Ranking fuzzy numbers is an important aspect of decision making in a fuzzy environment. In fuzzy decision making problems, fuzzy numbers must be ranked before an action is taken by a decision maker. This article is about ranking Fuzzy numbers and describes a ranking method for ordering LR fuzzy numbers based on the area of fuzzy numbers. This method is simple in evaluation and can rank various types of LR fuzzy numbers and also crisp numbers which are considered to be a special class of fuzzy numbers.

We study Ricci-semi symmetric, \(\phi\)-Ricci semisymmetric and \(\phi\)-symmetric Lorentzian \(\alpha\)-Sasakian manifolds. Also, we study a Lorentzia \(\alpha\)-Sasakian manifold satisfies \(S(X ,\xi).R = 0\) .

In this article, solvability of one the anisotropic Helmholtz-Shrodinger equation with the boundary conditions of the first and second type is investigated in the upper and lower half –space, (x5>0, x5<0), in 5 dimensions. Solvability of these boundary problems reduces to solvability of Rieman- Hilbert boundary problem, in general necessary and sufficient conditions for the correctness of the problem in the Sobolev space are presented as well as explicit formulas for a factorization of the Fourier symbol matrix of the one-medium problem. The solvability analysis is based on the factorization problem of some matrix-function.

In this paper, with the aid of symbolic computation, an algebraic algorithm is proposed to construct soliton-like solutions to (2+1)-dimensional differentialdifference equations. The famous (2+1)-dimensional Toda equation is explicitly solved and some new classes of soliton-like solutions are obtained.

The object of the present paper is to study a type of non-flat Riemannian manifold called almost pseudo concircularly symmetric manifold. The existence of an almost pseudo concircularly symmetric manifold is also shown by two non-trivial examples.

A method to determine the numerical solution of system of linear Volterra integro-differential equations (IDEs) is proposed. The method obtains Taylor expansion for the exact solution of system of linear Volterra IDEs at initial point \(x = 0\). In addition, we introduce a procedure to obtain an approximation for Taylor expansion of the exact solution at \(x\neq 0\). Moreover, error estimation of the proposed methods is presented. The efficiency and applicability of the presented methods is illustrated by some numerical examples.

Geometric programming is a methodology for solving algebraic nonlinear optimization problems. It provides a powerful tool for solving nonlinear problems where nonlinear relations can be well presented by an exponential or power function. This feature is especially advantageous in situations where the optimal value of the objective function may be all that is of interest. In such cases, calculation of the optimum design vectors can be omitted. The goal of this paper is to state the problem of Pressure vessel design and after that finding a better optimized solution using geometric programme.

In this paper, we establish an equivalent statement of minimax inequality for a special class of functionals. As an application, we discuss the existence of three solutions to the Dirichlet problem \[ \begin{cases} \Delta_{p}u=\lambda f(x,u)=a(x)|u|^{p-2}u,\,\,\,\,\, \texttt{in} \Omega,\\ u=0,\,\,\,\,\, \texttt{on} \partial \Omega. \end{cases} \]

The idea of irrigation is not a new topic and its history refers to pre-historic era. Even the idea of automatic irrigation is not new. At present, there is no efficient automatic irrigation system that can irrigate the plants optimally and use the minimum water in different stage of plant growth(1). Nowadays, computer-monitoring of green-house irrigation systems is very necessary. Many of the common control methods are based on two-state (on/off) control methods and/or proportionate closed-loop control methods which cause increase of energy waste and decrease in productivity. The present research paper provides a solution for an irrigation controller based on fuzzy logic. Firstly, the main problems of irrigation are discussed; then, the physical model for controlling green-house irrigation system is described. Subsequently, the stages of designing a green-house irrigation control system with the aid of fuzzy logic are presented. This system is able to determine the volume of water required by plants in a specific depth through collecting information from environmental conditions existing inside the green house, the characteristics of the soil, and the type of plants as well as employing famous models of irrigation and water evaporation from the soil surface.

In this paper, one analytical technique named Frequency-Amplitude Formulation Method (FAF) isused to obtain the behavior and frequency of theelectrostatically actuated microbeams. The main aim of the work is obtaining highly accurate analytical solution for nonlinear free vibration of a microbeam and investigates the dynamic behavior of the system. Results reveal that the nonlinear frequency of oscillatory system remarkably affected with the initial conditions. In contrast to the time marching solution results, the present analytical method is effective and convenient. It is predictable that the FAF can apply for various problems in engineering specially vibration equations.

