Maximum Distribution Reduction Research Articles

New fixation method for Pauwels type III femoral neck fracture: a finite element analysis of sliding hip screw, L-shaped, and L-shaped with medial plate.

In this study, we aimed to evaluate the biomechanical behavior of three fixations for Pauwels type III fractures (sliding hip screw (SHS), L-shaped, and L-shaped with medial plate), by finite element analysis (FEM). Three internal fixators were developed to treat Pauwels type III fracture by finite elements: SHS; L-shaped; and L-shaped with medial plate. Under the same conditions, localized and total vertical fracture displacement, maximum and minimum principal and von Mises stresses were evaluated. The localized and total vertical displacement evaluated for the SHS, L-shaped, and L-shaped with medial plate were 0.15mm, 0.17mm, and 0.07mm (localized), and 4.52mm, 6.97mm, and 6.83mm (total), respectively. The maximum values obtained in the upper region of the femoral neck for the internal fixations were 1.43MPa, 1.29MPa, and 1.24MPa, and the minimum values obtained in the lower region of the femoral neck were - 0.73MPa, - 1.09MPa, and - 1.03MPa, respectively. The maximum Von Mises peak stress values were 6.35MPa, 10.7MPa, and 16.2MPa for the fixation models using the SHS, L-shaped, and L-shaped with medial plate, respectively. The present FEM analysis showed that SHS yields better results in terms of total vertical displacements, maximum distribution, and Von Mises peak stresses reduction. On the other hand, the L-shaped construction plus a medial plate decreases localized vertical displacements and maximum principal distribution when compared to the SHS and L-shaped constructions. These results demonstrate that both constructions, SHS and L-shaped plus a medial plate, are biomechanically efficient for the fixation of Pauwels type III femoral neck fractures.

Quick general reduction algorithms for inconsistent decision tables

In the Pawlak rough set model, attribute reduction plays one of the important roles, and the preservation of different properties of the original decision table leads to different types of reduct definitions, such as relative relation reduct, positive-region reduct, distribution reduct, maximum distribution reduct, and assignment reduct. However, there are no general quick reduction approaches for obtaining various types of reducts; this motivated us to conduct the present study. We first establish a unified decision table model for five representative reducts in inconsistent decision tables, study the relative discernibility and relative discernibility reduct for the general decision table, and derive the corresponding properties. Then, two general reduction algorithms (GARA-FS△ and GARA-BS△) from the viewpoint of the relative discernibility in inconsistent decision tables are presented. Subsequently, to increase the efficiency of algorithms, two quick general reduction algorithms (QGARA-FS△ and QGARA-BS△) are proposed mainly by reducing the sort times to increase the efficiency of reduction algorithms. Finally, a series of experiments with UCI data sets are conducted to evaluate the effectiveness and performance of the proposed reduction algorithms.

Forward tentative selection with backward propagation of selection decision algorithm for attribute reduction in rough set theory

In rough set theory, attribute reduction is an important application. Many approaches to attribute reduction were developed using rough set theory. These approaches used various greedy heuristics to find a reduct approximation. In this paper, we propose forward tentative selection with backward propagation of selection decision (FTSBPSD) algorithm to find a reduct. The proposed algorithm is based on the principle of indiscernibility of rough set theory. It finds one of the prime implicants of the discernibility function as the reduct. The proposed algorithm works for various types of reducts, defined in the rough set theory. In this work, we have analysed the performance of distribution reduct, maximum distribution reduct, positive region reduct and possible reduct. The proposed algorithm was tested on various datasets found in University of California, machine learning repository. It has given good results for classification accuracy during tests performed on the datasets. Experimental results obtained by FTSBPSD algorithm have been found to give better classification accuracy when tested using C4.5 classifier in comparison to the results obtained by the Q-MDRA algorithm described in the literature.

A Feature Selection Approach of Inconsistent Decision Systems in Rough Set

Feature selection has been widely discussed as an important preprocessing step in data mining applications since it reduces a model's complexity. In this paper, limitations of several representative reduction methods are analyzed firstly, and then by distinguishing consistent objects form inconsistent objects, decision inclusion degree and its probability distribution function as a new measure are presented for both inconsistent and consistent simplified decision systems. New definitions of distribution reduct and maximum distribution reduct for simplified decision systems are proposed. Many important propositions, properties, and conclusions for reduct are drawn. By using radix sorting and hash techniques, a heuristic distribution reduct algorithm for feature selection is constructed. Finally, compared with other feature selection algorithms on six UCI datasets, the proposed approach is effective and suitable for both consistent and inconsistent decision systems.

