Axiomatic approaches to rough approximation operators via ideal on a complete completely distributive lattice

Gao, Ninghua; Li, Qingguo; Han, Heyou; Li, Zhaowen

doi:10.1007/s00500-017-2495-9

Cited by 7 publications

(2 citation statements)

References 39 publications

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“…To broaden the application ability of Pawlak's rough set theory in practical problems [11,15], it has been extended by generalized relations [16,17], various coverings [18][19][20] and several types of neighborhoods [4,21]. Moreover, it has been combined with several theories, including lattice theory [22], matrix theory [23], fuzzy set theory [24] and others [25,26].…”

Section: Introductionmentioning

confidence: 99%

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

Wang

Zhang

2022

Axioms

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Rough set theory provides a useful tool for data analysis, data mining and decision making. For multi-criteria decision making (MCDM), rough sets are used to obtain decision rules by reducing attributes and objects. However, different reduction methods correspond to different rules, which will influence the decision result. To solve this problem, we propose a novel method for MCDM based on rough sets and a fuzzy measure in this paper. Firstly, a type of non-additive measure of attributes is presented by the importance degree in rough sets, which is a fuzzy measure and called an attribute measure. Secondly, for a decision information system, the notion of the matching degree between two objects is presented under an attribute. Thirdly, based on the notions of the attribute measure and matching degree, a Choquet integral is constructed. Moreover, a novel MCDM method is presented by the Choquet integral. Finally, the presented method is compared with other methods through a numerical example, which is used to illustrate the feasibility and effectiveness of our method.

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Section: Introductionmentioning

confidence: 99%

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

Wang

Zhang

2022

Axioms

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“…Hence, Pawlak's rough sets have been extended by relations [14,15], coverings [16][17][18] and neighborhoods [6,19]. They have been combined with other theories including topology [20], lattice theory [21,22], graph theory [23,24] and fuzzy set theory [25,26].…”

Section: Introductionmentioning

confidence: 99%

Four Operators of Rough Sets Generalized to Matroids and a Matroidal Method for Attribute Reduction

Wang

Zhang

2018

Symmetry

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Rough sets provide a useful tool for data preprocessing during data mining. However, many algorithms related to some problems in rough sets, such as attribute reduction, are greedy ones. Matroids propose a good platform for greedy algorithms. Therefore, it is important to study the combination between rough sets and matroids. In this paper, we investigate rough sets and matroids through their operators, and provide a matroidal method for attribute reduction in information systems. Firstly, we generalize four operators of rough sets to four operators of matroids through the interior, closure, exterior and boundary axioms, respectively. Thus, there are four matroids induced by these four operators of rough sets. Then, we find that these four matroids are the same one, which implies the relationship about operators between rough sets and matroids. Secondly, a relationship about operations between matroids and rough sets is presented according to the induced matroid. Finally, the girth function of matroids is used to compute attribute reduction in information systems.

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Axiomatization on generalized neighborhood system-based rough sets

Zhao

2017

Soft Comput

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Axiomatic approaches to rough approximation operators via ideal on a complete completely distributive lattice

Cited by 7 publications

References 39 publications

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

A Novel Multi-Criteria Decision-Making Method Based on Rough Sets and Fuzzy Measures

Four Operators of Rough Sets Generalized to Matroids and a Matroidal Method for Attribute Reduction

Axiomatization on generalized neighborhood system-based rough sets

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