In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler and easier calculations as well as shortening in the procedures. The fuzzy fractional programming problem is the first reduced to a fractional programming problem and then solved with the technique to obtain the optimal solution. It has a power to give a best solution for supporting the solution theory proposed in this work, some numerical fuzzy fractional programming problem are included to ensure the advantage, efficiency and accuracy of the suggested algorithm. In addition, this research paper describes a comparison between our optimal solutions with other existing solutions for inequalities constrains fuzzy fractional program.
Background and Objective: Public demand for procedures to rejuvenate photodamaged facial skin have stimulated the use of fractional CO2 laser as a precise and predictable treatment modality. The purpose of this study was to assess the effect of fractional CO2 laser system for reducing periorbital rhytids.
Materials and Methods: twenty seven subjects with mild periocular wrinkles, and photoaged skin of the face were prospectively treated two to three times (according to clinical response) in the periorbital area with a fractional CO2 laser device equipped with a scanning hand piece. Improvements in eyelid wrinkles was evaluated clinically and photographically. Subjects also scored satisfaction and
... Show MoreTransformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe
... Show MoreThis paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time
... Show MoreIn this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami
... Show MoreIn This paper, we have been approximated Grűnwald-Letnikov Derivative of a function having m continuous derivatives by Bernstein Chlodowsky polynomials with proving its best approximation. As well as we have been solved Bagley-Torvik equation and Fokker–Planck equation where the derivative is in Grűnwald-Letnikov sense.
The research aims to determine the mix of production optimization in the case of several conflicting objectives to be achieved at the same time, therefore, discussions dealt with the concept of programming goals and entrances to be resolved and dealt with the general formula for the programming model the goals and finally determine the mix of production optimization using a programming model targets to the default case.
Charge transfer complex formation method has been applied for the spectrophotometric determination of cimetidine, in bulk sample and dosage form. The method was accurate, simple, rapid, inexpensive and sensitive depending on the formed charge- transfer complex between cited drug and, 2,3-Dichloro-5,6-dicyano-p- benzoquinone (DDQ) as a chromogenic reagent. The formed complex shows absorbance maxima at 587 nm against reagent blank. The calibration graph is linear in the ranges of (5.0 - 50.0) µg.mL-1 with detection limit of 0.268µg.mL-1. The results show the absence of interferences from the excipients on the determination of the drug. Therefore the proposed method has been successfully applied for the determination of cimetid
... Show MoreAnalytical field target function has been considered to represent the axial magnetic field distribution of double polepiece symmetric magnetic lens. In this article, with aid of the proposed target function, the syntheses procedure is dependent. The effect of the main two coffectin optimization parameters on the lens field distribution, polepieces shape, and the objective focal prosperities for lenses operated under zero magnification mode has been studied. The results have shown that the objective properties evaluated in sense of the inverse design procedure are in an excellent correspondence with that of analysis approach. Where the optical properties enhance as the field distribution of the electron lens distributed along a narrow axi
... Show MoreRate of penetration plays a vital role in field development process because the drilling operation is expensive and include the cost of equipment and materials used during the penetration of rock and efforts of the crew in order to complete the well without major problems. It’s important to finish the well as soon as possible to reduce the expenditures. So, knowing the rate of penetration in the area that is going to be drilled will help in speculation of the cost and that will lead to optimize drilling outgoings. In this research, an intelligent model was built using artificial intelligence to achieve this goal. The model was built using adaptive neuro fuzzy inference system to predict the rate of penetration in
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First: the problem of research and its importance
The teacher's success in facilitating the students' learning and growth according to the educational and educational goals set out, he must identify the problems of discipline of students in the classroom in terms of sources and reasons and types and methods of prevention and treatment and the teacher to remember that success in his teaching and instruction is not completed more fully once he has the information And knowledge of the subject of the lesson, but must understand the dynamics of the group (class group) and master the skills of classroom management, su
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