## Issue 4Volume 4 (2016)

ISSUE 4 Special Issue
• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : Generalized Hyers - Ulam Stability of Additive - Quadratic - Cubic - Quartic Functional Equation in Fuzzy Normed Spaces: A Direct Method Country : India Authors : M.Arunkumar and C.Devi Shyamala Mary

Abstract: In this paper, the authors investigate the generalized Hyers-Ulam-stability of AQCQ functional equation \begin{align*} f(x+2y)+f(x-2y)=4f(x+y)-4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) \end{align*} in fuzzy normed spaces using direct method.

Keywords: Fuzzy normed space, Additive, quadratic, cubic and quartic functional equation, Generalized Hyers-Ulam-Rassias stability.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : Generalized Hyers - Ulam Stability of Additive - Quadratic - Cubic - Quartic Functional Equation in Fuzzy Normed Spaces Using Fixed Point Method Country : India Authors : M.Arunkumar and C.Devi Shyamala Mary

Abstract: In this paper, the authors investigate the generalized Hyers-Ulam-stability of AQCQ functional equation \begin{align*} f(x+2y)+f(x-2y)=4f(x+y)-4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) \end{align*} in fuzzy normed spaces using fixed point method.

Keywords: Fuzzy normed space, Additive, quadratic, cubic and quartic functional equation, Generalized Hyers-Ulam-Rassias stability.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : Solution and Stability of a Functional Equation Originating From Consecutive Terms of a Geometric Progression Country : India Authors : M.Arunkumar, E.Sathya and T.Namachivayam

Abstract: In this paper, the author has proved the generalized Ulam-Hyers stability of a new type of the functional equation \begin{align*} \ell(uv)+\displaystyle{\ell\left(\frac{u}{v}\right)}=2\ell(u) \end{align*} with $v \ne 0$ which is originating from consecutive terms of a geometric progression. An application of this functional equation is also studied.

Keywords: Logarithmic functional equations, generalized Ulam- Hyers stability.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : Stability of a 2 - Variable AC - Mixed Type Functional Equation in Paranormed Spaces: Direct and Fixed Point Methods Country : India Authors : M.Arunkumar, John M.Rassias, S.Murthy and M.Arulselvan

Abstract: In this paper, authors established the generalized Ulam - Hyers stability of a 2 - variable AC - mixed type functional equation \begin{align*} f(2x+y, 2z+w) - f(2x-y, 2z-w)= 4[f(x+y, z+w) - f(x-y, z-w)]- 6f(y, w) \end{align*} in paranormed spaces using direct and fixed point methods.

Keywords: Additive functional equations, cubic functional equation, Mixed type AC functional equation, Ulam - Hyers stability, Paranormed space.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Disease Control in Eco-epidemic Prey-Predator Model: An Algebraic Study on Alternative Food Mechanism in Predator Country : India Authors : K.Sujatha and M.Gunasekaran

Abstract: In this paper, the complex dynamic behavior of a discrete time non-linear mathematical prey -- predator model with a disease in the prey population is analyzed. The existence, the boundedness and the stability of equilibrium points are studied algebraically. The main objective of this work is to provide a mathematical framework to study the response of a prey -- predator model to a disease in the prey population and to understand the role of supplying alternative food to predator as disease controller in the eco-epidemiological system.

Keywords: Mathematical modelling, Infected prey, Alternative food, stability, eco-epidemiology.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : The Dominator Coloring of Central and Middle Graph of Some Special Graphs Country : India Authors : J.Arockia Aruldoss and G.Gurulakshmi

Abstract: Let $G = (V, E)$ be an undirected graph. A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates every vertex of at least one color class. The convention is that if $\{V\}$ is a color class then V dominates the color class $\{V\}$. The Dominator Chromatic number $\chi_{d}(G)$ is the minimum number of colors required for a dominator coloring of G. Here we investigate the Dominator Chromatic number of middle and central graph of Tadpole graph and Snake graph.

Keywords: Proper coloring, Dominator coloring, Dominator Chromatic number, Middle graph , Central graph, Tadpole graph and snake graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Fundamental Operation of Differential Transformation Method Country : India Authors : T.Henson and G.Arunagiri

Abstract: This study deals about the application with fundamental operation of differential transformation method and is used to find the approximate solution for SIR model. SIR model are nonlinear system with fundamental operation of ordinary differential equation that has no analytic solution. DTM uses the fundamental operations of differential transformation function of the original nonlinear system. The result reveals that this method is accurate and efficient for solving systems of ordinary differential equations.