We first introduce fuzzy finite Markov chains and present some of their fundamental properties based on possibility theory. We also bring in a way to convert fuzzy Markov chains to classic Markov chains. In addition, we simulate fuzzy Markov chain using different sizes. It is observed that the most of fuzzy Markov chains not only do have an ergodic behavior, but also they are periodic. Finally, using Halton quasi-random sequence we generate some fuzzy Markov chains which compared to the ones generated by the RAND function of MATLAB. Therefore, we improve the periodicity behavior of fuzzy Markov chains.

The aim of this paper is to establish the existence of at least three weak solutions for the elliptic Dirichlet problem . Our main tool is a three critical point theorem and Therorem3.1 . of Gabriele Bonanno , Giovanni Molica Bisci [4] .

In today's competitive world, location-allocation (LA) decisions are one of the most important aspects of supply chain (SC) optimization. This LA decisions are including selection of known sites for construction of facilities and allocation of the distribution network between the levels of SC. In this paper, a nonlinear programming model to location facilities and allocate the supply chain distribution network in order to minimize both the cost and time of three-echelon are presented. The proposed model due to computational complexity in high dimensions cannot be solved with conventional and accurate methods, Therefore to achieve a solution of a method metaheuristic called genetic algorithm is used. Finally, to examine and the effectiveness of the proposed algorithm, computational results obtained are compared with output of lingo 12 software.

This paper studies a renewal reward process with fuzzy reward and fuzzy random inter arrival times. A theorem about the long run average fuzzy reward and fuzzy life time is proved. The original problem is evaluating the membership of the long run average fuzzy cost per unit time that for obtaining membership, we should solve a nonlinear programming problem. Finally, some application example is provided to illustrate the result.

This paper presents a new application of Artificial Neural Network (ANN) for modeling a Photovoltaic Thermal collector (PV/T). Both thermal and electrical modeling performed. Ambient temperature of collector, cell temperature, fluid temperature at duct inlet, fluid velocity in duct, solar identity and time are used in the input layer and the thermal efficiency and electrical efficiency are outputs. Networks with different hidden layers used for modeling and performances evaluated with maximum correlation coefficient \((R^2)\), minimum root mean square error (RMSE) and low coefficient of variance (COV). The results showed that the ANN with 1 hidden Layer and 10 neurons in this layer has the best performance. The experimental data measured at meteorological conditions of Zahedan were used as training data. The Levenberg-Marquard backpropagation algorithm has been used for training network. The results of this work indicated that for evaluating PV/T performance researchers can use this method by conducting limited experiments.

In this paper, Newton Harmonic Balancing Method (NHBM) is applied to scrutinize free vibration analysis of the nonlinear oscillatory systems. This method is combined by the Harmonic Balance and Newton's methods. Two classical cases are used to illustrate the applicable of NHBM and results compared by other analytical methods and ODE solver built in MATLAB. The results of the NHBM are shown that the solution quickly convergent and does not need to complicated calculations. So it is applied for various problems in engineering specially vibration equations.

The non-fixed destination multi-depot multiple traveling salesmen problem (MmTSP) is a generalization of well-known MTSP with several salesmen in each depot. In this research, time window is defined for each depot (city).the salesmen only can service the customers within these time windows and also some penalties are considered for any deviation of start time. The objective function of problem is to minimize the total costs and penalties of the tours. This problem is of a great complexity and belongs to NP-complete class of problems. So the exact algorithms cannot perform the best solution in problems with big dimension. So Meta heuristics algorithm is used to solve these problems efficiently. In this research we used hybrid simulated annealing and genetic algorithms.

The Adomian Decomposition Method is employed in the solution of the unsteady convective radiative equation. The Adomian Decomposition Method is provided an analytical solution in the form of an infinite power series. The comparison of the results obtained by ADM and VIM The effect of Adomian polynomials terms is considered on accuracy of the results. The temperature profiles in fin are obtained. Results show a good accuracy. The Adomian decomposition method (ADM) is used in obtaining more meaningful and valid solutions.

In this paper, a constrained optimal control problem is considered where constraint is elliptic partial differential equations of second order together with the boundary condition of Dirichlet type. The main purpose is detecting an appropriate solution for control and state function by using boundary element method in order to discretized PDEs. In this way, first a quadratic objective, linear constraints optimization problem rewritten respected to main problem, next it can be solved numerically with the help of appropriate solution algorithms, which should exploit the structure of the problem, we solved it by generalized Newton’s method. Some numerical experiments obtained by using boundary element method (BEM) and finite element method (FEM) are given in the final section of this paper.

