A General Set Theoretic Approximation Framework

Csajbók, Zoltán Ernő; Mihálydeák, Tamás

doi:10.1007/978-3-642-31709-5_61

Cited by 15 publications

(5 citation statements)

References 23 publications

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“…Let B ⊆ 2 U be a nonempty family of nonempty subsets of U . It is a natural assumption that D B is obtained (derived) form B by some sort of set type transformations (for the most important cases, see [5]). In order to build a generalized Pawlakian partial approximation framework, we define D B with the following definition:…”

Section: Fundamental Notions Of Partial Approximation Of Setsmentioning

confidence: 99%

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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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Section: Fundamental Notions Of Partial Approximation Of Setsmentioning

confidence: 99%

“…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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“…D IFFERENT systems of rough set theory were created in the last forty years: Pawlak's original theory of rough sets (see in e.g. [1]- [3]), covering systems relying on tolerance relations [4], general covering systems [5], [6], decisiontheoretic rough set theory [7], general partial approximation spaces [8], similarity based approximation spaces [9]. There is a very important common property: " all systems rely on given background knowledge represented by the system of base sets; " one cannot say more about an arbitrary set (representing a 'new' property) or about its members than the lower and upper approximations of the set make possible.…”

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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“…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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A General Set Theoretic Approximation Framework

Cited by 15 publications

References 23 publications

An Adequate Representation of Medical Data Based on Partial Set Approximation

An Adequate Representation of Medical Data Based on Partial Set Approximation

Algebraic structures gained from rough approximation in incomplete information systems

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

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