Double-Quantitative Generalized Multi-Granulation Set-Pair Dominance Rough Sets in Incomplete Ordered Information System

Since the rough sets theory based on the double quantification method was proposed, it has attracted wide attention in decision-making. This paper studies the decision-making approach in Incomplete Ordered Information System (IOIS). Firstly, to better extract the effective information in IOIS, combined with the advantages of set-pair dominance relation and generalized multi-granulation, the generalized multi-granulation set-pair dominance variable precision rough sets (GM-SPD-VPRS) and the generalized multi-granulation set-pair dominance graded rough sets (GM-SPD-GRS) are proposed. Moreover, we discuss their related properties. Secondly, considering the GM-SPD-VPRS and the GM-SPD-GRS describe information from relative view and absolute view, respectively, we further combine the two rough sets to obtain six double-quantitative generalized multi-granulation set-pair dominance rough sets (GM-SPD-RS) models. Among them, the first two models fuse the approximation operators of two rough sets, and investigate the extreme cases of optimistic and pessimistic. The last four models combine the two rough sets by the logical disjunction operator and the logical conjunction operator. Then, we discuss relevant properties and derive the corresponding decision rules. According to the decision rules, an associated algorithm is constructed for one of the models to calculate the rough regions. Finally, we validate the effectiveness of these models with a medical example. The results indicate that the model is effective for dealing with practical problems.

Classification of the galaxy Milky Way using variable precision rough sets technique

Astronomy image is regarded main source of information to discover outer space, therefore to know the basic contain for galaxy (Milky way), it was classified using Variable Precision Rough Sets technique to determine the different region within galaxy according different color in the image. From classified image we can determined the percentage for each class and then what is the percentage mean. In this technique a good classified image result and faster time required to done the classification process.

Studying the contribution of components and type of spiral galaxy NGC 6946 using digital image processing

NGC 6946 have been observed with BVRI filters, on October 15-18,2012, with the Newtonian focus of the 1.88m telescope, Kottamiaobservatory, of the National Research Institute of Astronomy andGeophysics, Egypt (NRIAG), then we combine the BVRI filters toobtain an astronomical image to the spiral galaxy NGC 6946 whichis regarded main source of information to discover the components ofthis galaxy, where galaxies are considered the essential element ofthe universe. To know the components of NGC 6946, we studied itwith the Variable Precision Rough Sets technique to determine thecontribution of the Bulge, disk, and arms of NGC 6946 according todifferent color in the image. From image we can determined thecontribution for each component and its percentage, then what is thepercentage mean. In this technique a good classified image resultand faster time required to done the classification process.

Application of the Variable Precision Rough Sets Model to Estimate the Outlier Probability of Each Element

In a data mining process, outlier detection aims to use the high marginality of these elements to identify them by measuring their degree of deviation from representative patterns, thereby yielding relevant knowledge. Whereas rough sets (RS) theory has been applied to the field of knowledge discovery in databases (KDD) since its formulation in the 1980s; in recent years, outlier detection has been increasingly regarded as a KDD process with its own usefulness. The application of RS theory as a basis to characterise and detect outliers is a novel approach with great theoretical relevance and practical applicability. However, algorithms whose spatial and temporal complexity allows their application to realistic scenarios involving vast amounts of data and requiring very fast responses are difficult to develop. This study presents a theoretical framework based on a generalisation of RS theory, termed the variable precision rough sets model (VPRS), which allows the establishment of a stochastic approach to solving the problem of assessing whether a given element is an outlier within a specific universe of data. An algorithm derived from quasi-linearisation is developed based on this theoretical framework, thus enabling its application to large volumes of data. The experiments conducted demonstrate the feasibility of the proposed algorithm, whose usefulness is contextualised by comparison to different algorithms analysed in the literature.