## Issue 4Volume 5 (2017)

ISSUE 4 − A ISSUE 4 − B ISSUE 4 − C ISSUE 4 − D ISSUE 4 − E ISSUE 4 − F
 Authors : B. K. Pedge and D. S. Palimkar Title : Three Point Boundary Value Problem for Random Differential Inclusions Volume, Issue, Year : 5(4−F)(2017) Pages : 809−813

Abstract: In this paper, we prove the existence of solution on a compact interval to a-three-point boundary value problem for a class of second order random differential inclusions. We shall employees random fixed point theorem for condensing maps due to Martelli.

Keywords: Three point boundary value problems, random differential inclusion, random fixed point.

 Authors : S. S. Hambarde and D. S. Palimkar Title : Existence of Solution for Functional Random Differential Equation Volume, Issue, Year : 5(4−F)(2017) Pages : 815−820

Abstract: In this paper, we discuss the existence of solution for functional random differential equation under caratheodory, compactness and monotonic conditions. Here, we shall employees random fixed point theorem of Dhage.

Keywords: Random functional differential equation, random fixed point theorem, caratheodory condition.

 Authors : R.Uma, P.Murugadas and S.Sriram Title : The Determinant and Adjoint of Fuzzy Neutrosophic Soft Matrices Volume, Issue, Year : 5(4−F)(2017) Pages : 821−833

Abstract: In this paper, we have introduced the determinant and adjoint of a square Fuzzy Neutrosophic Soft Matrices (FNSMs). Also we define the circular FNSM and study some relations on square FNSM such as reflexivity, transitivity and circularity.

Keywords: Fuzzy Neutrosophic Soft Set, Fuzzy Neutrosophic Soft Matrix, Determinant of a square FNSM, Adjoint of a square FNSM.

 Authors : Abdul-Qawe Kaed and Salem Abdullah Basardah Title : New Properties of Almost Finitely Cogenerated Module and New Result Volume, Issue, Year : 5(4−F)(2017) Pages : 835−838

Abstract: In \cite{ER13} The concept of almost finitely cogenerated is introduced and studied with some properties of it. recall that: Let $R$ be a ring with identity. An $R$-module $M$ is called almost finitely cogenerated if $M$ is not finitely cogenerated but every factor of $M$ is finitely cogenerated. In this paper we will introduce and study New properties of the almost finitely cogenerated $R$-module and prove a new result of it.

Keywords: A finitely cogenerated module, Almost finitely cogenerated module, A Hopfian module, A Co-Hopfian module.

 Authors : Manju Somanath, J. Kannan and K. Raja Title : On Polynomial Solutions of Quadratic Diophantine Equation Volume, Issue, Year : 5(4−F)(2017) Pages : 839−844

Abstract: Let $P:= P(t)$ be a polynomial in $Z\left[X\right]$. In this paper, we consider the polynomial solutions of Diophantine Equation $D:x^2-6y^2-10x+24y=0$. We also obtain some formulae and recurrence relations on the Polynomial solution $(x_n, y_n)$ of $D$.

Keywords: Diophantine equation, Polynomial solution, Pell・s equation, Continued fraction expansion.

 Authors : A.K.Bincy and B.Jeba Presitha Title : Graph Coloring and its Real Time Applications an Overview Volume, Issue, Year : 5(4−F)(2017) Pages : 845−849

Abstract: Graph coloring is one of the most important concepts in graph theory and it has huge number of applications in daily life. Various coloring methods are available and can be used on requirement basis. The proper coloring of a graph G is the coloring of the vertices and edges with minimal number of colors such that no two vertices should have the same color. The minimum number of color is called the chromatic number $\chi(G)$ and the graph \textit{G} is called properly colored graph. This paper presents the applications of graph coloring and its importance in various fields.

Keywords: Chromatic number $\chi(G)$, Edge coloring, Vertex coloring.