Keywords: Fundamental operations of differential transformation method, Epidemiology and SIR model.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : A Comparative Study on the Teaching Methods in Schools Using Similarity Measures on Fuzzy Soft Sets Country : India Authors : S.Johnson Savarimuthu and A.Esther Joicy

Abstract: In this paper, we have made decision making using the concept of Similarity measures between two Fuzzy soft sets. There are three types of Similarity measures namely Similarity measure based on (i) set theoretic approach (ii) matching function and (iii) distance. We have applied the Similarity measure based on set theoretic approach and matching function to compare the different teaching methods in schools. We have made decision making on the best teaching method with respect to few attributes.

Keywords: Fuzzy soft sets, Similarity measures, teaching methods and decision making.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
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• Corresponding Autho r
 Article Type : Research Article Title : Dominator Chromatic Number, Bondage Number and Domatic Number of Some Named Graphs Country : India Authors : J.Arockia Aruldoss and G.Gurulakshmi

Abstract: Let $G = (V,E)$ be an undirected graph. A dominator coloring of a graph G is a proper coloring in which every vertex of G dominates each vertex of at least one color class. The Dominator chromatic number $\chi_{d}(G)$ is the minimum number of colors required for a dominator coloring of G. In this paper, we found the Dominator chromatic number, Bondage number and Domatic number of some named graphs.

Keywords: Proper coloring, Dominator coloring, Dominator Chromatic number, Bondage number, Domatic number, Fruncht graph, Herschel graph, Wagner graph, Moser Spindle graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : On 3-Rainbow Domination Number of Silicate Network Country : India Authors : L.Jethruth Emelda Mary and A.Isabeline

Abstract: Given an undirected graph $G=(V, E)$ and a set of k-colors numbered 1,2{\dots},k. The 3-rainbow domination defined as $f : V(G)\to \mathcal{þ}\{1,2,3\}$ such that for each vertex $v \in V(G)$ with $f(v)=\emptyset$. We have, $\bigcup_{u\in N(v)}{f\left(u\right)=\{1,2,3\}}$ Such a function f is called a 3-rainbow dominating function (3RDF) and minimum weight of such function is called the 3-rainbow domination number of G and is denoted by ${\gamma}_{r3}(G)$. In this paper we find the 3-rainbow domination number of interconnection network.

Keywords: Domination number, 3-rainbow domination number, Interconnection network, silicate network.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : The b-Chromatic Number of Central Graph of Some Special Graphs Country : India Authors : Jethruth Emelda Maryl and Kavithaa

Abstract: Let $G= (V, E)$ be an undirected and loopless graph. The b- chromatic number of a graph G is the largest integer k such that G admits a proper k- coloring in which every color class contains atleast one vertex adjacent to some vertex in all the other color classes .In this paper we investigate the b-chromatic number of central graph of cycle, path, snake, wheel, helm and denoted as C(C${}_{n}$), C(P${}_{n}$), C(T${}_{n}$), C(W${}_{n}$) and C(H${}_{n}$) respectively.

Keywords: Proper coloring, Chromatic number, b-Coloring, b-Chromatic number, central graph, cycle, path, snake, wheel and helm.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : The B-Chromaticnumber, Bondage Number and Connected Domination Number of Some Special Graphs Country : India Authors : Jethruth Emelda Maryl and Kavithaa

Abstract: Let $G= (V, E)$ be an undirected and loopless graph. In this paper we determinedtherelationship for b-chromatic number, bondage number and connected domination numberfor Barbell graph, Harary graph, Book graph,Grotzsch graph, Wagner graph respectively.

Keywords: Proper coloring, Chromatic number, b-Coloring, b-Chromatic number, bondage number, connected domination number, Barbell graph, Harary graph, Book graph, Grotzsch graph and Wagner graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : On the Star Coloring of Graphs Formed From the Cartesian Product of Some Simple Graphs Country : India Authors : L.Jethruth Emelda Mary and A.Lydia Mary Juliette Rayen

Abstract: Let $G= (V, E)$ be an undirected simple graph. The star chromatic number of a graph G is the least number of colors needed to color the path on four vertices with three distinct colors. The purpose of this paper is to study the star coloring of some graph families formed from the Cartesian product of some simple graphs.

Keywords: Proper coloring, Chromatic number, Star coloring, Star chromatic number, Cartesian product of graphs, Prism graph, Barbell graph, Fan graph, Windmill graph, Lollipop graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Race, Genes and Intelligence: Bayesian Methodology Country : India Authors : N.John Britto

Abstract: In this review paper, introduction to Race, genes and intelligence is related (correlated) influencing factor understanding, using Bayesian Methodology Hidden Markow Chain (HMC) is discussed.

