Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows - Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve suc

Many fuzzy clustering are based on within-cluster scatter with a compactness measure , but in this paper explaining new fuzzy clustering method which depend on within-cluster scatter with a compactness measure and between-cluster scatter with a separation measure called the fuzzy compactness and separation (FCS). The fuzzy linear discriminant analysis (FLDA) based on within-cluster scatter matrix and between-cluster scatter matrix . Then two fuzzy scattering matrices in the objective function assure the compactness between data elements and cluster centers .To test the optimal number of clusters using validation clustering method is discuss .After that an illustrate example are applied.

This work is concerned with designing two types of controllers, a PID and a Fuzzy PID, to be used
for flying and stabilizing a quadcopter. The designed controllers have been tuned, tested, and
compared using two performance indices which are the Integral Square Error (ISE) and the Integral
Absolute Error (IAE), and also some response characteristics like the rise time, overshoot, settling
time, and the steady state error. To try and test the controllers, a quadcopter mathematical model has
been developed. The model concentrated on the rotational dynamics of the quadcopter, i.e. the roll,
pitch, and yaw variables. The work has been simulated with “MATLAB”. To make testing the
simulated model and the controllers m

This paper is focused on orthogonal function approximation technique FAT-based adaptive backstepping control of a geared DC motor coupled with a rotational mechanical component. It is assumed that all parameters of the actuator are unknown including the torque-current constant (i.e., unknown input coefficient) and hence a control system with three motor control modes is proposed: 1) motor torque control mode, 2) motor current control mode, and 3) motor voltage control mode. The proposed control algorithm is a powerful tool to control a dynamic system with an unknown input coefficient. Each uncertain parameter/term is represented by a linear combination of weighting and orthogonal basis function vectors. Chebyshev polynomial is used

     In this study, we investigate about the run length properties of cumulative sum (Cusum) and The exponentially weighted moving average (EWMA) control charts, to detect positive shifts in the mean of the process for the poisson distribution with unknown mean. We used markov chain approach to compute the average and the standard deviation for run length for Cusum and EWMA control charts, when the variable under control follows poisson distribution. Also, we used the Cusum and the EWMA control charts for monitoring a process mean when the observations (products are selected from Al_Mamun Factory ) are identically and independently distributed (iid) from poisson distribution i

The efficient behavior of a low-concentrating photovoltaic-thermal system with a micro-jet channel (LCPV/T-JET) and booster mirror reflector is experimentally evaluated here. Micro-jets promote the thermal management of PV solar cells by implementing jet water as active cooling, which is still in the early stages of development. The booster mirror reflector concentrates solar irradiance into solar cells and improves the thermal, electrical, and combined efficiencies of the LCPV/T-JET system. The LCPV/T-JET system was tested under ambient weather conditions in the city of Bangi, Selangor, Malaysia, and all data was recorded between 10:00 a.m. and 4:00 p.m. Parametric studies were conducted to compare the performance of the LCPV/T-JET system

In this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti

      The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics.   

Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studie

The transportation problem (TP) is employed in many different situations, such as scheduling, performance, spending, plant placement, inventory control, and employee scheduling. When all variables, including supply, demand, and unit transportation costs (TC), are precisely known, effective solutions to the transportation problem can be provided. However, understanding how to investigate the transportation problem in an uncertain environment is essential. Additionally, businesses and organizations should seek the most economical and environmentally friendly forms of transportation, considering the significance of environmental issues and strict environmental legislation. This research employs a novel ranking function to solve the transpor