Rule Acquisition Based on Inconsistent Decision-Making Information System

Rule acquisition is a hot topic in the field of data mining. And the inconsistent information systems are widespread nowadays. However, rules acquisition methods are always the difficulty of rough set theory application in inconsistent decision information systems; So the paper proposes a new rule acquisition method. Firstly, we use maximum distribution reduction method for knowledge reduction in single decision-making inconsistent information system and then we use decision-making resolution matrix and decision-making matrix function to get the decision rules. Finally, we mine the rules from inconsistent decision-making information systems.

Quick attribute reduction in inconsistent decision tables

This paper focuses on three types of attribute reducts in inconsistent decision tables: assignment reduct, distribution reduct, and maximum distribution reduct. It is quite inconvenient to judge these three types of reduct directly according to their definitions. This paper proposes judgment theorems for the assignment reduct, the distribution reduct and the maximum distribution reduct, which are expected to greatly simplify the judging of these three types of reducts. On this basis, we derive three new types of attribute significance measures and construct the Q-ARA (Quick Assignment Reduction Algorithm), the Q-DRA (Quick Distribution Reduction Algorithm), and the Q-MDRA (Quick Maximum Distribution Reduction Algorithm). These three algorithms correspond to the three types of reducts. We conduct a series of comparative experiments with twelve UCI (machine learning data repository, University of California at Irvine) data sets (including consistent and inconsistent decision tables) to evaluate the performance of the three reduction algorithms proposed with the relevant algorithm QuickReduct [9,34]. The experimental results show that QuickReduct possesses weak robustness because it cannot find the reduct even for consistent data sets, whereas our proposed three algorithms show strong robustness because they can find the reduct for each data set. In addition, we compare the Q-DRA (Quick Distribution Reduction Algorithm) with the CEBARKNC (conditional entropy-based algorithm for reduction of knowledge without a computing core) [43] because both find the distribution reduct by using a heuristic search. The experimental results demonstrate that Q-DRA runs faster than CEBARKNC does because the distribution function of Q-DRA has a lower calculation cost. Instructive conclusions for these reduction algorithms are drawn from the perspective of classification performance for the C4.5 and RBF-SVM classifiers. Last, we make a comparison between discernibility matrix-based methods and our algorithms. The experimental results indicate that our algorithms are efficient and feasible.

New method for maximum distribution reduction in inconsistent decision information systems

In order to get the maximum distribution attribute reduction rapidly in inconsistent decision information systems,a new decision maximum distribution binary relation was defined after analyzing the existing methods.And the judgment theorems for judging maximum distribution consistent sets were obtained,from which we can provide a new maximum distribution attribute reduction algorithm in inconsistent decision information systems.Moreover,the characterization of core attributes,relative necessary attributes,unnecessary attributes were discussed based on decision maximum distribution binary relation.Finally,a case study illustrates the validity of the method.

Methods for knowledge reduction in inconsistent ordered information systems

Knowledge reduction is one of the most important problems in the study of rough set theory. However, in real-world, most of information systems are based on dominance relations in stead of the classical equivalence relation because of various factors. The ordering of properties of attributes plays a crucial role in those systems. To acquire brief decision rules from the systems, knowledge reductions are needed. The main objective of this paper is to deal with this problem. The distribution reduction and maximum distribution reduction are proposed in inconsistent ordered information systems. Moreover, properties and relationship between them are discussed. Furthermore, judgment theorem and discernibility matrix are obtained, from which an approach to knowledge reductions can be provided in inconsistent ordered information systems.

Approaches to knowledge reduction based on variable precision rough set model

This paper deals with approaches to knowledge reduction based on variable precision rough set model. The concepts of β lower distribution reduct and β upper distribution reduct based on variable precision rough sets (VPRS) are first introduced. Their equivalent definitions are then given, and the relationships among β lower and β upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated. It is proved that for some special thresholds, β lower distribution reduct is equivalent to the maximum distribution reduct, whereas β upper distribution reduct is equivalent to the possible reduct. The judgement theorems and discernibility matrices associated with the β lower and β upper distribution reducts are also established, from which we can obtain the approaches to knowledge reduction in VPRS.

Approaches to knowledge reductions in inconsistent systems

This article deals with approaches to knowledge reductions in inconsistent information systems (ISs). The main objective of this work was to introduce a new kind of knowledge reduction called a maximum distribution reduct, which preserves all maximum decision classes. This type of reduction eliminates the harsh requirements of the distribution reduct and overcomes the drawback of the possible reduct that the derived decision rules may be incompatible with the ones derived from the original system. Then, the relationships among the maximum distribution reduct, the distribution reduct, and the possible reduct were discussed. The judgement theorems and discernibility matrices associated with the three reductions were examined, from which we can obtain approaches to knowledge reductions in rough set theory (RST). © 2003 Wiley Periodicals, Inc.