Keywords: Elements of classical genetics; Definition of Race, genes and intelligence; Hardy – Weinberg law; Birth – Death Law (Passion Law) Survivorship model (data) Analysis Binomial Pooled Sampling.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Inter Relations Between Fuzzy Door Space and Some Fuzzy Topological Spaces Country : India Authors : S.Anjalmose and G.Thangaraj

Abstract: In this paper the concept of fuzzy Door space are studied. Several relations between fuzzy Door space and some fuzzy topological spaces are investigated with suitable examples in this paper.

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

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Fuzzy Soft Matrix Theory and its Multi Criteria Decision Making on Radio Frequency Country : India Authors : J.Jon Arockiaraj and S.Madhanraj

Abstract: In this paper, we have to discussed about the fuzzy square matrix and its theory with some basic results. The study of this paper is based on the Multi Criteria Decision Making Problem with Suitable examples.

Keywords: Fuzzy soft Matrices, fuzzy Matrix, t-norm operator.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Control of Epidemics Using SIS Model Country : India Authors : T.Henson and B.Suriyakala

Abstract: A mathematical model is described for the system of epidemic by non-linear difference equations. In this paper, we have dealt with SIS epidemic Model in which study on the anticipation of epidemic by Population thresholds and control of epidemics.

Keywords: SIS model, deterministic chaos.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Application of Pentagonal Fuzzy Number in Neural Network Country : India Authors : A.Vigin Raj and S.Karthik

Abstract: Neural Network is and used to be a principal component of mathematics education. Many models have been developed in the literature for the description of the neural network. In this paper, we use fuzzy number choose the best machine for a job by Feed-Forward Neural Network.

Keywords: Fuzzy Number, Pentagonal Fuzzy Number, Feed-Forward Neural Network.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Solving the Decision Making Problem Using Decagonal Fuzzy Number and Fuzzy Matrix Country : India Authors : A.Virginraj and S.Hemavathi

Abstract: The field of decision-making are the most useful and interesting area of applications fuzzy set theory. In this paper, we use decagonal fuzzy number and decagonal fuzzy number matrix to choose the winner of the participant in a dance competition decision making model.

Keywords: Decision making, decagonal fuzzy number, decagonal fuzzy number matrix, decision maker.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

• Citation
• Abstract
• Corresponding Autho r
 Article Type : Research Article Title : On 3-rainbow Domination Number of Certain Graphs Country : India Authors : L.Jethruth Emelda Mary and A.Isabeline

Abstract: Given an undirected graph G=(V,E) and a set of k-colors numbered 1,2{\dots}.k. The 3-rainbow domination defined as $f : V(G)\to þ\{1,2,3\}$ such that for each vertex $v \in V(G)$ with $f(v)=\phi$ $\bigcup_{u\in N(v)}{f\left(u\right)=\{1,2,3\}}$ Such a function is called a 3-rainbow dominating function (3RDF) and minimum weight of such function is called the 3-rainbow domination number of G and is denoted by ${\gamma}_{r3}(G)$. In this paper we found the 3-rainbow domination number of certain graphs.

Keywords: Domination number, 3-rainbow domination number, wheel graph, triangular snake graph, double triangular snake graph, n-barbell graph, n-sunlet graph, n-centipede graph, crown graph, clebsch graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : On the Star Coloring of Circulant Graphs Country : India Authors : L.Jethruth Emelda Mary and A.Lydia Mary Juliette Rayen

Abstract: Let $G= (V, E)$ be an undirected simple graph. The star chromatic number of a graph G is the least number of colors needed to color the path on four vertices with three distinct colors. The aim of this paper is to determine the star chromatic number of some Circulant graphs.

Keywords: Proper coloring, Chromatic number, Star coloring, Star chromatic number, Circulant graphs, Harary graphs, Andra ́sfai graph, Cocktail Party graph, Musical graph, Crown graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Fuzzily Determined the Game Value for Decision Making of an Interval Matrix Game on Four Players Country : India Authors : J.Jon Arockiaraj and S.Madhanraj

Abstract: In this paper, we consider a solution for Fuzzy matrix game with fuzzy pay offs. The Solution of Fuzzy matrix games with pure strategies with max min – min max principle is discussed. A method takes advantage of the relationship between fuzzy sets and fuzzy matrix game theories can be offered for multicriteria decision making. To model such uncertainty in matrix games, we consider interval-valued game matrices In this paper we extend the results of classical strictly-determined matrix games to fuzzily determined interval matrix games.

