Attribute reduction (also called feature subset selection) plays an important role in rough set theory. Different from the classical attribute reduction algorithms, the methods of attribute reduction based on covering rough sets appear to be suitable for numerical data. However, it is time-consuming in dealing with the large-scale data. In this paper, we study the problem of attribute reduction...

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation of fuzzy coverings for fuzzy covering rough sets, the concepts of fuzzy subcoverings, the reducible and intersectional elements, the union and intersection o...

Very large-scale neighborhood search (VLSNS) is a technique intensively used in single-objective optimization. However, there is almost no study of VLSNS for multiobjective optimization. We show in this paper that this technique is very efficient for the resolution of multiobjective combinatorial optimization problems. Two problems are considered: the multiobjective multidimensional knapsack pr...

A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a covering system. A famous conjecture of Erdös from 1950 states that the least modulus of a covering system can be arbitrarily large. This conjecture remains open and, in its full strength, appears at present to be unattackable. Most of the effo...

the growing scarcity of fresh water is driving the implementation of wastewater treatment and water reuse on an increasingly large scale. various methods have been developed and used for water reuse from wastewater; however, the membrane distillation (md) process, as a promising separation technology, has recently gained more attention. the md process is a non-isothermal membrane-based separati...

in this paper, we describe our implementation of an interior point algorithm for large scale systems. first we identify system with small and medium methods convex optimization, then we use interior point method for identification. finally we offer an interior point method that uses nonlinear cost function and see that we achieve a good trade-off between error and cpu time. actually, in this pa...