In this work, firstly we introduce the new information divergence measure, characterize it and get the mathematical relations with other divergences. Further, we introduce new information inequalities on the new generalized f- divergence measure in terms of the well-known one parametric generalized divergence. Further, we obtain bounds of the new divergence and the Relative J- divergence as an application of new information inequalities by using Logarithmic power mean and Identric mean, together with numerical verification by taking two discrete probability distributions: Binomial and Poisson. Approximate relations of the new divergence and Relative J- divergence with Chi- square divergence, have been obtained respectively.

The paper discusses fuzzy real and complex linear equations and system of linear equations with coefficients as crisp and the right-hand side as generalized trapezoidal fuzzy number where fuzzy numbers have been represented with mean and semi width. We have solved each case by using the concept of Strong and Weak solution with numerical examples.

Different scholars in the world design wide varieties of systems for automatic face recognition process. The face recognition process is dependent on different variables, such as the illumination and the different poses of the image. Therefore, face recognition process is still a fundamental issue in image processing. In this paper, we have developed a new method for face recognition based on ant colony algorithm. To assess the performance and effectiveness of the designed system, face images available in ORL database are used. The results obtained indicate that the proposed method for face recognition accuracy is about 97.3 percent. Besides, comparisons indicate that the performance of the proposed method compared to other methods enjoys a remarkable accuracy.

A Farsi font recognition algorithm based on the fonts of some frequent text samples is proposed. Some features are extracted from the connected components of a text image. The feature vectors are clustered by using a Self-Organizing Map (SOM) clustering method. The clusters with more members determine the most frequent connected components (MFCCs). A number of members of these big clusters are extracted from the input image. This procedure is applied to both training and test images. Since the frequent samples in different Farsi texts are very similar, it can be guaranteed that a large number of samples of the detected MFCCs for a test image surely are in the extracted training samples set. The font type and font style of the extracted test samples are recognized by matching between them and the training samples. The most frequent recognized font of the extracted samples is considered as the font of the input text. To achieve a more accurate algorithm with lower complexity, the font size is determined in the second phase after the phase of the font type and style recognition. Using a lexicon reduction procedure reduces the complexities and processing time. The font size estimation is carried out based on the size of a particular MFCC in a text image. Experiments show that the proposed method outperforms other font recognition methods.

The present paper is devoted to the study of fuzzy soft grill structure. The notions of fuzzy soft grill and fuzzy soft grill base are defined and the connections between them are given. Two types of second order image and reimage of fuzzy soft grill base is defined and also some of their properties are observed.

Nowadays, mostly security solutions are mainly focused on how to defend against various threats, including insider threats and outsider threats, instead of trying to solve security issues from their sources. This paper proposes a security modeling process and an approach to modeling and quantifying component security based on Petri Nets (PN) in the software design phase. Security prediction in the design phase provides the possibility to investigate and compare different solutions to the target system before realization. The analysis results can be used to trace back to the critical part for security enhancing.

In this paper we introduces the new generalized difference sequences spaces \(\left[\hat{V}, \lambda, f, P\right]_0(\Delta^r_u,E), \left[\hat{V}, \lambda, f, P\right]_1(\Delta^r_u,E), \left[\hat{V}, \lambda, f, P\right]_{\infty}(\Delta^r_u,E), \hat{S}_\lambda(\Delta^r_u,E)\) and \(\hat{S}_{\lambda_0}(\Delta^r_u,E)\) (where \(E\) is any Banach space) which arise from the notion of generalized de la Vallée- Poussin means and the concept of modulus function. We also give some inclusion relations between these spaces.

In this paper, a brief description of finite automata and the class of problems that can be solved by such devices is presented. The main objective is to introduce the concept of length product, illustrate its application to finite automata, and prove some related results.