Keywords: Fuzzy set, fuzzy payoffs, fuzzy matrix games, strategy.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Harmonious Coloring of Middle and Central Graph of Some Special Graphs Country : India Authors : J.Arockia Aruldoss and S.Margaret Mary

Abstract: Let $G (V, E)$ be an undirected graph. The Harmonious coloring of a graph G is a proper vertex coloring in which each pair of colors appears on at most one pair of adjacent vertices. The Harmonious chromatic number is minimum number of colors needed for the harmonious coloring of G. In this paper we investigate the harmonious chromatic number of middle and central graph of some special graphs.

Keywords: Proper coloring, Middle graph, Central graph, Tadpole graph Web graphs.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Harmonious Chromatic Number, Bondage Number, Domatic Number of Some Special Graphs Country : India Authors : J.Arockia Aruldoss and S.Margaret Mary

Abstract: Let $G(V,E)$ be an undirected graph. The Harmonious coloring of a graph G is a proper vertex coloring in which each pair of colors appears on at most one pair of adjacent vertices. The Harmonious chromatic number is minimum number of colors needed for the harmonious coloring of G. In this paper we found the Harmonious chromatic number, Bondage number, and Domatic number of some special graphs.

Keywords: Proper Coloring, Bondage Number, Domatic Number, Moser Spindle Graph, Golden Harary Graph, Tietze’s Graph, Soifer Graph.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Fuzzy Systems for Multi-criteria Decision Making with Interval Data Country : India Authors : J.Jon Arockiaraj and N.Murali

Abstract: Oceans cover more than 70\% of Earth's space and has a vast number of living organisms and underwater vegetation. During early centuries Seas helped us in provision of food and rare medicinal herbs from its vegetation. There are numerous species of fishes which are caught and consumed as food. In this paper the TOPSIS method is used to assess most commonly consumed fishes and evaluate the favorable one corresponding to people's preference.

Keywords: Fuzzy TOPSIS, Fuzzy Matrix, Decision Support Systems, Multi-criteria Decision Making.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Fuzzy Matrix Analysis of Seasonal Fishing in Cuddalore District Country : India Authors : J.Jon Arockiaraj and N.Murali

Abstract: Fuzzy matrices play an important role in the formulation and analysis of many classes of discrete structural models which are in physical, biological, medical, social and engineering sciences. The aim of this paper is study the Seasonal fishing of fishermen. To study the life style of fishermen we use various fuzzy matrix techniques.

Keywords: Fuzzy matrix, CETD matrix, ATD matrix.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : An Application of Intuitionistic Pentagonal Fuzzy Relation in Medical Diagnosis Country : India Authors : A.Virgin Raj and R.Muthamizhselvan

Abstract: In this paper, we study Sanchez's method of medical diagnosis by using Intuitionistic Pentagonal Fuzzy Relation. To develop Intuitionistic Pentagonal Fuzzy Relation and using score and accuracy function for to solve medical diagnosis decision making problem. In this paper it is presented the procedures based on Intuitionistic Pentagonal Fuzzy Number for medical diagnosis using a numerical example to verify the proposed approach.

Keywords: Medical Diagnosis, Intuitionistic Pentagonal Fuzzy Relation, Score, Accuracy.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Vertex Odd Mean and Even Mean Labeling of Fan Graph, Mongolian Tent and $\bar{K}_{2}+C_{n}$ Country : India Authors : J.Arockia Aruldoss and S.Pushparaj

Abstract: A graph G with p vertices and q edges is a mean graph if there is an injective function f from the vertices of G to $\{0,1,2,\dots,q\}$ such that when each edge uv is labeled with $\frac{(f(u)+f(v))}{2}$ if $(f(u)+f(v))$ is even and $\frac{(f(u)+f(v)+1)}{2}$ if $(f(u)+f(v))$ is odd then the resulting edges are distinct. A fan graph Fm,n is defined as the graph join $\bar{K}_m+P_n$ where $\bar{K}_m$ is the empty graph on m nodes and $P_n$ is the path graph on n nodes. The case $m=1$ corresponds to the usual fan graphs. In this paper we investigate vertex odd and even mean labeling of Fan graph, Mongolian tent and $\bar{K}_2+\mathcal{C}_n$.

