ADVANCES IN MATHEMATICAL MODELING
Year:2017 | Volume:7 | Issue:1 |Papers Count:6

Estimation methods of parameters of fuzzy least-squares regression have very sensitivity to unusual data (e.g. outliers). In the presence of outliers, most of the existing estimation methods of parameters of this kind of models using least-squares approach provide unexpected and unreliable estimators with amounts of errors. Therefore, in this paper a robust least trimmed squares fuzzy regression model is described for modeling for crisp input-fuzzy output variables. In this approach, the constructed target function in model parameter estimation problem in such a way which minimizes the sum of the h smallest squared residuals. This method has an algorithm that estimates the optimal values of the parameters based on different selected combinations of h good observations of the data set of size n. Therefore, this method has the ability of reducing the effects of such a data in estimation of the parameters of the model. Finally, the investigated fuzzy regression model is applied and studied to modeling real-world data set in hydrology which sometimes contains outlier points. In this regard, a comparison study between the proposed method and ordinary least squares fuzzy regression method is considered. The comparison results of the applied study reveal that for this particular data set the proposed method performs better fitting than the well-known ordinary fuzzy least-squares regression model. Also the proposed method identified the points that have bad effect on estimation problem of the parameters.

The Beta regression model is usually used for modeling the rates or proportions confined in an open interval (0, 1). In some studies, the data may also include zero and one. In this paper, an augmented Beta regression model that is a mixture of Beta distribution with two degenerated distributions at 0 and 1 is presented for rates or proportions confined in [0, 1]. For the augmented mixed Beta model with reparametrization of Beta distribution, the mean and precision parameters were modeled including fixed and random effects. This is while taking into account that the random effects make these models applicable to correlated data. Here, the augmented mixed Beta model is presented. Then this model is evaluated in a simulation study. Next, the application of this model is shown for analyzing the proportions of employed persons in every household. Finally, conclusion and results are presented.

Cluster analysis is one of the most important methods in classification in which the observations of each cluster has maximum similarity in terms of some desirable variables. In general the clustering methods are divided into two parts, crisp and fuzzy. In usual clustering methods an observation is in only one cluster whereas in fuzzy clustering it may fall into two or more clusters simultaneously. Yang and Ko (1996) introduced a fuzzy clustering method. Their method is an extension of the usual k-means clustering method as they assumed that the observations are fuzzy. A fuzzy regression model is used for studying the relationship between the explanatory variables and dependent variable. In some situations when some observations are dispersed and are heterogeneous, the regression model may not have a goodness of fit for data. To solve this problem Yang and Ko classified data and then based on fuzzy observations fitted a regression model to each cluster. In this paper we first explain the semi-parametric regression model introduced by Hesamian et al. [2017] and then use their model to perform our clustering method for fuzzy observations. Finally, based on some suggested goodness of fit criterions. We compare our results with those of Yang and Ko.

The sharp decline in oil resources and environmental pollutions are the most important motivations for the development of green fuels in Iran. Among the different raw materials used for the production of green fuels, microalgae is considered as one of the most important resources and have attracted a lot of attentions globally. In order to accelerate the development of this industry, it is essential to design an efficient microalgae-based biofuel supply chain. For this purpose, this paper proposes robust programming approaches for the design and optimization of the microalgae biofuel supply chain under uncertainty. The proposed supply chain optimization model is formulated based on two robust optimization approaches under different uncertainty sets. In a case study, the performance of the two robust supply chain design models is evaluated by considering the different degrees of conservatism level of decision makers. The results of the robust models and sensitivity analysis show that the developed supply chain model can be used for the development of microalgae biofuel in the future.

Contamination transport in the river is expressed using advection-dispersion-reaction partial differential equation (ADRE). There are a variety of analytical and numerical methods for solving the aforementioned equation. Analytical solutions such integral transforms are very powerful and useful tools in solving ADRE. In the present study, one-dimensional ADRE with space-dependent coefficients in river has been solved using generalized integral transform technique (GITT). Forward and inverse transformations are defined in GITT technique which using them in problem solving leads to generating time-dependent system of ordinary differential equations. Analytical solution verification was accomplished using the comparison of the results of mathematical models with analytical solutions and also numerically model based on finite differences method. To inspect the accuracy of models’ results, statistical indicators were calculated. Comparison of GITTs’ result with analytical solutions that used in verification and numerical solution implied high accuracy of the proposed solution. Also to show the importance of the application of variable coefficients in ADRE in river, the results of solving equation with constant and variable coefficients were compared.

In this paper, a new three-step method based on cubic spline will be construct to the numerical solution of a class of partial differential equations well-known as Burgers’-Huxley and Burgers’-Fisher. As we know, the maximum order achieved using cubic spline for interpolating is O(h4), but this order is reduced when it is used for the solution of differential equations. Here we will find an O(h6) super convergent approximation for the solution of Burgers’-Huxley and Burgers’-Fisher equations by defining some proper end conditions and constructing a three step deferred-correction algorithm. We will discuss the convergence and error bounds of the method using Green’s function definition in details. In addition, to verify the obtained error bounds, some numerical examples will be presented. Finally, we will try to show the applicability and efficiency of the method by comparing the results with other existing methods.