 Authors : G. Uthra, K. Thangavelu and P. Kannagi Title : Intuitionistic Fuzzy Replacement Problem with Change in Money Value Volume, Issue, Year : 5(4−F)(2017) Pages : 851−856

Abstract: Due to lack of accuracy or fluctuation in collected data, often it is too difficult to evaluate the precise value, especially in the continuous degradation element or system. To overcome this challenge, fuzzy set theory is employed to assess the performance. In this paper, the imprecise costs of the replacement problem, whose money value changes with time are taken as Triangular Intuitionistic Fuzzy Numbers (TIFN). A method is proposed to find the optimum replacement time and the effectiveness of the same is illustrated by an example.

Keywords: Intuitionistic Fuzzy Set, Triangular intuitionistic fuzzy number, intuitionistic fuzzy replacement problem.

 Authors : R. Pradeep Kumar, D. Soner Nandappa and M. R. Rajesh Kanna Title : Minimum Dominating Partition Energy of a Graph Volume, Issue, Year : 5(4−F)(2017) Pages : 857−865

Abstract: In this paper we compute minimum dominating partition energies of a star graph, complete graph, crown graph and cocktail party graphs. We also establish upper and lower bounds for minimum dominating partition energy $PE_{D}(G)$ of a graph $G$.

Keywords: Minimum dominating set, Minimum dominating partition matrix, Minimum dominating partition eigenvalues, Minimum dominating partition energy of a graph.

 Authors : R. Rathika, S. Subramanian and R. Balakumar Title : Age Group of Men Medical Representatives Affected by Stress in Pharmaceutical Company in Thanjavur and Kumbakonam City of Tamil Nadu Using Intuitionistic Fuzzy Soft Matrix Volume, Issue, Year : 5(4−F)(2017) Pages : 867−874

Abstract: The Paper Comprises of a case study which is done on men medical representatives in the age group of 25 to 58 years. Stress is a most persisting factor in professional and modern life. It is a natural and unavoidable feature of life experienced at one time or another by the vast majority of those engaged in professional work. Our objective of this paper to find out the peak age of men medical representatives gets stress in Thanjavur and Kumbakonam workers. For that we have studied the job stress among men workers. It has been classified into seven symptoms as don't sleep well, Muscle pain, frequent headache, Restlessness, Hair loss, Stomach pain, Wake-up tried. The concept of Intuitionistic fuzzy soft Matrix is applied to identify the age group of men medical representatives (based on age) worst affected.

Keywords: Soft Set, Fuzzy soft set, Intuitionistic Fuzzy soft set, Intuitionistic fuzzy soft Matrix.

 Authors : K.Dhurai and A.Karpagam Title : New Membership Function and New Ranking Function on Heptagon Fuzzy Number Volume, Issue, Year : 5(4−F)(2017) Pages : 875−878

Abstract: The Fuzzy set theory has been applied in many fields such as management, Engineering etc. In this paper, a new membership function and new ranking function introduce on Heptagon fuzzy number and a new ranking method based on heptagon fuzzy numbers used to a Travelling Salesman problems.

Keywords: Membership function, Ranking Function, Heptagon Fuzzy numbers, Travelling Salesman problem.

 Authors : Manju Sharma and Rajvir Singh Title : Study of Retrial Chain with Non Continued Clients Along with Orbital Search Volume, Issue, Year : 5(4−F)(2017) Pages : 879−891

Abstract: In this paper, we expand the search approach to a syntactically complicated alone server retrial queueing specimen with non consistent clients. We account a retrial queueing prototype with circular search in which an identifying subscriber after some failed retrials allocates up further repetitions as well as abdicates the mechanism (Almasi, \cite{1}). Let $I_{p}$ be the liability that after the pth approach fails, a consumer will make the $(p+1)^{th}$ one. The set of chances $(p+1)^{th}$ is labeled the persistence exercise. We assume that the chance of a call restarts after downfall of a duplicate attempt, does not depend on the count of previous attempts (i.e., $I_{2} = I_{3}= \dots$) algebraic calculations in telephone networks display that this is a realistic accumulation in conduct to such networks. One consequential characteristic of the model below consideration is that, for frequent difficulties, the cases $I_{2}<1$ and $I_{2}<1$ yield centrally asymmetric acquisitions. The case $I_{2} = 1$ can be examined in complete detail whiles the case $I_{2}<1$ is far more complex along with sealed form acquisition is attainable only for exponential service time distribution (Wang et. al., \cite{2}). This paper is arranged as succeeds. In section 2, we explain the algebraic prototype: For the cases $I_{2} = 1$, the simulation is examined in full assembly in section 3. In section 3.1, consistency clause is derived along with in 3.2, the bounding detachment of the mechanism state is acquired based on the supplementary-variable approach. The architecture of the active duration as well as its assertion in clauses of Laplace adapts have been consulted in 3.4 In section 3.5, we assign a direct procedure of algorithm for the first along with second circumstances attendant the busy time. In section 4, the case $I_{2}<1$ is counted along with the locked form solution is acquired for the exponential sustenance time separation in conditions of hyper geometric series. In section 4, we demonstrate many numerical examples to demonstrate the effect of the guidelines on the mechanism activity.

