##### 2-Tuple Prioritized Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

Zhiming Zhang

Journal of Advances in Mathematics and Computer Science, Page 2278-2297
DOI: 10.9734/BJMCS/2014/10710

Aims: The aim of this paper is to present some 2-tuple prioritized aggregation operators for handling the multiple attribute group decision making problems where there exists a prioritization relationship over the attributes and decision makers.
Study Design: Motivated by the idea of the prioritized aggregation (PA) operators, we first develop two 2-tuple prioritized aggregation operators called the 2-tuple prioritized weighted average (2TPWA) operator and the 2-tuple prioritized weighted geometric (2TPWG) operator.
Place and Duration of Study: We examine their desirable properties.
Methodology: The significant feature of these operators is that they not only deal with the linguistic and interval linguistic information but also take the prioritization relationship among the arguments into account.
Results: Then, based on the proposed operators, we propose an approach to multiple attribute group decision making under linguistic environment in which the attributes and decision makers are in different priority level.
Conclusion: Finally, an illustrative example is employed to show the reasonableness and effectiveness of the proposed approach.

##### An Age-structured Model for the Spread of Buruli Ulcer: Analysis and Simulation in Ghana

Ebenezer Bonyah, Isaac Dontwi, Farai Nyabadza, Fatmawati .

Journal of Advances in Mathematics and Computer Science, Page 2298-2319
DOI: 10.9734/BJMCS/2014/10040

Despite the advances in medical research on its treatment and intensive public education on prevention and control, the Buruli ulcer (BU) continues to be a major public health problem that continues to overwhelm authorities in Ghana. Ghana is the second most endemic country after the Ivory Coast at the global level. While it is common knowledge in literature that the disease can affect people of all ages, the mode of transmission is still evasive. The studied model is expressed as a system of hyperbolic (first order) partial differential equations. We first, employ a representation from the method of characteristics and a fixed point argument and also prove the existence and uniqueness of solutions to the nonlinear system. We establish the mathematical well-posedness of the time evolution problem using the semigroup theory approach. We then determine the basic reproduction ratio R0. Then we present a numerical scheme to model the dynamics of BU. The simulation results showed that Mycobacterium ulcer has peak period of spread and reduced subsequently.

##### On Orthogonal Double Covers of Complete Bipartite Graphs by an Infinite Certain Graph-Path and Graph-Cycle

R. A. El-Shanawany

Journal of Advances in Mathematics and Computer Science, Page 2320-2325
DOI: 10.9734/BJMCS/2014/10724

Let F be a certain graph, the graph F-Path denoted by d+1(F) path of length d with d + 1 ver-tices (i.e. Every edge of this path is one-to-one corresponding to an isomorphic to the graph F). In the same manner, we define the graph F-Cycle as d(F) cycle on d vertices. In this paper, we construct orthogonal double covers (ODCs) of complete bipartite graph Kn,n by d+1(F) and d(F).

##### The Multi-fractal Spectrum Model for the Measurement of Random Behaviour of Asset Price Returns

Bright O. Osu, Joy I. Adindu-Dick

Journal of Advances in Mathematics and Computer Science, Page 2326-2343
DOI: 10.9734/BJMCS/2014/10971

To forecast the market risk, assessing the stock price indices is the foundation. Multi-fractal has lots of advantage when explaining the volatility of the stock prices. The asset price returns is a multi-period (multi-fractal dimension) market depending on market scenarios which are the measure points. This paper considers the multi-fractal spectrum model (MSM) to measure the random character of asset price returns, aimed at deriving the MSM version of the random behaviour of equity returns of the existing ones in literature. We investigate the rate of returns prior to market signals corresponding to the value for packing dimension in fractal dispersion of Hausdorff measure. Furthermore, we give some conditions which determine the equilibrium price, the future market price and the optimal trading strategy.

