On the Extension of Rough Sets under Incomplete Information

Stefanowski, Jerzy; Tsoukiàs, Alexis

doi:10.1007/978-3-540-48061-7_11

Cited by 223 publications

(134 citation statements)

References 5 publications

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“…Problems arise when information systems contain imperfect data, which occasionally happens in the real world. Controversial rough set research mostly considers that imperfect data in information systems comes from missing values [4,5,6,8,11,12,23,24,25,26]. An information system with missing values is called incomplete information system [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…In studies of rough sets in incomplete information systems, probabilistic solutions have been introduced based on the possibility of "missing value" [4,17,18,19,23,24]. Among them, some approaches [4,23] suppose a priori assumption that there exists a uniform probability distribution on every attribute domain and compute valued tolerance (or similarity) classes based on the joint probability distribution.…”

Section: Introductionmentioning

confidence: 99%

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Rough Sets and Rule Induction in Imperfect Information Systems

Nguyen¹,

Yamada²,

Unehara³

2014

IJCA

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The original rough set theory deals with precise and complete data, while real applications frequently contain imperfect information. A typical imperfect data studied in rough set research is the missing values. Though there are many ideas proposed to solve the issue in the literature, the paper adopts a probabilistic approach, because it can incorporate other types of imperfect data including imprecise and uncertain values in a single approach. The paper first discusses probabilities of attribute values assuming different type of attributes in real applications, and proposes a generalized method of probability of matching. This probability is then used to define valued tolerance/similarity relations and to develop new rough set models based on the valued tolerance/similarity relations. An algorithm for deriving decision rules based on the rough set models is also studied and proposed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rough Sets and Rule Induction in Imperfect Information Systems

Nguyen¹,

Yamada²,

Unehara³

2014

IJCA

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“…Recently rough set theory was extended to handle incomplete data sets (with missing attribute values) [1][2][3][4][5][6][7][8][9][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…Incomplete decision tables in which all attribute values are lost, from the viewpoint of rough set theory, were studied for the first time in [6], where two algorithms for rule induction, modified to handle lost attribute values, were presented. This approach was studied later, e.g., in [18,19], where the indiscernibility relation was generalized to describe such incomplete data. Furthermore, an approach to incomplete data based on relative frequencies was presented in [19].…”

Section: Introductionmentioning

confidence: 99%

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Local and Global Approximations for Incomplete Data

Grzymała-Busse

Rząsa

2006

Lecture Notes in Computer Science

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Abstract. For completely specified decision tables, where lower and upper approximations are unique, the lower approximation is the largest definable set contained in the approximated set X and the upper approximation of X is the smallest definable set containing X. For incomplete decision tables the existing definitions of upper approximations provide sets that, in general, are not minimal definable sets. The same is true for approximations based on relations that are generalizations of the equivalence relation. In this paper we introduce two definitions of approximations, local and global, such that the corresponding upper approximations are minimal. Local approximations are more precise than global approximations. Global lower approximations may be determined by a polynomial algorithm. However, algorithms to find both local approximations and global upper approximations are NP-hard.

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Tolerance Dominance Relation in Incomplete Ordered Decision Systems

Guan

Huang

Han

2017

Int. J. Intell. Syst.

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To deal with inconsistencies coming from consideration of criteria, that is, attributes with preference-ordered domains (scales), such as product quality, market share, and debt ratio, the dominance-based rough set approach has been proposed. However, it is not much useful for analyzing incomplete information. In this paper, we attempt to present research focusing on incomplete ordered decision systems where all attributes are considered as criteria and some objects' criterion values are unknown. Under the assumption that all unknown values are the "do not care" semantics, the concept of tolerance dominance relation is introduced. Then, the rough approximations induced by it are obtained. And their properties are investigated. Especially, the important properties of rough approximations, such as rough inclusion, complementarity, identity, and monotonicity, are preserved well-known in the presented methodology. Moreover, an example is employed to illustrate these results. We expand the potential applications of dominance-based rough set approach. C 2017 Wiley Periodicals, Inc.

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On the Extension of Rough Sets under Incomplete Information

Cited by 223 publications

References 5 publications

Rough Sets and Rule Induction in Imperfect Information Systems

Rough Sets and Rule Induction in Imperfect Information Systems

Local and Global Approximations for Incomplete Data

Tolerance Dominance Relation in Incomplete Ordered Decision Systems

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