On Definability and Approximations in Partial Approximation Spaces

Ciucci, Davide; Mihálydeák, Tamás; Csajbók, Zoltán Ernő

doi:10.1007/978-3-319-11740-9_2

Cited by 10 publications

(1 citation statement)

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“…In many practical cases some attribute values of an object are unknown and so these values are missing, therefore the information system is not complete. Recently researchers constructed partial approximation spaces for rough sets based on an incomplete information system [13]. In the current paper we aim to give an approach for rough sets based on " an incomplete information system, especially on objects whose properties of certain attributes can be known or not known; " taking into consideration all possible systems of attribute values (not only those for which there is an object in the information system with a system of attribute values).…”

Section: Introductionmentioning

confidence: 99%

Algebraic structures gained from rough approximation in incomplete information systems

Hannusch¹,

Mihálydeák²

2022

Communication Papers of the 17th Conference on Computer Science and Intelligence Systems

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We give an algebraic approach for defining rough sets on incomplete information systems. The constructed approximation sets are based on objects. Given several attributes, the value of each attribute can be known or unknown for each object. In the current paper, we introduce four different approaches, a real value, a binary, a ternary and a likelihood approach. Furthermore, we define operations on the elements of the introduced approximation sets. For all three cases we can show that the achieved structure is a quasi-Brouwer-Zadeh distributive lattice with the defined operations. We also show that the introduced lower and upper approximations build up commutative monoids with the introduced operations.

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Section: Introductionmentioning

confidence: 99%