##### Multi-clustering Gives Robustness to Modules in Networks

Alain Guénoche

Journal of Advances in Mathematics and Computer Science, Page 2344-2351
DOI: 10.9734/BJMCS/2014/10472

Aims/ Objectives: A protein-protein interaction network is considered as a simple indirected graph, weighted or non weighted. A partition of the vertex set, into connected, eventually overlapping, clusters having an edge density larger than the whole graph, is searched. Such a cluster is denoted as a module. The cellular functionality of proteins is predicted from this network decomposition. To improve the prediction quality, we need to evaluate the robustness of these modules.

Methodology: We propose a new method which consists in: selecting a non deterministic algorithm for graph partitioning into separate clusters (optimizing a modularity criterion);  applying this algorithm several times to generate a set of close partitions; calculating a consensus partition from this set.

Results: This set of partitions permits to evaluate the robustness of any class as the average percentage of partitions joining any protein pair in this class. This robustness function can be applied to compare the consensus partition resulting of this procedure to the usually single partition computed from the graph. Then, we develop a simulation protocol selecting random graphs having a more or less strong community structure. We show that the multi-clustering method provides modules closer to the communities which are more robust than those of a single partition. Finally, we present a simple procedure to extend a strict partition into an overlapping class system, making multi assignment for proteins that could be placed equally into several modules, because their contributions to modularity are similar.

##### Positive Solutions of Singular Periodic Boundary Value Problems for Second Order Impulsive Differential Equations

Ying He

Journal of Advances in Mathematics and Computer Science, Page 2352-2360
DOI: 10.9734/BJMCS/2014/11628

This paper is devoted to study the existence of positive solutions for singular second-order periodic boundary value problem with impulse effects. Existence is established via the theory of fixed point theorem in cones.

##### On Summable Bases in Banach Spaces

Mangatiana A. Robderai

Journal of Advances in Mathematics and Computer Science, Page 2361-2372
DOI: 10.9734/BJMCS/2014/11589

We introduce the notion of summable bases that naturally generalizes the notion of unconditional sequence bases for Banach spaces. We shall be particularly interested in some classical results on sequences and series in separable Banach spaces that carry over or naturally extend to the case of non-separable Banach spaces.

##### On Continuity of Browder Type Fixed Points

Qi-Qing Song, Mengzhuo Luo

Journal of Advances in Mathematics and Computer Science, Page 2373-2380
DOI: 10.9734/BJMCS/2014/11216

To study the stability of Browder type fixed points, two kinds of usual metrics for set-valued mappings are discussed. Noting that the set of fixed points for a Browder type set-valued mapping may be noncompact, a metric is introduced to construct a complete metric space on a kind of these mappings. Some results for continuity of Browder type fixed points are obtained, and we prove that each fixed point for each Browder type set-valued mapping is essentially stable.

##### Tuba’s Representation of the Pure Braid Group on Three Strands

Noura Y. Maanna, Mohammad N. Abdulrahim

Journal of Advances in Mathematics and Computer Science, Page 2381-2402
DOI: 10.9734/BJMCS/2014/8776

We consider Tuba’s representation of the pure braid group, P3, defined by the map Ψ: P3GL(V ), where V is an algebraically closed field. We then specialize the indeterminates used in defining the representation to non- zero complex numbers. Our objective is to find necessary and sufficient conditions that guarantee the irreducibility of Tuba’s representations of the pure braid group P3 with dimensions d = 2 and d = 3.

##### Image Enhancement Methods: A Review

Gabriel Babatunde Iwasokun, Oluwole Charles Akinyokun

Journal of Advances in Mathematics and Computer Science, Page 2251-2277
DOI: 10.9734/BJMCS/2014/10332

Image processing is faced with a number of challenges ranging from unequal resolutions, format variations, non uniform illuminations, distortions and noise. It is also affected by orientation and contrast differences. In view of these challenges, most digital image processing applications or devices employ enhancement procedure prior to the use of the captured image for intended purposes. This paper reports on the review of some of the existing digital image enhancement methods with emphasis on methodologies, strengths, limitations and application areas. The specific application of some of these methods by different authors is also presented.