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The fuzzy-C-means (FCM) algorithm is one of the most famous fuzzy clustering algorithms, but it gets stuck in local optima. In addition, this algorithm requires the number of clusters. Also, the density-based spatial of the application with noise (DBSCAN) algorithm, which is a density-based clustering algorithm, unlike the FCM algorithm, should not be pre-numbered. If the clusters are specific and depend on the number of clusters, then it can determine the number of clusters. Another advantage of the DBSCAN clustering algorithm over FCM is its ability to cluster data of different shapes. In this paper, in order to overcome these limitations, a hybrid approach for clustering is proposed, which uses FCM and DBSCAN algorithms. In this method, the optimal number of clusters and the optimal location for the centers of the clusters are determined based on the changes that take place according to the data set in three phases by predicting the possibility of the problems stated in the FCM algorithm. With this improvement, the values of none of the initial parameters of the FCM algorithm are random, and in the first phase, it has been tried to replace these random values to the optimal in the FCM algorithm, which has a significant effect on the convergence of the algorithm because it helps to reduce iterations. The proposed method has been examined on the Iris flower and compared the results with basic FCM algorithm and another algorithm. Results shows the better performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the inverse eigenvalue problem for the bordered diagonal matrices are reconsidered whose elements are equal to zero except for the first row, the first column and the diagonal elements. The necessary and sufficient conditions for existence of a symmetric bordered diagonal matrix from special spectral data have been determined. A new algorithm to make such matrices is derived and some numerical examples are given to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

We present the quantum equation and synthesize an optimal control procedure for this equation. We develop a theoretical method for the analysis of quantum optimal control system given by the time depending Schrödinger equation. The Legendre wavelet method is proposed for solving this problem. This can be used as an efficient and accurate computational method for obtaining numerical solutions of different quantum optimal control problems. The distinguishing feature of this paper is that it makes the method, previously used to solve non-quantum control equations based on Legendre wavelets, usable by using a change of variables for quantum control equations. [ABSTRACT FROM AUTHOR]

The problem of reconstructing a matrix with a specific structure from a partial or total spectral data is known as inverse eigenvalue problem which arises in a variety of applications. In this paper, we study a partially described inverse eigenvalue problem of periodic Jacobi matrices and prove some spectral properties of such matrices. The problem involves the reconstruction of the matrix by one eigenvalue of each of its leading principal submatrices and one eigenvector of the required matrix and one more additional piece of information. The conditions for solvability of the problem are presented and finally an algorithm and some numerical results are given. [ABSTRACT FROM AUTHOR]

A new method is proposed for finding a set of efficient solutions to bi-objective fractional transportation problems with fuzzy numbers using ranking function. This method is an important tool for the decision makers to obtain efficient solutions and select the preferred optimal solution from the satisfaction level. The procedure allows the user to identify next efficient solution to the problem from the current efficient solution. This new approach enables the decision makers to evaluate the economic activities and make satisfactory managerial decisions when they are handling a variety of logistic problems involving two objectives. An illustrative example is presented to clarify the idea of the proposed approach. [ABSTRACT FROM AUTHOR]

Image zooming is one of the important issues of image processing that maintains the quality and structure of image. Zooming an image necessitates placing the extra pixels in the image data. Moreover, adding the data to the image must be consistent with the texture in the image in order to prevent artificial blocks. In this study, the required pixels are estimated using barycentric rational interpolation. The proposed method is a non-linear one which can preserve the edges and reduces the blur and block artifacts on the zoomed image. Numerical results are presented using PSNR and SSIM fidelity measures and they are compared to some other methods. The average PSNR of the original image and image zooming was 33.08 which can prove that image zooming is very similar to the original image. The experimental results reveal that the proposed method has a better performance compared to other methods and can provide good image quality. [ABSTRACT FROM AUTHOR]

The hybrid fuzzy differential equations (HFDEs) are natural way to model dynamic systems with embedded uncertainty and have a wide range of applications in science and engineering that make them useful. The present study is an attempt to obtain the numerical solutions of HFDEs through homotopy perturbation method (HPM). The convergence of the HPM to solve HFDEs is investigated in detail in this paper. In addition, the validity and efficiency of the proposed method is investigated and verified by several numerical examples. [ABSTRACT FROM AUTHOR]

Consider anmatrix polynomialand a setconsisting ofdistinct complex numbers. In this paper, a (weighted) spectral norm distance fromto the matrix polynomials whose spectra include the specified set, is defined and studied. An upper and a lower bound for this distance are obtained, and an optimal perturbation ofassociated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds. [ABSTRACT FROM PUBLISHER]