Keywords: Retrial chain, non continued clients, complex retrial.

 Authors : M. Kavitha, P. Murugadas and S. Sriram Title : Computing the Greatest X-eigenvector of Fuzzy Neutrosophic Soft Matrix Volume, Issue, Year : 5(4−F)(2017) Pages : 893−907

Abstract: A Fuzzy Neutrosophic Soft Vector(FNSV) x is said to be a Fuzzy Neutrosophic Soft Eigenvector(FNSEv) of a square max-min Fuzzy Neutrosophic Soft Matrix (FNSM) A if $A\otimes x=x$. A FNSEv x of A is called the greatest X-FNSEv of A if $x \in X=\{x:\underline{x}\leq x\leq \overline{x}\}$ and $y\leq x$ for each FNSEv $y\in X$. A max-min FNSM A is called strongly X-robust if the orbit $x,A \otimes x,A^{2}\otimes x,...$ reaches the greatest X-FNSEv with any starting FNSV of X. We suggest an $O(n^{3})$ algorithm for computing the greatest X-FNSEv of A and study the strong X-robustness. The necessary and sufficient condition for strong X-robustness are introduced and an efficient algarithm for verifying these conditions is described.

Keywords: Fuzzy Neutrosophic Soft Set (FNSS), Fuzzy Neutrosophic Soft Matrices(FNSMs), Fuzzy Neutrosophic Soft Eigenvectors(FNSEv), Interval vector, max-min Fuzzy Neutrosophic Soft Matrix(FNSM).

 Authors : J. Paulraj Joseph and N. Shunmugapriya Title : Total Resolving Number of Power Graphs Volume, Issue, Year : 5(4−F)(2017) Pages : 909−913

Abstract: Let $G = (V, E)$ be a simple connected graph. An ordered subset $W$ of $V$ is said to be a resolving set of $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $W.$ The minimum cardinality of a resolving set is called the \textit{resolving number} of $G$ and is denoted by $r(G).$ As an extension, the total resolving number was introduced in \cite{F} as the minimum cardinality taken over all resolving sets in which $\left\langle W \right\rangle$ has no isolates and it is denoted by $tr(G).$ In this paper, we obtain the bounds on the total resolving number of power graphs. Also, we characterize the extremal graphs.

Keywords: Resolving number, total resolving number, power graph.

 Authors : P. Jayalakshmi and N. Ramya Priya Title : Homeomorphism of Fuzzy Topological Graph Volume, Issue, Year : 5(4−F)(2017) Pages : 915−922

Abstract: This paper provides solid theoretical foundation for studying Fuzzy Topological Graph theory. The concepts such as subdivision, homeomorphism and connectedness of a fuzzy topological graph is established. In addition to this an attempt is made to study about planar and minimal non planar fuzzy topological graphs. These concepts are illustrated through examples.

Keywords: Homeomorphism, Fuzzy Topological Graph, Subdivision, Planar Fuzzy Topological Graph, Minimal Non Planar Fuzzy Topological Graph, Connectedness of Fuzzy Topological Graph.

