Fuzzy Systems

G. T. Shakila Devi ¹, C. Vijayalakshmi ²

Affiliations
1 Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, IN
2 School of Advance Sciences, Department of Mathematics Division, VIT University, Chennai, IN

Abstract

This paper mainly deals with the analysis of multiple server queues (M/M/C):(GD/∞/∞) and (M/M/∞): (GD/∞/∞). c parallel servers for (c≥1) is considered for (M/M/C):(GD/∞/∞), so that, c customers may be in service at the same time. Further, it is assumed that all the channels have the same service (exponential) distribution with mean rate μ per unit time. Since the probability of one service is μh, the probability that one out of n (n≤c) services are completed during h follows a binomial distribution. (M/M/∞): (GD/∞/∞) model describes a situation with state dependent service rates where the number of servers is directly proportional to the number in the system. This unlimited server situations may occur in self-service facilities. Based on the numerical calculations and Graphical representations, the feasibility of the system is analyzed. When the mean system size and the queue size is high, optimized value is obtained so that the total expected cost is minimized. The aim of this study is to compare the properties namely mean service rate and based on the length of the queues. Probability of service of the models (M/M/C):(GD/∞/∞) and (M/M/∞):(GD/∞/∞) have been discussed. By using numerical calculation and graphical representations, analysis of such a queue can be done by solving mean system size and queue size.

Keywords

Multiple-Server Queue Model, Steady-State Condition, Kendall's Notation for Queuing Models Arrival Rate and Service Rate.

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C. Kavitha ¹, C. Vijayalakshmi ¹

Affiliations
1 Mathematics Department, Sathyabama University, Chennai, IN

Abstract

Manufacturing firm focuses on maximizing the profit by satisfying the customer demands with respect to quantity, quality, cost etc. To achieve the goal they give importance to optimum utilization of available resources. Information available in real life system is of vague, imprecise and uncertain nature. The impreciseness and uncertainty aspects are handled using fuzzy sets to obtain optimal solution. In practice, choosing membership thresholds arbitrarily may result in an infeasible optimization problem. Even though we can adjust minimum satisfaction degree to get fuzzy efficient solution it sometimes makes the process of interaction more complicated. The present paper demonstrates how vagueness and imprecision in the objective function values can be quantified by membership functions in a Fuzzy multi objective frame work. It focuses on optimizing production management model using real world data of a packaging industry. Production model intends to determine the sales value of each product produced in order to achieve objectives (i.e.) maximize profit, minimize wastes etc. Multiple objective functions in the linear programming model are handled by fuzziness in the parameters. Fuzzy linear programming approach exhibits greater computational efficiency by employing the linear membership functions to represent fuzzy numbers.

Keywords

Production Management, Fuzzy Multiple Objective Linear Programming, Fuzzy Set Theory.

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C. Vijayalakshmi ¹, R. Kokila ²

Affiliations
1 School of Advanced Sciences (Mathematical Division), VIT University, Chennai Campus, IN
2 Department of Mathematics, Seethalakshmi Ramaswai College, Trichy-2, IN

Abstract

There has been increased interest in the development of fuzzy pattern recognition based medical imaging that contributes to solve the problems in early diagnosis and prognosis. Fuzzy set theory plays a key role in formalizing uncertainties for medical diagnosis and prognosis. This paper deals with some of the algorithmic approaches of fuzzy techniques.

Keywords

Fuzzy Pattern, Diagnosis, Algorithmic Approach, Telemetric, Network.

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