The Rough Sets Theory and Evidence Theory

1990 ◽  
Vol 13 (3) ◽  
pp. 245-262
Author(s):  
Andrzej Skowron
Keyword(s):  
Rough Sets ◽  
Evidence Theory ◽  
Decision Table ◽  
Combination Rule ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Rough Sets Theory ◽  
Decision Attributes ◽  
Lower And Upper Approximations ◽  
Sets Theory

The aim of the paper is to show some connections between the rough sets theory and the Dempser-Shafer approach. We prove that for every Pawlak’s approximation space there exists a Dempster-Shafer space with the qualities of the lower and upper approximations of sets in the approximation space equal to the credibility and plausibility of sets in the Dempster-Shafer space, respectively. Analogous connections hold between approximation spaces generated by the decision tables and Dempster-Shafer spaces, namely for every decision table space there exists a Dempster-Shafer space such that the qualities of the lower and upper approximations (with respect to the condition attributes) of sets definable in the decision table by condition and decision attributes coincide with the credibility and plausibility of sets in the Dempster-Shafer space, respectively. A combination rule in approximation spaces analogous to the combination rule used in the Dempster approach is derived.

Feature Extraction from Engine's Data Based on Rough Sets Theory

2011 ◽  
Vol 120 ◽  
pp. 410-413
Author(s):  
Feng Wang ◽  
Li Xin Jia
Keyword(s):  
Feature Extraction ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Rough Set Theory ◽  
Technical Condition ◽  
Decision Table ◽  
Discernibility Matrix ◽  
Rough Sets Theory ◽  
Sets Theory

The speed signal of engine contains abundant information. This paper introduces rough set theory for feature extraction from engine's speed signals, and proposes a method of mining useful information from a mass of data. The result shows that the discernibility matrix algorithm can be used to reduce attributes in decision table and eliminate unnecessary attributes, efficiently extracted the features for evaluating the technical condition of engine.

Product Function: Component Modeling Using Rough Sets

2009 ◽  
Author(s):  
Toshiharu Miwa ◽  
Hideki Aoyama
Keyword(s):  
Product Development ◽  
Rough Sets ◽  
Early Stage ◽  
Modeling Method ◽  
Rough Sets Theory ◽  
Development Cycle ◽  
Product Function ◽  
Lower And Upper Approximations ◽  
Sets Theory ◽  
Manufacturing Parameters

The acceleration of the product development cycle continues to be a significant challenge for manufacturing firms around the world. The misunderstanding of important relationships between product functions and components leads the delay of product development. The present paper describes an identification method of the relationships between product functions and components at the early stage of product development. The proposed product function-component modeling method using rough sets theory extracts the characteristic relationships between product functions and components from a small amount of the qualitative and linguistically-expressed knowledge data. The advantage of using the rough sets is that the combination of necessary and possible sets (lower and upper approximations) represents the vague knowledge. The present paper describes an example of a conventional cutting process with 6 manufacturing parameters that this method contributes to the identification of cutting mechanism from a small amount of sampling data (7% of whole event) compared to the conventional statistical modeling method.

One Fusion Approach of Fault Diagnosis Based on Rough Sets Theory and Dempster-Shafer Theory

2012 ◽  
Vol 241-244 ◽  
pp. 405-409 ◽  
Author(s):  
Yan Qin Su ◽  
Ji Hong Cheng ◽  
Ting Xue Xu
Keyword(s):  
Fault Diagnosis ◽  
Rough Sets ◽  
Decision Table ◽  
Combination Rules ◽  
Rough Sets Theory ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Shafer Theory ◽  
Sets Theory ◽  
Fusion Approach

There is the advantage of Rough Sets Theory for redundant condition reduction and D-S Theory for combination rules reasoning, one fusion approach based on the two theories was given. Firstly, the test data was discretizated and attribution reduced to get the reduction decision table. Then, the basic probability assignment was gotten through calculating the condition attribution of the decision table while the condition attribution was regarded as evidence input and the decision attribution as discernment frame. Finally, the evidence was combination reasoned and the fault diagnosis results were gotten, and the application example was verified its validity.

scholarly journals Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Yang ◽  
Taihua Xu ◽  
Fan Zhao
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Boundary Region ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Rough Sets Theory ◽  
Fuzzy Distance ◽  
Rough Approximation ◽  
Sets Theory

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence.

scholarly journals Rough sets analysis with antisymmetric and intransitive attributes: classification of brazilian soccer clubs

2008 ◽  
Vol 28 (2) ◽  
pp. 217-230 ◽  
Author(s):  
Annibal Parracho Sant'Anna
Keyword(s):  
Rough Sets ◽  
Rough Sets Theory ◽  
Decision Attributes ◽  
Sets Theory

This work aims to develop alternative classifications for teams in a Championship. Data from the 2005 Brazilian National Soccer Championship are analyzed. Rough Sets Theory (RST) is employed in this analysis. By evaluating the quality of the approximation in terms of probabilities of concordance and discordance between the classification by the set of decision attributes and by the set of condition attributes of a randomly chosen pair of objects as discernible or indiscernible, the modification of RST employed allows to consider antisymmetric and intransitive relations. The balance between the numbers of goals scored by the pairs of clubs in direct confrontations is one such relation.

Compound-Fault Diagnosis of Bearing Based on Order Tracking Wavelet Packet and Rough Sets

2011 ◽  
Vol 130-134 ◽  
pp. 1681-1685 ◽  
Author(s):  
Guang Tian ◽  
Hao Tian ◽  
Guang Sheng Liu ◽  
Jin Hui Zhao ◽  
Li Ping Luo
Keyword(s):  
Fault Diagnosis ◽  
Rough Sets ◽  
Wavelet Packet ◽  
Decision Rules ◽  
Vibration Signals ◽  
Rough Sets Theory ◽  
Equal Angle ◽  
Order Tracking ◽  
Start Up ◽  
Sets Theory

The diagnosis of compound-fault is always a difficult point, and there is not an effective method in equipment diagnosis field, then a new method of compound-fault diagnosis was presented. The vibration signals at start-up in the gearbox are non-stationary signals, and traditional ways of diagnosis have low precision. Order tracking and wavelet packet and rough sets theory are introduced in the compound-fault diagnosis of bearing. First, the vibration signals at start-up were resampled using computer order tracking arithmetic and equal angle distributed vibration signals were obtained, and wavelet packet has been used for equal angle distributed vibration signals decomposition and reconstruction. Then, energy distribution of every frequency band can be calculated according to normalization process. A new feature vector can be obtained, then clear and concise decision rules can be obtained by rough sets theory. Finally, the result of compound-fault example proves that the proposed method has high validity and more amplitude appliance foreground.

Next-day peak electricity price forecasting using NN based on rough sets theory

2008 ◽  
Author(s):  
Hirofumi Toyama ◽  
Tomonobu Senjyu ◽  
Shantanu Chakraborty ◽  
Atsushi Yona ◽  
Toshihisa Funabashi ◽  
...  
Keyword(s):  
Rough Sets ◽  
Electricity Price ◽  
Price Forecasting ◽  
Rough Sets Theory ◽  
Electricity Price Forecasting ◽  
Sets Theory
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