In basic design of offshore or onshore structures, prediction of surface waves due to uniform motion of the floating body is essential to achieve an optimum body shape. Whereas, in the practical hydrodynamics, using of towing tanks is common and so cost and time consuming to conduct it, so a reliable numerical tank is interesting. A wide channel with constant depth constitutescomputational domain. It assumes that fluid is incompressible and non-viscous and the flow is irrotational. Therefore, Laplace’s equation could describe flow field.3D Boundary Element method based on second Green’s Identityis implemented to solveLaplace’s equation. Impermeable boundary condition is satisfied by Image method and Cauchy integral theorem and Poisson summation formula is used to determine Principle value integral. In this study, numerical simulation is conducted for a hemisphere and added mass and generated wave profile is presented.

Steel beam-to-column joints are often subjected to a combination of bending and axial forces. The level of axial forces in the joint may be significant, typical of pitched-roof portal frames, sway frames or frames with incomplete floors. An approach, based on finite element modelling, is presented in order to numerically investigate the seismic performance of bolted steel end-plate moment connection by including the effect of axial forces in the connection. Current specifications for steel joints do not take into account the presence of axial forces (tension and/or compression) in the joints. A single empirical limitation of 10% of the beam’s plastic axial capacity is the only enforced provision in Annex J of Eurocode 3.The methods for applying loads to the connection were considered to be only monotonic loadings. For the nonlinear finite element analysis the modelling process was carried out using ABAQUS computer program. The results of the finite element analysis of the connection showed that by applying the tensile axial load of the beam into the connection the ultimate bending capacity of the connection will decrease. Finally, it reveals that the presence of an axial force on the beam significantly modifies the joint response.

It is quite known that there are various methods for treatment of cancer. Although virus therapy has been proved to effective in the improvement of cancer, this method is still at its primary stage. Therefore, treatment methods such as chemotherapy and radiotherapy are still versatile. In these methods, drugs are prescribed. The most important question in the treatment of brain tumors is the rate of drug prescription for the patient so that it can help the patient recover and minimize damages to the healthy cells. A.El-Ghohary demonstrated that a mathematical model of brain tumor system can be seen in an optimal nonlinear control problem. In this paper, attempt is made to transform the nonlinear optimal control problem into an optimal control problem in the measure theory and to approximate a new problem with a linear programming problem and subsequently, to specify the drug dose for the patients with cancer. In addition, we deal with the examination of stability of system balance points. Using drug dose control stabilizes the unstable balance points of the tumor system. In the end, a comparison is made between the results obtained from the above mentioned method and the approximate solution proposed by Al-Gohary.

We investigate the existence of three distinct solutions for a class of quasilinearDirichlet ellipticsystems involving the (p,q)-Laplacian operator. Our main tool is a recentthree critical points Theorem of B. Ricceri [On a three critical points theorem, Arch. Math (Basel) 75 (2000) 220-226.

In this paper, an analytic method, namely the homotopy analysis method (HAM) is applied to obtain approximations to the analytic solution of special form of the generalized nonlinear Benjamin- Bona-Mahony-Burgers equation (BBMB). This approximate solution, which is obtained as a series of exponentials, has a reasonable residual error. The results reveal that the presented method is very effective and convenient.

Fuzzy pattern trees induction was recently introduced as a novel machine learning method for classification. Roughly speaking, a pattern tree is a hierarchical, tree-like structure, whose inner nodes are marked with generalized fuzzy logical or arithmetic operators and whose leaf nodes are associated with fuzzy predicates on input attributes. Operators perform an important role in fuzzy pattern trees. These operators include arithmetic and logical operators. Unlike arithmetic operators,logical operators that were used in these trees are not parameterized. As arithmetic operators, we can choose weighted arithmetic mean and ordered weighted arithmetic mean. There are several families which contain the standard triangular norms and conorms as special cases. This way, we would implicitly select from an infinite number of operators, just like in the case of arithmetic operators. We develop this algorithm by proposing a method to using parameterized logical operators and tuning their parameters by imperialist competitive algorithm. In experimental studies, we compare our method to previous version of algorithm, showing that our method is significantly outperformsthe previous method in terms of predictive accuracy andflexibilityin operator selection.