Covering rough sets based on neighborhoods: An approach without using neighborhoods

Rough set theory, a mathematical tool to deal with inexact or uncertain knowledge in information systems, has originally described the indiscernibility of elements by equivalence relations. Covering rough sets are a natural extension of classical rough sets by relaxing the partitions arising from equivalence relations to coverings. Recently, some topological concepts such as neighborhood have been applied to covering rough sets. In this paper, we further investigate the covering rough sets based on neighborhoods by approximation operations. We show that the upper approximation based on neighborhoods can be defined equivalently without using neighborhoods. To analyze the coverings themselves, we introduce unary and composition operations on coverings. A notion of homomorphismis provided to relate two covering approximation spaces. We also examine the properties of approximations preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin

Efficient schemes on solving fractional integro-differential equations

Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for th

Identifying Effective Features and Classifiers for Short Term Rainfall Forecast Using Rough Sets Maximum Frequency Weighted Feature Reduction Technique

Precise rainfall forecasting is a common challenge across the globe in meteorological predictions. As rainfall forecasting involves rather complex dynamic parameters, an increasing demand for novel approaches to improve the forecasting accuracy has heightened. Recently, Rough Set Theory (RST) has attracted a wide variety of scientific applications and is extensively adopted in decision support systems. Although there are several weather prediction techniques in the existing literature, identifying significant input for modelling effective rainfall prediction is not addressed in the present mechanisms. Therefore, this investigation has examined the feasibility of using rough set based feature selection and data mining methods, namely Naïve Bayes (NB), Bayesian Logistic Regression (BLR), Multi-Layer Perceptron (MLP), J48, Classification and Regression Tree (CART), Random Forest (RF), and Support Vector Machine (SVM), to forecast rainfall. Feature selection or reduction process is a process of identifying a significant feature subset, in which the generated subset must characterize the information system as a complete feature set. This paper introduces a novel rough set based Maximum Frequency Weighted (MFW) feature reduction technique for finding an effective feature subset for modelling an efficient rainfall forecast system. The experimental analysis and the results indicate substantial improvements of prediction models when trained using the selected feature subset. CART and J48 classifiers have achieved an improved accuracy of 83.42% and 89.72%, respectively. From the experimental study, relative humidity2 (a4) and solar radiation (a6) have been identified as the effective parameters for modelling rainfall prediction