Comparison of Twelve Types of Rough Approximations Based on j-Neighborhood Space and j-Adhesion Neighborhood Space

In this paper, we generalize six kinds of rough set models based on j-neighborhood space (i.e., reflexive 1 j-neighborhood rough set, reflexive 2 j-neighborhood rough set, reflexive 3 j-neighborhood rough set, similarity 4 j-neighborhood rough set, similarity 5 j-neighborhood rough set, and similarity 6 j-neighbor\\hood rough set), and investigate some of their basic properties. Further, we propose a new neighborhood space called j-adhesion neighborhood based on six types of rough set models (i.e., reflexive 7 j-adhesion neighborhood rough set, reflexive 8 j-adhesion neighborhood rough set, reflexive 9 j-adhesion neighborhood rough set, similarity 10 j-adhesion neighborhood rough set, similarity 11 j-adhesion neighborhood rough set, and similarity 12 j-neighbor\\hood rough set) to reduce the boundary region and the accuracy. The fundamental properties of approximation operators based on j-adhesion neighborhood space are investigated. The relationship between the properties of these types is explained. Finally, we give comparisons between the proposed approach with the previous approach (i.e., Abo-Tabl's approach and Dai et al.'s approach) from six types of rough set models. Consequently, the accuracy from the proposed approach is improved.

Fagin’s Criminal Thought in Charles Dickens’ Oliver Twist

This research aims to reveal Fagin’s criminal thought in Charles Dickens’ Oliver Twist and to examine the factors that influence Fagin’s criminal thought presented in the novel. This research is classified into library research. The subject of the research is Oliver Twist, Charles Dickens’ fiction novel. The novel is used as the primary source, while books, journals, and articles related to criminal thought theories in psychology were taken as the secondary source. A psychological approach is applied to analyze the data. The collected data were analyzed qualitatively. In analyzing the data, the researcher took five steps. The data were collected from reading and re-reading the text, identifying those that embody criminal thinking, categorizing them based on the objectives of the research, comparing them to the theoretical frameworks, and finally interpreting them using a psychological approach. After conducting the research, it can be drawn some conclusions; first, by seeing the eight aspects of criminal thought, Fagin has five aspects which are classified in the high category, and second, the factors that influence Fagin’s criminal thought reflected in the novel are societal and economic, neighbor-hood and local institutions, and drugs.

A Novel Neighborhood Calculation Method by Assessing Users' Varying Preferences in Collaborative Filtering

To recommend an item to a target user, Collaborative Filtering (CF) considers the preferences of other similar users or neighbors. The accuracy of the recommendation depends on the effectiveness of assessing the neighbors. But over the time, the mutual likings of two individuals change; hence, the neighbors of the target user also should change. However, this shifting of preferences is not considered by traditional methods of calculating neighborhood in CF. As a result, the calculated set of neighbors does not always reflect the optimal neighborhood at any given point of time. In this paper, we argue for considering the continuous change in likings of the previous similar users and calculating the neighbor- hood of a target user based on different time periods. We propose a method that assesses the similarity between users in the different time period by using K-means clustering. This approach significantly improves the accuracy in the personalized recommendation. The performance of the proposed algorithm is tested on the MovieLens datasets (ml-100k and ml-1m) using different performance metrics viz. MAE, RMSE, Precision, Recall, F-score, and accuracy.

An Approach for Extracting Neighborhood Points of Surface Intersection Curves

This paper comes up with an approach for surface reconstruction from arbitrary, unorganized and intersecting curves. First of all, camera calibration determines the interior and exterior camera parameters. Based on laser triangulation measurement, the point in world coordinate system can be computed. The extracted curves are processed in a volumetric in which a vector field is built and updated to compute the neighbor-hood points. Then the surface reconstruction can be obtained with MC algorithm. This approach makes surface reconstruction and curves registration a unified procedure. This algorithm solves the problem of linear complexity respect to input curves, and makes it suitable for interactive modeling. The experiment verifies its available, reduces the effect of registration errors and has a good result.

Equivalence among some neighborhood structures in fuzzy topology

We deepen the study of two known neighborhood structures, which here will be calledf⋅k-neighborhood structures andf⋅q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies byf⋅k-neighbor-hood structures. Moreover we introduce and discuss the notions off⋅k-neighborhood prestructure andf⋅m-neighborhood structure in the same context. At last we prove that the three neighborhood structures mentioned above are equivalent.

The integral formula for the reduced algebraic multiplicity of meromorphic operator functions

Throughout this paper A denotes an operator function, holomorphic on a deletedneighborhood of a complex number λo, with values in the space ℒ(X,Y) of boundedlinear operators between two complex Banach spaces X and Y. In his survey article(7), I. C. Gohberg has defined for such an arbitrary operator function A the algebraic multiplicity RM(A;λo) and the reduced algebraic multiplicity RM(A;λo) of A at λo. In earlier papers (e.g., (8, 16)) these notions have been defined and studied for morerestricted classes of operator functions. In (8) Gohberg and Sigal treated the case when A is finite-meromorphic at λo, A(λ) is bijective for λ in some deleted neighbor-hood of λo and the constant term A0 in the Laurent expansion of A at λo is aFredholm operator. They proved that in this case