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.

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.

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

A Novel Methodology to Manage Uncertainty for Multidisciplinary Design and Optimization in Conceptual Design

2008 ◽  
Vol 44-46 ◽  
pp. 225-232 ◽  
Author(s):  
Xin Yu Shao ◽  
Xue Zheng Chu ◽  
Liang Gao ◽  
Hao Bo Qiu
Keyword(s):  
Conceptual Design ◽  
Probabilistic Method ◽  
Kriging Model ◽  
Design Stage ◽  
Design And Optimization ◽  
Rough Sets Theory ◽  
Innovative Methodology ◽  
Traditional Approaches ◽  
Sets Theory

Uncertainty in design and simulation affects the quality of product directly during the process of MDO, which should be considered to help designers to make the design decisions, especially at conceptual design stage. In traditional approaches, this uncertainty is ignored in the hope that it is not significant to the decision making. In this investigation, firstly, three main uncertainties in MDO of conceptual design are pointed out and carefully analyzed. Then, an innovative methodology integrating extract knowledge and probabilistic method to manage these uncertainties is presented. Considering practical application and eliminating the uncertainty in configuration, we propose a promising method combining Fuzzy c-means algorithm (FCM) and Rough Sets theory (RST) to deduce the configuration rule. Furthermore, probabilistic kriging model is utilized as an approximation model to reduce global computational expense of complex product. Sensitivity analysis (SA) is used to reduce uncertainty of inputs of simulation, and mean square error (MSE) is employed to assess model error to reduce model uncertainty. Finally, the validity and necessity of this methodology are demonstrated through the conceptual design of bulk carrier.

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