 Authors : K.K.M. Sarma and Yohannes Gebru Title : Fixed Point Theorems for Generalized $(\psi,\phi)$-contractive Mappings in a Complete Strong Fuzzy Metric Space Volume, Issue, Year : 5(4−F)(2017) Pages : 923−938

Abstract: In this paper, we introduce generalized $(\psi,\phi)$-contractive mapping in strong fuzzy metric spaces and prove fixed point theorems to this class of maps. Further we introduce a generalized $(\psi,\phi)$-contractive mapping $f$ with respect a mapping $g$ and prove common fixed point theorems. We provide examples in support of our results.

Keywords: Strong fuzzzy metric space, generalized $(\psi,\phi)-$contractive mappings, generalized $(\psi,\phi)-$ contractive for a pair of mappings.

 Authors : Lakhan Nagar, Pradeep Porwal, V.K. Gupta and S.K. Tiwari Title : A Tuberculosis Mathematical Model with Infected Population and Vaccination Volume, Issue, Year : 5(4−F)(2017) Pages : 939−943

Abstract: Tuberculosis is an infectious disease that usually affects the lungs. World Health Organization has declared that tuberculosis Disease can cause global warming. So, TB must be solved especially in prediction and vaccination. In this model the infected population is divided into two groups, namely infectious infected and noninfectious infected population. This paper explains about the equilibrium point, and analyzing the stability model.

Keywords: Basic reproduction number, vaccination, tuberculosis, stability.

 Authors : S. Anjalmose, G. Thangaraj and R. Kanimozhi Title : Some Remarks on Fuzzy Hausdorf spaces Volume, Issue, Year : 5(4−F)(2017) Pages : 945−950

Abstract: In this paper the concept of fuzzy Hausdorf space are studied. Several properties and examples of fuzzy Hausdorf space are given to illustrate the concept and relations between fuzzy hausdorf space and some fuzzy topological spaces are discussed.

Keywords: Fuzzy open, fuzzy dense, fuzzy nowhere dense, fuzzy first category, fuzzy Hausdorf space, fuzzy Baire space, fuzzy D-Baire space and fuzzy $D^{\prime}$-Baire space.

 Authors : P.V. Jain and Kusumlata Rajak Title : $f\omega \alpha-$Continuous Maps in Fine-Topological Spaces Volume, Issue, Year : 5(4−F)(2017) Pages : 951−957

Abstract: In the present paper, we have introduced a new class of continuous functions called $f\alpha g -$continuous maps, $fgp-$continuous, strongly $fg-$continuous, $fg-$closed, $f\omega \alpha -$ closed, pre-$f\alpha -$closed etc. Also we have introduced a new class of maps pre-$f\omega \alpha -$continuous, $f\omega \alpha$ -continuous maps, $f\omega \alpha -$irresolute, $f\omega$ -irresolute maps, $f\omega \alpha -$irresolute homeomorphism and studied some properties of these functions.

Keywords: $\omega \alpha -$closed set, $\omega \alpha -$open set, $\omega \alpha -$continuous, $\omega \alpha -$irresolute and fine-irresolute map.

 Authors : P. Priyadharsini and A. Parvathi Title : Tri-b-Continuous Function in Tri Topological Spaces Volume, Issue, Year : 5(4−F)(2017) Pages : 959−962

Abstract: The purpose of this paper is to study the properties of tri-b open sets and tri-b closed sets and introduce tri-b continuous functions in tri topological spaces.

Keywords: Tri topological spaces, tri-b open sets, tri-b interior, tri-b closure, tri-b continuous function.

 Authors : Berhanu Assaye, Mihret Alamneh and Tilahun Mekonnen Title : Autometrized Implicative Almost Distributive Lattices Volume, Issue, Year : 5(4−F)(2017) Pages : 963−970

Abstract: In this paper,we introduce two binary operations + and $-$ on an IADL and we obtain few results concerning the operation defined.We introduce a binary operation * on IADL L and prove that (L, *) is a metric space. We introduce the concept of Autometrized Implicative Almost Distributive Lattices(AIADLs)as extension of Autometrized algebra in the class of Almost Distributive Lattices and also regular autometrized IADL. We discuss some theorems of AIADL L and show that * on L is not a group operation.

