Minimal attribute reduction plays an important role in both theory and practice, but it has been proved that finding a minimal reduct of a given decision table is a NP-hard problem. Some scholars have also pointed out that current heuristic algorithms are incomplete for minimal attribute reduction. Based on the decomposition principles of a discernibility function, a complete algorithm CAMARDF ...

A modification of the fuzzy backpropagation (FBP) algorithm called QuickFBP algorithm is proposed, where the computation of the net function is significantly quicker. It is proved that the FBP algorithm is of exponential time complexity, while the QuickFBP algorithm is of polynomial time complexity. Convergence conditions of the QuickFBP, resp. the FBP algorithm are defined and proved for: (1) ...

We propose a novel feature ranking technique using discernibility matrix. Discernibility matrix is used in rough set theory for reduct computation. By making use of attribute frequency information in discernibility matrix, we develop a fast feature ranking mechanism. Based on the mechanism, two heuristic reduct computation algorithms are proposed. One is for optimal reduct and the other for app...

This article proposes the concept lattice reduction based on the improved discernibility matrix using discernibility matrix of rough set, and with examples, proves that the improved reduction algorithm costs shorter time, makes reduction speed faster, and also saves storage space in comparison with the original discernibility matrix reduction algorithm. Keywordsformal context, concept lattice, ...

Given an array with n elements, we want to rearrange them in ascending order. In this paper, we introduce Quick Sort, a divide-and-conquer algorithm to sort an N element array. We evaluate the O(NlogN) time complexity in best case and O(N) in worst case theoretically. We also introduce a way to approach the best case.

In this paper, we present an improved version of recently proposed Quick Hypervolume algorithm for calculating exact hypervolume of the space dominated by a set of d-dimensional points. This value is often used as a quality indicator in multiobjective evolutionary algorithms and other multiobjective metaheuristics and the efficiency of calculating this indicator is of crucial importance especia...

Most existing rough set-based feature selection algorithms suffer from intensive computation of either discernibility functions or positive regions to find attribute reduct. In this paper, we develop a new computation model based on relative attribute dependency defined as the proportion of the projection of the decision table on a condition attributes subset to the projection of the decision t...

The rough set theory provides a formal framework for data mining. Reduct is the most important concept in rough set application to data mining. A reduct is the minimal attribute set preserving classification power of original dataset. Finding a reduct is similar to feature selection problem. In this paper, we propose two reduct algorithms. One is based on attribute frequency in discernibility m...

Article history: Received 3 August 2013 Received in revised form 15 May 2015 Accepted 22 June 2015 Available online 2 July 2015 Attribute reduction is an important preprocessing step in datamining and knowledge discovery. The effective computation of an attribute reduct has a direct bearing on the efficiency of knowledge acquisition and various related tasks. In real-world applications, some at...