Keywords: Mean labeling, Mongolian tent, Fan graph, vertex odd mean labeling and vertex even mean labeling.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Applying Fuzzy Analytic Hierarchy Process to Evaluate the Motive of Healthcare Towards Patients Country : India Authors : S.Johnson Savarimuthu and A.Rathina Raj

Abstract: Humans and other living organisms are infected by many diseases due to intensive pollution in this world. Medicine is the vital importance to cure living organisms from most of these diseases. At present there are different healthcare and hospitals, which administer different medical practices and medications to patients. In this research paper, the Fuzzy AHP technique is used to find the motive of these healthcare and hospitals towards the patients.

Keywords: Fuzzy Analytical Hierarchy Process (FAHP), Multi Criteria Decision Making (MCDM).

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Analysis of the Problems of Female Sports Persons Using Induced Fuzzy Associative Memory Models Country : India Authors : S.Johnson Savarimuthu and S.Reeba Joy

Abstract: In this paper, we use Fuzzy Associative Memories (FAM), Induced Fuzzy Associative Memories (IFAM) model to analyse the problems of female sports persons and derived some conclusions. And also we use the method of thresholding to clarify the problems faced by the female sports persons which we mentioned. Through this paper we have explained how female sports persons come to know to manage the problems and to give the best performance.

Keywords: Fuzzy Associative Memories (FAM), Induced Fuzzy Associative Memories (IFAM), Fixed point, Limit cycle.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Solving Delay Differential Equations of Fractional Order Country : India Authors : T.Henson and C.M.Senthamil Mozhi

Abstract: In this paper, we implement Adomian decomposition method and Modified Laguerre wavelets method for solving numerically linear and non-linear delay differential equations of fractional order. The fractional derivative will be in the caputo sense. Computational work is fully supportive of compatibility of proposed algorithm and hence the same may be extended to other physical problems also. Some numerical examples are presented to illustrate the accuracy and ability of the proposed method.

Keywords: Adomian decomposition method, delay differential equations, Method of steps, Modified Laguerre wavelets method, fractional delay differential equations.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Analysis of Defence Persons Duty Time Using Fuzzy Matrix Country : India Authors : S.Johnson Savarimuthu and S.Reeba Joy

Abstract: In this paper we use Fuzzy Matrix to analyze the defence persons how alternatively spending the time securing the duty of their given task as defensive position to save our nation. The land saved by Army, the sea boundaries saved by Navy, and the space by Air force. This objective was shown by graphical method. In this paper we come to know how defence persons sacrificing their life for the people of India.

Keywords: Fuzzy matrix, CETD matrix, ATD matrix.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Analysing the Performance of Women Gym-Goers Using Generalized Intuitionistic Fuzzy Soft Sets Country : India Authors : J.Jon Arockiaraj and S.Sharmila

Abstract: This paper introduces the concept of generalized intuitionistic fuzzy soft sets for solving multi attribute decision making problem. Generalized intuitionistic fuzzy soft set is the extension of intuitionistic fuzzy soft sets. In this paper, we are analysing the performance of women gym -goers and also finding the best gym-goer who is reducing her weight in a particular month by using generalized intuitionistic fuzzy soft set theory.

Keywords: Fuzzy soft sets, Generalized fuzzy soft sets, Generalized intuitionistic Fuzzy soft sets and multi criteria decision making problem.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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• Corresponding Autho r
 Article Type : Research Article Title : Analysis of Health Problems Faced by Residents Around Sipcot in Cuddalore Using Induced Fuzzy Associative Memory (IFAM) Model Country : India Authors : S.Johnson Savarimuthu and A.Sharveena

Abstract: In this paper we have analyzed the impact of the pollution in sipcot cuddalore by using Induced Fuzzy Associative Memory (IFAM) model and Fuzzy Associative Memory (FAM) model. The sipcot chemical industrial estate in cuddalore is one among many such clusters of polluting industries in India. Residents living in and around the sipcot chemical industrial estate had the problem of health hazards due to chemical pollutions. Based on our study we made our conclusions and suggested some remedial measures.

Keywords: IFAM, FAM, Health hazards, sipcot cuddalore, limit cycle, hiddern pattern.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Problems Faced by Road Workers Using Induced Fuzzy Relational Mapping (IFRM) Country : India Authors : S.Johnson Savarimuthu and A.Sharveena

Abstract: In this paper, we have dealt with the problems faced by Road workers in Cuddalore by using the Fuzzy Relational Mapping (FRM) and Induced Fuzzy Relational Mapping (IFRM). We have used the method of thresholding to discuss the problems of the road workers which we have mentioned. Based on our study we made our conclusions on the problems of the road workers and suggested few remedial measures.

