A unified framework for characterizing rough sets with evidence theory in various approximation spaces

Tan, Anhui; Wu, Wei-Zhi; Tao, Yuzhi

doi:10.1016/j.ins.2018.04.073

Cited by 22 publications

(8 citation statements)

References 43 publications

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“…In [26,27], a fault diagnosis method of induction motor based on sparse noise reduction self-encoder was proposed, and it reduced the risk of network overfitting in small samples. e theory evidence is an uncertainty theory [28][29][30][31], the major characteristics of which are measuring and addressing various kinds of uncertain information and using the synthetic principle to obtain multi-information entropy. In this way, the theory evidence can process multi-information and conflicting information better and thus has been widely used in areas such as information fusion and uncertain reasoning.…”

Section: Introductionmentioning

confidence: 99%

Composite Fault Diagnosis for Rotating Machinery of Large Units Based on Evidence Theory and Multi‐Information Fusion

Xiao

Zhang

et al. 2019

Shock and Vibration

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Due to the complexity of the structure and process of large-scale petrochemical equipment, different fault characteristics are mixed and present multiple couplings and ambiguities, leading to the difficulty in identifying composite faults in rotating machinery. This paper proposes a composite faults diagnosis method for rotating machinery of the large unit based on evidence theory and multi-information fusion. The evidence theory and multi-information fusion method mainly deal with multisource information and conflict information, synthesize multiple uncertain information, and obtain synthetic information from multiple data sources. To detect faults in rotating machinery, the dimensionless index ranges of composite faults are first used to form a feature set as the reference. Then, a two-sample distribution test is applied to compare the known fault samples with the tested fault samples, and the maximum statistical distance is used. Finally, the multiple maximum statistical distances are fused by evidence theory and identifying fault types based on the fusion result. The proposed method was applied to the large petrochemical unit simulation experiment system, the results of which showed that our proposed method could accurately identify composite faults and provide maintenance guidance for composite fault diagnosis.

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Section: Introductionmentioning

confidence: 99%

Composite Fault Diagnosis for Rotating Machinery of Large Units Based on Evidence Theory and Multi‐Information Fusion

Xiao

Zhang

et al. 2019

Shock and Vibration

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“…There is such a strong link between rough set theory and the DST that it is difficult to find a more general theory among them [27]. Some arguments in favor of the DST may be found in [28], but we have no doubts that the DST is more general, because in contrast to the rough set theory, it generates many derived theories.…”

Section: Propositionsmentioning

confidence: 94%

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Sevastjanov

Dymova

Kaczmarek

2021

Entropy

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In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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“…It is a significant method to deal with imprecision, fuzziness and uncertainty. It also doesn't need any prior information beyond the data set that the problem needs to be processed [17], [35]. RST, based on classification mechanism, regards classification as equivalence relation in a specific space, and equivalence relation constitutes the division of space.…”

Section: A Research Background and Related Workmentioning

confidence: 99%

Feature Selection for Interval-Valued Data Based on D-S Evidence Theory

Peng

Zhang

2021

IEEE Access

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Feature selection is one basic and critical technology for data mining, especially in current "big data era". Rough set theory (RST) is sensitive to noise in feature selection due to the strict condition of equivalence relation. However, D-S evidence theory is flexible to measure uncertainty of information. This paper introduces robust feature evaluation metrics "belief function" and "plausibility function" into feature selection algorithm to avoid the defect that classification effect is affected by noise. First of all, similarity between information values in an interval-valued information system (IVIS) is given and a variable parameter to control the similarity of samples is introduced. Then, θ-lower approximation and θ-upper approximation in IVIS are put forward. Next, belief function and plausibility function based on θlower approximation and θ-upper approximation are put forward. Finally, four feature selection algorithms in an IVIS based on D-S evidence theory are proposed. The experimental results on four real interval-valued datasets show that the proposed metrics are robust to noise, and the proposed algorithms are more effective than the existing algorithms.

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A unified framework for characterizing rough sets with evidence theory in various approximation spaces

Cited by 22 publications

References 43 publications

Composite Fault Diagnosis for Rotating Machinery of Large Units Based on Evidence Theory and Multi‐Information Fusion

Composite Fault Diagnosis for Rotating Machinery of Large Units Based on Evidence Theory and Multi‐Information Fusion

On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Feature Selection for Interval-Valued Data Based on D-S Evidence Theory

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