Abstract: Soft set theory was initiated by Molodtsov in 1999. In the past years, this theory had been applied to many branches of mathematics, information science and computer science. In 2003, Maji et al. introduced some operations of soft sets and gave some operational rules. Recently, some of these operational rules are pointed out to be not true. Furthermore, Ali et al., in their paper, introduced and discussed some new operations of soft sets. In this paper, we further investigate these operational rules given by Maji et al. and Ali et al.. We obtain some sufficient-necessary conditions such that corresponding operational rules hold and give correct forms for some operational rules. These results will be help for us to use rightly operational rules of soft sets in research and application of soft set theory.
Abstract: In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.
Abstract: A color image edge detection algorithm is proposed in
this paper using Pseudo-complement and matrix rotation operations.
First, pseudo-complement method is applied on the image for each
channel. Then, matrix operations are applied on the output image of
the first stage. Dominant pixels are obtained by image differencing
between the pseudo-complement image and the matrix operated
image. Median filtering is carried out to smoothen the image thereby
removing the isolated pixels. Finally, the dominant or core pixels
occurring in at least two channels are selected. On plotting the
selected edge pixels, the final edge map of the given color image is
obtained. The algorithm is also tested in HSV and YCbCr color
spaces. Experimental results on both synthetic and real world images
show that the accuracy of the proposed method is comparable to
other color edge detectors. All the proposed procedures can be
applied to any image domain and runs in polynomial time.