Partial approximative set theory: A generalization of the rough set theory

Csajbók, Zoltán Ernő

doi:10.1109/socpar.2010.5686424

Cited by 9 publications

(3 citation statements)

References 48 publications

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“…Based on this membership function we can define the lower approximation (set of elements are surely inside) and the upper approximation (set of elements are possibly inside) of a set. The pair of lower and upper approximation defines a rough set [4,5].…”

Section: Rough Clusteringmentioning

confidence: 99%

Email labelling by rough clustering

Aszalós

Mihálydeák

2015

Proceedings of the 9th International Conference on Applied Informatics, Volume 1

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Previously, there were little possibilities to sort mails and later emails: we could only arrange them into folders. One mail or email could be put into exactly one folder, based on sender, subject or priority. Later in Gmail the labelling of emails was introduced: virtual folders were generated by the multiple labels that could be assigned to one email. This kind of labeling was taken by other mailers, photo and music organizer softwares, too.It is a pleasure to use a well organized collection, but usually paintaking to set up the its labelling. We simplify these kind of tasks by using our experience in rough set theory and clustering. The clustering is a well-known part of the data mining, where the elements are grouped by their similarity. The similarity is an inexact concept in real life, e. g. we easily mix up two Japanese persons, however a Chinese man easily differentiates them. We suggest that the rough clustering could help to combine data based on similarities from different sources, because it has some error-correcting property.In this article we present a method to label emails and its mathematical background.

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Section: Rough Clusteringmentioning

confidence: 99%

Email labelling by rough clustering

Aszalós

Mihálydeák

2015

Proceedings of the 9th International Conference on Applied Informatics, Volume 1

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“…Thus, not only the pairwise disjoint property but also the covering of the universe are given up. This basically new approach is referred to as partial approximation of sets [5,6,10].…”

Section: Introductionmentioning

confidence: 99%

An Adequate Representation of Medical Data Based on Partial Set Approximation

Csajbók

Mihálydeák

Ködmön

2013

Computer Information Systems and Industrial Management

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Abstract. Computer aided medical diagnosis and treatment require an adequate representation of uncertain or imperfect medical data. There are many approaches dealing with such type of data. Pawlak proposed a new method called rough set theory. In this paper, beyond classical and recent methods, the authors propose a basically new approach. It relies on a generalization of rough set theory, namely, the partial covering of the universe of objects. It adequately reflects the partial nature of real-life problems. This new approach called the partial approximation of sets is presented as well as its medical informatics application is demonstrated.

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“…Pawlak's answers are 'yes' for both questions (so in his system each object has exactly one property from the given family), whereas covering rough set systems say 'yes' for the first question and no for the second one. A generalization of the theory of rough sets (see in [15], [16]) does not commit itself to answer 'yes' for any mentioned question: It does not suppose either the representations of properties belonging to mentioned family cover the discourse universe or the representations form a pairwise disjoint family of sets. From the approximation point of view the generalization can be considered as a system of partial approximation of sets.…”

Section: Introductionmentioning

confidence: 99%

Partial first-order logic relying on optimistic, pessimistic and average partial membership functions

Mihálydeák¹

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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One of the common features of decision-theoretic rough set models is that they rely on total background (available) knowledge in the sense that the knowledge covers the discourse universe. In the proposed framework the author gives up this requirement and allows that available knowledge about the discourse universe may be partial. It is shown by introducing optimistic, average and pessimistic partial membership functions that a decision-theoretic rough set model can be based on a very general version of partial approximation spaces. Different membership functions may serve as a base of the semantics of a partial first-order logic. The proposed logical system gives an exact possibility to introduce different semantic notions of logical consequence relations which can be used in order to make clear the consequences of our decisions.

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Partial approximative set theory: A generalization of the rough set theory

Cited by 9 publications

References 48 publications

Email labelling by rough clustering

Email labelling by rough clustering

An Adequate Representation of Medical Data Based on Partial Set Approximation

Partial first-order logic relying on optimistic, pessimistic and average partial membership functions

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