucci (2018); Cattaneo, Ciucci, and Dubois (2011); Mani (2008Mani ( , 2009aMani ( , 2011; Pagliani (2016); Ślȩzak and Wasilewski (2007) and these lead to many contradictions as in (1) contradictions Pagliani (1998) which are not false but that represent topological boundaries; (2) contradictions Pagliani (2000) which are not false but lie between an absolute and local false; (3) contradictions Pagliani (2016) which lead to at least a paraconsistent and a paracomplete logic. • The view that dialectical negation is glutty negation (example Brandom (2008);…”

Section: Dialectical Negationmentioning

confidence: 99%

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Dialectical Rough Sets, Parthood and Figures of Opposition-I

Mani

2019

Transactions on Rough Sets XXI

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In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for antichain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted -while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalised, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. Her methods become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.

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“…In this work, we consider the approximation operators given by interior and closure operators obtained from the composition of operators in an isotone Galois connection [3,8], which has been built from a slight modification of the operators in [27]. This idea has been already considered in other works, as [14,17,20,21], and has two important advantages: N. Madrid-Partially supported by the Spanish Ministry of Sciences project PGC2018-095869-B-I00, by the Junta de Andalucíca project UMA2018-FEDERJA-001 (European Regional Development Funds) and by the European Cooperation in Science & Technology (COST) Action CA17124. E. Ramírez-Poussa-Partially supported by the 2014-2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in projects TIN2016-76653-P and PID2019-108991GB-I00, and with the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia in project FEDER-UCA18-108612, and by the European Cooperation in Science & Technology (COST) Action CA17124.…”

Section: Introductionmentioning

confidence: 99%

Representative Set of Objects in Rough Sets Based on Galois Connections

Madrid

Ramírez‐Poussa

2020

Lecture Notes in Computer Science

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This paper introduces a novel definition, called representative set of objects of a decision class, in the framework of decision systems based on rough sets. The idea behind such a notion is to consider subsets of objects that characterize the different classes given by a decision system. Besides the formal definition of representative set of objects of a decision class, we present different mathematical properties of such sets and a relationship with classification tasks based on rough sets.

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Covering Rough Sets and Formal Topology – A Uniform Approach Through Intensional and Extensional Constructors

Cited by 10 publications

References 27 publications

The Seismic Shock Prediction Algorithm based on the Rock Mass behaviour data

The Seismic Shock Prediction Algorithm based on the Rock Mass behaviour data

Dialectical Rough Sets, Parthood and Figures of Opposition-I

Representative Set of Objects in Rough Sets Based on Galois Connections

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