Keywords: FRM, IFRM, Health hazards, Road workers, limit cycle, hidden pattern.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : A Decagonal Fuzzy Number and its Vertex Method Country : India Authors : J.Jon Arockiaraj and N.Sivasankari

Abstract: The decision data of human judgements with preferences are often vague so that the usual ways of using crisp values are in adequate in many real life situation. Also using fuzzy numbers such as triangular, trapezoidal are not suitable in few cases where the uncertainties arises in ten different points. Therefore, Decagonal Fuzzy Number (DFN) and its arithmetic operations based on $\alpha$-cut are introduced. Also, the linguistic terms can be expressed in Decagonal fuzzy numbers and a vertex method is defined to calculate the distance between two Decagonal fuzzy numbers.

Keywords: Fuzzy Arithmetic, Linguistic values, Decagonal Fuzzy Number (DFN), $\alpha$ cut.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : A Study on Critical Path Method Using Interval Valued Fuzzy Numbers Country : India Authors : D.Stephen Dinagar and D.Abirami

Abstract: In this paper, Fuzzy critical path in project network is studied with the aid of Interval valued fuzzy numbers. Interval valued trapezoidal fuzzy numbers (IVTFNS) are used to represent activity times in the project network. The L\_R type interval valued fuzzy numbers(L\_RIVFNS) have been studied with new arithmetic operations. A new ranking value of fuzzy number approach on this fuzzy number is discussed to solve the problem. A comparison have been made between sanguansat and chen ranking method and the above discussed ranking approach with a numerical example.

Keywords: Critical path method, Fuzzy Project Network, Fuzzy ranking method, Interval Valued fuzzy numbers.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Sentiment Analysis for Online Product Reviews using NLP Techniques and Statistical Methods Country : India Authors : S.Muthukumaran, P.Suresh and A.Victoria Anand Mary

Abstract: Opinion mining or sentiment analysis is the computational study of opinions or emotions towards aspects or things. The aspects are nothing but attributes or components of the individuals, events, topics, products and organizations. Opinion mining has been an active research area in Web mining and Natural Language Processing (NLP) in recent years. Online reviews are now popularly used for judging quality of product or service and influence decision making of users while selecting a product or service. Due to innumerous number of customer reviews on the web, it is difficult to summarize them which require a faster opinion mining system to classify the reviews. Reviews is proposed as there are many user generated product reviews available online many researchers have explored various supervised and unsupervised machine learning techniques for binary classification of reviews. In this paper, we can show that the statistical methods are often combined with traditional linguistic rules and representations. In view of these facts, we argue that the Naive Bayes classification model and Hidden Markov Models is applied to analyze the polarity of the sentiment on online product reviews due to its computational simplicity and stochastic robustness.

Keywords: Sentiment analysis (SA), Opinion mining, Machine learning, Naive Bayes (NB), Support Vector Machine (SVM), online reviews, Hidden Markov (HMM).

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Harvesting Herbivore with Plant in Refuge on Plant-Herbivore System with Allee Effect Country : India Authors : S.Vijayalakshmi and M.Gunasekaran

Abstract: In this paper, we study plant-herbivore interactions where the herbivore is exposed to the risk of disease and harvesting while the plant has the ability to use a refuge. The feasibility and stability conditions of the equilibrium points of the system and the numerical simulations were verified to analyze the theoretical results and to investigate the properties of the system.

Keywords: Allee effect, susceptible herbivore - infective herbivore, constant refuge-random refuge, stability analysis.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : A Study on the Medical Diagnosis using Hexagonal Intuitionistic Fuzzy Relation Country : India Authors : A.Virgin Raj and R.Muthamizhselvan

Abstract: In this paper, we propose Intuitionistic Hexagonal Fuzzy Relation through the well known Sanchez’s approach for medical diagnosis using fuzzy max-min composition and score, accuracy function. We extend our approach in application of these Intuitionistic Hexagonal Fuzzy Relation in medical diagnosis decision making method. Finally given a numerical example to verify the proposed approach.

Keywords: Medical Diagnosis, Intuitionistic Hexagonal Fuzzy Relation.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Dusty Couple Stress Fluid Heated Below in Hydromagnetic Field Through Porous Medium Country : India Authors : W.Stanly and R.Vasanthakumari

Abstract: The Combined effect of Solute gradient and Magnetic field on Dusty Couple stress fluid through Porous medium is considered. The analysis is carried out within the framework of linear stability theory and normal mode technique. For the case of stationary convection, solute gradient has stabilizing effect whereas Dust particles are found to have a destabilizing effect on the system. Couple – Stress and Medium permeability have dual character to its stabilizing effect in the absence of magnetic field and rotation. Magnetic field has succeed in stabilizing effect in the absence of rotation. The oscillatory modes are introduced due to the presence of magnetic field in the system. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics.

