##### The Classification of Alternatives Based a Multi-criteria Analysis Technique and the Combination of AHP and the Weighted Sum

Chaibi Ghizlane, El Khomssi Mohammed

Journal of Advances in Mathematics and Computer Science, Page 1-18
DOI: 10.9734/BJMCS/2016/23247

The difficulty of the methods of decision aid is what seeking optimal solutions to complex problems in general and for nature multicriteria, or the concept of optimality is no sense in a multicriteria context.

In this paper, we propose a mathematical modelling, in the context of multicriteria multi- decision-makers aid methods, with a decision-making process allowing the decision-makers to choose the most appropriate solutions according to their orientations, an independent manner, taking into account the objective of the problem.

After identifying the objective and determining the set of actions, we decompose the objective to different dimensions, which gives a system of criteria to different levels.

We use the principle of the AHP method to calculate different weight, related to our decomposition.  Also the weighted sums method helps us transform the multi-criteria problem to a mono criterion problem, and obtain a mathematical expression of actions evaluation on which each decision maker bases to choose the optimal action. Therefore, we get a partial order of potential actions on each dimension, and a global order examining all the criteria of the studied system. Which allows to mathematically judge the selection of an action rather than another.

Finally, we start with the data of the company Rabat-Sale tramway and apply the proposed process to judge the choice of the tram as a means of transport instead of the bus.

This is a concrete example of large financial size showing the effectiveness of our proposal.

##### Global Attractivity and Almost Periodic Solution of a Discrete Multispecies Lotka-Volterra Mutualism System with Feedback Controls

Hui Zhang

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/23336

In this paper, we consider an almost periodic discrete multispecies Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result.

##### Adomain Sumudu Transform Method for the Blasius Equation

O. M. Ogunlaran, H. Sagay-Yusuf

Journal of Advances in Mathematics and Computer Science, Page 1-8
DOI: 10.9734/BJMCS/2016/23104

This paper presents a new method namely, Adomain Sumudu Transform Method, a coupling of the Sumudu transform and Adomain decomposition method, for handling a differential equation of mixing layer that arises in viscous incompressible fluid. In order to apply the condition at infinity, we converted the obtained series solution into rational function by using Padé approximant.

##### A Distance Measure Based on Fuzzy D-implications: Application in Pattern Recognition

A. G. Hatzimichailidis, G. A. Papakostas, V. G. Kaburlasos

Journal of Advances in Mathematics and Computer Science, Page 1-14
DOI: 10.9734/BJMCS/2016/23993

A new distance measure between fuzzy sets (FSs) based on fuzzy D-implications is introduced in this paper. The proposed measure uses a matrix representation of each set in order to encode its information, where matrix norms in conjunction with fuzzy D-implications can be applied to measure the distance between the two FSs. It is worth noting that the applied technique in deriving the proposed measure gives the flexibility to construct several distance measures by incorporating different fuzzy implications, extending its applicability to several applications where the most appropriate implication is used. Apart from the analysis in constructing a D-implication based distance measure, a detailed discussion of its main properties is also presented. Moreover, an appropriate set of experiments has taken place in order to examine the performance of the proposed distance compared to well-known fuzzy implications, in some pattern classification problems from the literature. The corresponding results are promising and show that the proposed measure can classify the patterns correctly and with high degree of confidence.

##### Using Arabic Skeleton Morphology and Maximum Entropy for Arabic Document Classification

O. G. El-Barbary

Journal of Advances in Mathematics and Computer Science, Page 1-9
DOI: 10.9734/BJMCS/2016/23055

The morphology of Arabic plays an important role of computational natural language processing systems. The rich morphology, and the complexity of word formation all contribute to making morphological approaches to Arabic very challenging. In this paper, we present a new method for Arabic document classification using maximum entropy and morphological derivation of Arabic words. In this paper, maximum entropy and Arabic word derivative morphology for text classification by estimating the conditional distribution of the class variable given the document.  Using these derivatives we can find a related words in the document which contains words and its derivatives. The proposed approach is designed for vowel and unvowel Arabic document.

##### Performance Evaluation of an Improved Self-organizing Feature Map and Modified Counter Propagation Network in Face Recognition

I. A. Adeyanju, O. O. Awodoye, E. O. Omidiora

Journal of Advances in Mathematics and Computer Science, Page 1-12
DOI: 10.9734/BJMCS/2016/22588

Aim: To carry out performance evaluation of an Improved Self-Organizing Feature Map (SOFM) and Modified Counter Propagation Network (CPN) techniques in face recognition. These two techniques were examined, implemented and evaluated by using metrics such as recognition accuracy, sensitivity and computation time.

Problem/Study Design: In lieu of threat to global peace and criminal activities in our society today, it is then imperative to adopt a non-linear techniques that might improve the recognition performance of face recognition system because of their intrinsic characteristics. A comprehensive evaluation of these two selected artificial neural network techniques was performed to address these challenges and to estimate the preferred technique that had manifested an improved system.

Place and Duration of Study: Ladoke Akintola University of Technology (LAUTECH), Ogbomoso, Nigeria and was done during the period of the Master Study.

Methodology: An Africa database of 240 face images was created by capturing six face images from 40 persons with a digital camera. Image pre-processing was carried out using MATLAB and normalized using local histogram equalization for contrast enhancement. Principal Component Analysis (PCA) was used to extract distinctive features and reduce the dimensionality of each image from 600 x 800 pixels to four different dimensions; 50 x 50, 100 x 100, 150 x 150 and 200 x 200 pixels. SOFM and CPN techniques were used as classifiers for face recognition then evaluated using 140 images for training and 100 images for testing with best selected similarity threshold value. The two techniques were evaluated using recognition accuracy and computation time as performance metrics.

Results: The results of evaluation showed that, at 50 x 50 pixels, SOFM had 81% accuracy with computation time of 243 s while CPN gave 84% accuracy in a time of 174 s. Correspondingly, at 100 x 100 pixels, SOFM had 83% accuracy with a time of 244s whereas CPN had 88% accuracy with a time of 179 s. Similarly, at 150 x 150 pixels, SOFM gave accuracy of 87% with a time of 245 s while CPN generated 90% accuracy with a time of 190s. Furthermore, at 200 x 200 pixels, SOFM resulted in accuracy of 92% with a time of 249 s, however, CPN had 95% accuracy with computation time of 234 s respectively.

Conclusion: This research has shown that CPN outperformed SOFM techniques in face recognition based on recognition accuracy and computational time.

##### Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iteration Procedure

B. M. Ikramul Haque, M. M. Ayub Hossain, Md. Bayezid Bostami, Md. Rakib Hossain

Journal of Advances in Mathematics and Computer Science, Page 1-7
DOI: 10.9734/BJMCS/2016/23263

Solution of the nonlinear singular oscillator has been obtained based on an iteration procedure. Here we have used a simple technique and taking a truncated Fourier series to determine the approximate analytic solution of the oscillator. The percentage of error between exact frequency and the third approximate frequency obtained by the adopted technique is as low as 0.696%. That is the third approximate frequency of the nonlinear singular oscillator shows a good agreement with its exact value. The convergent rate is high compared to other existing results. The modified technique introduces hopeful contrivance for many nonlinear oscillators.