Rough sets and Boolean reasoning

Pawlak, Zdzisław; Skowron, Andrzej

doi:10.1016/j.ins.2006.06.007

Cited by 855 publications

(330 citation statements)

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“…Rough Set Theory (RST), first described by [5], is a formal approximation of a crisp set in terms of a pair of sets giving the lower and upper approximation of the original set, respectively. Recently, it has been applied in artificial intelligence [6], knowledge discovery [7], data mining, pattern recognition and machine learning [8]. The Rough Set Theory characterizes an objective approach to a deficiency in data.…”

Section: A Basic Rough Set Approachmentioning

confidence: 99%

http://www.mecs-press.org/ijmecs/ijmecs-v8-n3/v8n3-6.html

Sagar¹,

Tiwari²

2016

IJMECS

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Abstract-The present paper proposes a new approach for the effective weighted association rule mining. The proposed approach utilizes the power of Rough Set Theory for obtaining reduct of the targeted dataset. Additionally, approach takes the benefit for weighted measures and the Genetic Algorithm for the generation of the desired set of rules. Enough analysis of proposed approach has been done and observed that the approach works as per the expectation and will be beneficial in situation when there is a requirement for the consideration of hidden rules(maximizing generated rules) in decisionmaking process.

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Section: A Basic Rough Set Approachmentioning

confidence: 99%

http://www.mecs-press.org/ijmecs/ijmecs-v8-n3/v8n3-6.html

Sagar¹,

Tiwari²

2016

IJMECS

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“…The director gave the examples of evaluation as shown in Table 1. The example contains eight students described by means of four attributes: By the decision attribute, the universe is partitioned into subsets such that U/IND({d}) = {Bad, Medium, Good} = {{x 1 , x 3 , x 5 , x 7 }, {x 2 , x 6 , x 8 }, {x 4 }}. If each attribute is employed to construct an equivalence relation, we then obtain the following multigranulation approximations:…”

Section: Illustrative Examplementioning

confidence: 99%

“…Rough set theory 1,2,3,4 , proposed by Pawlak, has been demonstrated to be useful in pattern recognition, knowledge discovery 5,6 , decision support 7,8 , data mining, feature selection, medical diagnosis and so on. Pawlak's rough set, is constructed on the basis of an indiscernibility relation, which is an equivalence relation and then such model can be used to unravel decision rules from the information system with decision attributes, such system can also be referred to as decision system in many rough set literatures.…”

Section: Introductionmentioning

confidence: 99%

Local and Global Measurements of MGRS Rules

Yang¹,

Zhang²,

Yang³

2012

IJCIS

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Since the multigranulation rough sets (MGRS) can be considered as the compositions of multiindependent Pawlak's rough sets, the multigranulation rough set rules (MGRS rules) are then the compositions of decision rules, which are supported by multi-independent Pawlak's rough sets. To measure MGRS rules, both the local and global views are employed in this paper. In local view, the support, certainty and coverage factors are proposed to measure MGRS rules, which are support by an object; while in global view, these three factors are proposed to measure MGRS rules, which are coexisting in a decision system. The necessary conditions for these factors to achieve maximal and minimal values are also addressed. Some numerical examples are employed to substantiate the conceptual arguments.

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“…Rough set theory [1,2] can effectively deal with the formulation of vague concepts [3][4][5][6][7][8][9][10]. Traditional rough-set-based methods use discretization methods to deal with quantitative attributes.…”

Section: Introductionmentioning

confidence: 99%

Incorporating Grey Total Influence into Tolerance Rough Sets for Classification Problems

Chiu

2018

Applied Sciences

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Tolerance-rough-set-based classifiers (TRSCs) are known to operate effectively on real-valued attributes for classification problems. This involves creating a tolerance relation that is defined by a distance function to estimate proximity between any pair of patterns. To improve the classification performance of the TRSC, distance may not be an appropriate means of estimating similarity. As certain relations hold among the patterns, it is interesting to consider similarity from the perspective of these relations. Thus, this study uses grey relational analysis to identify direct influences by generating a total influence matrix to verify the interdependence among patterns. In particular, to maintain the balance between a direct and a total influence matrix, an aggregated influence matrix is proposed to form the basis for the proposed grey-total-influence-based tolerance rough set (GTI-TRS) for pattern classification. A real-valued genetic algorithm is designed to generate the grey tolerance class of a pattern to yield high classification accuracy. The results of experiments showed that the classification accuracy obtained by the proposed method was comparable to those obtained by other rough-set-based methods.

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Rough sets and Boolean reasoning

Abstract: In this article, we discuss methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis.

Cited by 855 publications

References 84 publications

http://www.mecs-press.org/ijmecs/ijmecs-v8-n3/v8n3-6.html

http://www.mecs-press.org/ijmecs/ijmecs-v8-n3/v8n3-6.html

Local and Global Measurements of MGRS Rules

Incorporating Grey Total Influence into Tolerance Rough Sets for Classification Problems

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