Keywords: Dusty Couple Stress Fluid, Hydromagnetic Field, Porous Medium.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Application of Fuzzy Linguistic SAW and TOPSIS Multiple Criteria Group Decision Making Method using Pentagonal Fuzzy Number for Supplier Selection Problem Country : India Authors : A.Arokia Mary and S.Sangeetha

Abstract: In this paper, a Multiple Criteria Group Decision Making (MCGDM) technique based on Pentagonal Fuzzy Number and Fuzzy Linguistic SAW-TOPSIS method is used to solve the medical supplier selection problem. The aim of this paper is to develop a methodology which can be take into consideration by some important criteria which affect the process of supplier selection and calculating the weights for each criterion based on SAW and TOPSIS method. The entire methodology is illustrated with the help of a numerical example.

Keywords: Supplier Selection, MCGDM, Linguistic SAW, TOPSIS, Pentagonal Fuzzy Number.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Ranking of Generalized Hexagonal fuzzy numbers based on Rank, Mode, Divergence and Spread Country : India Authors : A.Virgin Raj and V.Ezhilarasi

Abstract: Ranking of fuzzy number used mainly in risk analysis,decision making, data analysis etc. In this paper, a new approach for ranking of generalized hexagonal fuzzy number. The proposed approach based on rank, mode, divergenge and spread.The proposed approach is compared with different existing approaches.

Keywords: Ranking function, Generalised hexagonal fuzzy number, centroid points.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : On Determinant of Hexagonal Fuzzy Number Matrices Country : India Authors : D.Stephen Dinagar and U.Hari Narayanan

Abstract: The fuzzy set theory has been applied in many fields such as management, engineering, theory of matrices and so on. In this paper, some elementary operations on hexagonal fuzzy numbers (HFNs) have been studied. We also studied some special operations on hexagonal fuzzy matrices (HFMs). The notion of ‘Determinant on HFM’ is also introduced and discussed. Some of their relevant properties have also been verified.

Keywords: Fuzzy Arithmetic, Fuzzy number, Hexagonal fuzzy number, Hexagonal fuzzy matrices.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : On t-Conorm Operators of Interval-Valued Fuzzy Soft Matrix and its Application in MCDM Country : India Authors : D.Stephen Dinagar and A.Rajesh

Abstract: Fuzzy Soft Set theory is a newly emerging mathematical tool to deal with uncertain problems. In our daily life we often face some problems in which the correct decision making is essential. In this paper, to overcome this problem, the Multi-Criteria Decision Making (MCDM) approach based on t-Conorm operators of interval-valued fuzzy soft matrix have been discussed. Some relevant properties have also been studied. Finally the algorithm based on t-Conorm operators of interval-valued fuzzy soft matrix is proposed with an example to illustrate the new approach.

Keywords: Soft Set, Fuzzy Soft Set, Interval-Valued Fuzzy Soft Set, Interval-Valued Fuzzy Soft Matrix, Operators of t-Conorm, Decision Making Problem.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Direct Method of Fuzzy Transportation Problem Using Hexagonal Fuzzy Number with Alpha Cut Country : India Authors : A.Arokia Mary and R.Sivasankari

Abstract: The purpose of this paper is to find an optimal solution of fuzzy transportation problem, where transportation cost, supply and demand are fuzzy quantities. Using the method of robust ranking, we find the rank [a b c d e f] of hexagonal fuzzy number by arithmetic operation. We develop a new algorithm to find a fuzzy optimal solution with alpha-level cut for computation. The parameter such as supply, demand and fuzzy coefficients are represented by fuzzy numbers. We have derived it with numerical illustration.

Keywords: Fuzzy set, Hexagonal fuzzy number, Robust ranking, Fuzzy transportation problem, Optimal solution.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Solution of Fuzzy Game Problem Using Hexagonal Fuzzy Numbers Country : India Authors : J.Jon Arockiaraj and N.Sivasankari

Abstract: In this paper, we consider a two person zero sum game with imprecise values in payoff matrix. The imprecise values are assumed to be hexagonal fuzzy numbers. An approach for solving problems by using ranking of the fuzzy numbers has been considered to solve the fuzzy game problem. By using ranking to the payoffs we convert the fuzzy value game problem to crisp valued game problem, which can be solved using the traditional method minimax-maximin principle.

