K. Selvakumari ¹, S. Lavanya ²

Affiliations
1 Department of Mathematics, Vel’s University, Chennai-600117,Tamil Nadu, IN
2 Department of Mathematics, D.G.Vaishnav College, Chennai-600106, Tamil Nadu, IN

Abstract

In this paper we consider a two person zero sum game with imprecise values in payoff matrix. All the imprecise values are assumed to be triangular or trapezoidal 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 valued game problem to crisp valued game problem, which can be solved using the traditional method.

Keywords

Fuzzy Set, Fuzzy Number, Triangular Fuzzy Number, Trapezoidal Fuzzy Number, Ranking Of Fuzzy Numbers

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S. Pavitra ¹, S. Lavanya ², S. A. Khan ³, Asha Crasta ⁴

Affiliations
1 Department of Mathematics, B. I. T, Mangalore - 574153, Karnataka, IN
2 Department of Mathematics, P.A.C.E, Mangalore - 574153, Karnataka, IN
3 Department of Mechanical Engineering, Faculty of Engineering, IIUM, Gombak Campus, Kuala Lumpur, MY
4 Department of Mathematics, MITE, Moodbidre - 574225, Karnataka, IN

Abstract

In the present paper a theory for 2D slender bodies at high angle of attack in hypersonic flow has been developed to determine the aerodynamic derivatives in pitch for different Mach numbers. The present theory has been applied to a sharp thick wedge with attached shock case. Using the theory, a relation for a piston moving in a cylinder at any velocity and relations for stiffness and damping derivatives are obtained for zero incidence of the wedge and it is found to be dependent on flight Mach number and wedge semi vertex angle. The present method includes the thin wedge case as well, which was covered by Lighthill piston theory, and applies only for small amplitude and low reduced frequency case. Effect of viscosity and secondary wave reflections have been neglected. The results are obtained for wedges of different semi vertex angles and Mach numbers. It is observed that the stiffness and Damping derivatives increase with increase in the semi vertex angle and decrease with an increase in Mach number. At very high Mach number the Mach number independence principle holds good.

Keywords

Aerodynamic Derivative, Hypersonic Flow, Mach Number, Semi Vertex Angle, Stability Derivative.

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Purnima Harinath ¹, S. Lavanya ²

Affiliations
1 Bharathiyar University, Coimbatore - 641046, Tamil Nadu, IN
2 Bharathi women’s College (Auotomous), Chennai - 600108, Tamil Nadu, IN

Abstract

Objectives: To find the vertex cohesive number and edge cohesive number of Gear and Bistarfuzzy graph structure. Methods/ Statistical Analysis: Gear graph and Bistar graph is converted into a fuzzy graph by assigning membership function for vertices and edges. The edges with same membership function are grouped to get a gear and Bistar fuzzy graph structure. For this Gear and Bistar fuzzy graph structure, vertex and edge cohesive number are computed. Findings: The vertex and edge cohesive number of Gear and Bistar fuzzy graph structure are found. Application: In any organisation, the employees can be treated as vertices. Keeping in mind how one employee co-ordinates with other employee, one can study how employees can work in groups.

Keywords

Bistar Graph, Gear Graph, Graph Structures, Hamacheer Product, Vertex and Edge Cohesive Numbers.

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S. Ramya ¹, S. Lavanya ²

Affiliations
1 R. M. K. Engineering College, Bharathiar University, Coimbatore, R. S. M. Nagar, Kavaraipettai - 601206, Tamil Nadu, IN
2 Department of Mathematics, D. G. Vaishnav College, Chennai - 600106, Tamil Nadu, IN

Abstract

The objective of this paper is to generalize and improve the domination variant called perfect domination. In this paper we have defined and derived some results related to the two new parameters perfect k-domination and perfect edge domination. The same can be applied in the networks arising from system of parallel computers.

Keywords

Fuzzy Graph, Fuzzy Dominating Set, Perfect K-Dominating Set, Perfect Edge Dominating Set, Perfect K-Edge Dominating Set

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S. Lavanya ¹, S. Prakasam ¹

Affiliations
1 Department of CSA, SCSVMV University, Kanchipuram - 631561, Tamil Nadu, IN

Abstract

Objective: Reliability and Energy conservation are two main factors to be considered in wireless sensor networks. Wireless Sensor Networks (WSN) is widely used in time-critical applications. WSN are resource constrained, so developing energy efficient protocols is a major concern in sensor networks. Multilayer clusters are preferred for sensors used in Remote Monitoring applications. When the position of sensor changes then it becomes very difficult to conserve energy as the cluster head is mainly responsible for delivery of the data. Protocols like EADUC, TLPER follows Multilayer clustering approach. The main aim of this paper is to develop dynamic clusters with less energy consumption. Methods/Statistical Analysis: The proposed method D-MCDA is efficient when the location of nodes varies dynamically and the clusters are formed based on their locations which proves efficient when compared to other protocols. First all the nodes are involved in the formation of the cluster and then the Cluster head is selected. The actual data packet is sent from the source to destination and the consumption of energy is calculated for various protocols and their results are compared. Findings: As energy consumption was the main motivation, use of multilayer and additional cluster heads have reduced the energy consumption by 0.019. The Proposed D-MCDA algorithms have performed better in terms of average energy consumption per node and in the process of designing a cluster. The proposed algorithm is compared with the existing algorithm like TLPER and MCDA. Applications/Improvements: Energy Consumption is very essential in applications like Remote monitoring, process control and automations. Reliability is another issue to be considered as it is another major reason for energy depletion. Reliability on the basis of congestion avoidance scheme, acknowledgement mechanisms can be considered which can reduce the energy consumption to a major level.

Keywords

Cluster Analysis, Cluster Head, Energy Consumption, Sensor Networks.

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