Keywords: Almost Distributive Lattice, Implicative Algebras, Implicative Almost Distributive lattice, Autometrized Algebra, Regular Autometrized Algebra, Autometrized Implicative Almost Distributive and Regular Autometrized Implicative Almost Distributive Lattice.

 Authors : K. Kaliraj Title : Equitable Edge Coloring of Some Join Graphs Volume, Issue, Year : 5(4−F)(2017) Pages : 971−975

Abstract: The notion of equitable coloring was introduced by Meyer in $1973$. Let $G\left(V,E\right)$ be a graph. For $k-$proper edge coloring $f$ of graph $G$, if $\left|\left|E_i\right|-\left|E_j\right|\right|\leq 1,$ $i, j=0,1,2,\cdots k-1$, where $E_i\left(G\right)$ is the set of edges of color $i$ in $G$, then $f$ is called a $k-$equitable edge coloring of graph $G$, and $\chi_e^\prime\left(G\right)=\min \{k|$ there is a k equitable edge-coloring of graph G$\}$ is called the equitable edge chromatic number of $G$. In this paper, we obtain the equitable edge chromatic number of the join graph of $P_l\vee K_{m,n}$ and $P_m\vee K_{1,n,n}$.

Keywords: Equitable edge coloring, Join graph, Path, Complete bipartite and double star graph.

 Authors : R.Anbuselvi and K.Usha Title : On Ternary Quadratic Diophantine Equation $z^2=40x^2+y^2$ Volume, Issue, Year : 5(4−F)(2017) Pages : 977−983

Abstract: The Ternary Quadratic Diophantine equation $z^2=40x^2+y^2$ is analyzed for its non-zero distinct integral points on it. A few interesting properties among the solutions are presented.

Keywords: Integral points, Ternary quadratic, Polygonal numbers, Pyramidal numbers and special numbers.

 Authors : S. Sridevi and K. Gunasekaran Title : On Schur Complements in Range Quaternion Hermitian Matrices Volume, Issue, Year : 5(4−F)(2017) Pages : 985−991

Abstract: It is established that under contain conditions a schur complement in a q-EP matrix is as well as q-EP matrix. As an application a decomposition of a partitioned matrix into a sum of q-EP matrices is given.

Keywords: q-EP matrix, Schur Complement in q-EP, Complementary summands of q-EP.

 Authors : R. Anandhi and P. Priya Title : A Comparison of Triangular Fuzzy Numbers and Intuitionistic Triangular Fuzzy Numbers Using Apex Base Least Cost Method Volume, Issue, Year : 5(4−F)(2017) Pages : 993−997

Abstract: The transportation model is a special class of the linear programming problem. In real world problems, optimization techniques are useful for solving problems like, project schedules, assignment problems and network flow analysis. The objective is to minimize the transportation cost of some commodities through a capacitated network when the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers. Here, we are proposed for solving fuzzy transportation problem, where fuzzy demand and supply all are in the form of triangular fuzzy numbers and Intuitionistic triangular fuzzy numbers. In this paper a new method is ABLC for finding an optimal solution for a wide range of fuzzy transportation problem. This method is very easy to understand and use compared to other methods. A numerical example is solved using the proposed algorithm.

Keywords: Triangular Fuzzy number, Intuitionistic triangular fuzzy number, Initial Basic Feasible Solution, Apex and Base Angles, Least adjust cost method.

 Authors : D.Radhika, S.Pious Missier and S.Jackson Title : Fuzzy Matrix Analysis in Aqua Culture Volume, Issue, Year : 5(4−F)(2017) Pages : 999−1005

Abstract: Fuzziness is a fruitful concept introduced by Zadeh to eradicate the vagueness arising in quite common datas of real world problems. It has been found extensive applications in the field of Decision making.Aquaculture is a fast developing industry with great focus on feeding behavior. This paper is devoted to choose the appropriate feed, in which the uncertain information gathered by experimentally using Azolla microphyla as a feed to the fishes Cyprinus Carpio, analysed using Fuzzy Matrices. Using the concept of ATD, RTD, CETD fuzzy matrices the best feed level is decided for the fish Cyprinus Carpio.

Keywords: Azolla microphylla, ATD, RTD, CETD, Decision making, Cyprinus Carpio.