Keywords: Fuzzy Set, Fuzzy Numbers, Hexagonal Fuzzy Numbers, Ranking of Fuzzy Numbers, Fuzzy Game Problem, pay off matrix.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : A Batch Arrival Two Types of Bulk Service Queue with Server Breakdown and Modified M-Vacation Country : India Authors : G.Ayyappan, R.Vimala Devi and S.Suganya

Abstract: In this paper a batch arrival two types of general bulk service queuing system with server breakdown and modified M-vacation is considered. The service is done in bulk with a minimum of $a$' customer and a maximum of $b$' customers. At first the server provides first essential service (FES) bulk service) to the arriving customers and sequentially the server must provide second essential services (SES). At the completion of two types of service, if the server is breakdown with probability $\pi$, then the renovation of service station will be consider. After completing the renovation of service station or there is no breakdown of the service with probability $(1-\pi)$, the queue length is less than $a$' then the server will avail of multiple vacations till the queue length reaches $a'$ or consequently he completes M number of vacations, which occurs first, After completing the M-th vacation, if the queue length is still less than a then the server remains in the system till it reaches a (this period is known as dormant period). At a vacation completion epoch or a two type of services completion epoch or during the dormant period, if the queue length $\xi$ is at least a, the server service a batch of minimum $(\xi, b)$ customers where $b\ge a$. The probability generating function of queue science at the random epoch is obtained.

Keywords: Batch arrival, bulk service, breakdown, M-vacation.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Solving Fuzzy Assignment Problem for Hexagonal Fuzzy Number Using Ones Assignment Method and Robust's Ranking Technique Country : India Authors : A.Arokiamary and S.Nithya

Abstract: In this paper, ones assignment method is used to solve fuzzy assignment problem and Robust's ranking technique to find maximum and minimum objective function. $C_{ij}$ is considered to be hexagonal fuzzy number. From this, we find the optimal assignment and it gives as the required optimal total cost for the problem. Finally, examples are given to explain this method.

Keywords: Fuzzy assignment problem, ones assignment algorithm, hexagonal fuzzy number and Robust's ranking technique method.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Solving Fuzzy Assignment Problem for Hexagonal Fuzzy Number Using Revised Ones Assignment Method Country : India Authors : A.Arokiamary and S.Nithya

Abstract: In this paper, revised ones assignment method is used to solve the fuzzy assignment problem to find maximum and minimum objective function using hexagonal fuzzy number. Finally, examples are given to explain this method. We find the minimum total cost and maximum total cost.

Keywords: Fuzzy assignment problem, revised ones assignment algorithm and hexagonal fuzzy number.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : A Batch Arrival Two Types of Bulk Service Queue with Vacation Interrupted, Optional Service and Closedown Country : India Authors : G.Ayyappan, S.Suganya and R.Vimala Devi

Abstract: In this paper a batch arrival two types of general bulk service queuing system with vacation interrupted, optional service and closedown is considered. The service is done in bulk with a minimum of $a$' customer and a maximum of $b$' customers. At first the server provides first essential service (FES) (bulk service) to the arriving customers and sequentially the server must provide second essential services (SES). At the completion of two types of service the leaving batch of customers may request for optional service with probability $\pi$. If no request for optional service is made after the completion of two type of service or after completion of optional service and number of customers in the queue is less than $a$' then the server closed down its work. After that the server goes for single vacation. If the queue size reaches $a$' during the vacation, the server terminates the vacation abruptly and resumes for FES. On completion of the vacation the server remains in the system (dormant period) until the queue length reaches $a$'. After the completion of optional service with $\pi$ or after completion of two type of service with $(1-\pi)$ and the number of customer in the queue is greater than $a$' the server will continue the batch service with general bulk service rule. The probability generating function of queue science at the random epoch is obtained.

Keywords: Batch Arrival, Vacation Interrupted, Optional Service, Closedown.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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 Article Type : Research Article Title : Fuzzy Critical Path Analysis In A Project Network Using Fuzzy Topsis Method Country : India Authors : A.Arokiamary and Prathipa Jayapalan

Abstract: In this Paper, we present the project scheduling problem using fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method. The ratings of each activity and the weight of each criterion are given in terms of linguistic Variables which are expressed in terms of pentagonal fuzzy number. Then, by the relative closeness coefficient, we compute the ranking order of each alternative and the alternative with the highest ranking score is chosen to be the fuzzy critical path of the project network. An illustration is given to explain the method.

Keywords: Pentagonal fuzzy number, Fuzzy TOPSIS method, linguistic Variables and fuzzy project network.

Dr.Anjal Mose
Department of Mathematics, St. Joseph's College of Arts \& Science, Manjakuppam, Cuddalore (Tamil Nadu), India.
E-mail: ansalmose@gmail.com

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