In this work, we propose an approach for computing the compromised solution of an LR fuzzy Linear system by using of a ranking function when the coefficient matrix is a crisp m´n matrix. To do this, we use expected interval to find an LR fuzzy vector, X~, such that the vector Â(AX~) has the least distance from Â(b~) in 1-norm and the 1-cut of X~ satisfies the crisp Linear system AX=b. Then, we solve the constrained LP-problem by using LINGO 11 software package and obtain optimal fuzzy number solution. Finally, we illustrate the proposed method by solving two numerical examples.

Remediation of heavy metals polluted soils by physical and chemical methods requires large investments and complicated technologies. Phytoremediation is a relatively new technology that employs plants to decontaminate soils, water, sediments and atmosphere. This technology, compared to other technological approaches, is an environmental-friendly, easy to use and inexpensive method. Modeling Phytoremediation process is needed for further understanding the governing process and also to manage the contaminated soils. The objective of this study was to present a macroscopic phytoremediation model for of Ni-Polluted Soil. For this purpose, a new formulation was derived based on soil and plant responses to Ni pollutants. This approach assumes that relative yield reduction function can resemble the total Ni concentration in the soil. Combining the related functions of soil and plant responses to soil Ni concentrations, the phytoremediated amounts of Ni were predicted. In order to verify the proposed models, large quantities of soil was thoroughly polluted with Ni. After achieving soil and pollutants equilibrium, the contaminated soils were then carefully packed into pots. Upland Cress (Lepidum sativum) seeds were germinated in these pots. The Ni of soil samples and plant materials were extracted by 4M HNO3 oxidation and wet oxidation methods, respectively. Ni concentrations in the soil extracts and plant digestion were measured by Atomic Absorption Spectrometer (Shimadzu, AA 670-G) and Inductively Coupled Plasma Optical Emission Spectrometry (Varian Vista-PRO). The results indicated that relative yield reduction function followed a non-Linear reduction trend. The results indicated that the proposed model for quantifying Ni concentration in plant can simulate the experimental data well (R2>0.93). The results also indicated that combining the non-Linear relative yield reduction function and the proposed power model for Ni concentration in plant, provides a reasonable performance to predict Ni phytoremediation (R2>0.93).

Fuzzy Linear programming problems can be used to model a wide variety of practical applications in which all or some decision parameters are stated in an imprecise fashion. These problems have been investigated and expanded by many researchers from various points of view. In this paper, we study a class of in finite-dimensional Linear programming problems, so-called separated continuous Linear programs with a fuzzy valued objective function. For this class of problem, we develop a strong duality result and present an approximation algorithm. The basic idea is to use the discretization technique to establish a relationship between the problem and an ordinary fuzzy Linear programming problem.

Quality of products and services is considered as a key factor for customer satisfaction. Quality function deployment (QFD) is known as a critical tool for translating voice of customers to prioritize technical requirements of a production. The level of this satisfaction depends on the number of fulfilled requirements. It should be noted that this level varies according to the possible constraints.This paper aims to maximize customer satisfaction based on the possible limitations by using a fuzzy Linear programming model. In this regard, customer requirements are prioritized by using fuzzy Delphi method and then the problem is changed to a Linear programming model considering to the possible relationships in QFD.The proposed model is used as a case study for construction industry.After running the model, the percentage of optimal performance for each of the technical production requirements is defined.

Prediction and control flood is essential in water resource management. Studying and analysis on this problem is done using flood routing methods in hydraulic science. The Muskingum model is one of the best methods in the hydrologic flood routing rivers. In order to estimate of the Muskingum parameters have been used experiential methods as trial and error method, least squares. Genetic algorithm is one of the estimation methods of the parameters. Comparison between experiential methods results and genetic algorithm show that Genetic algorithm method is benefit and easy method for estimated the Muskingum parameters. The determining of objective function is most important in this method (GA). In this paper, different objective functions have been selected for Linear and non-Linear Muskingum models and are optimized using genetic algorithm then the effects of objective function are investigated on prediction of Muskingum parameters and computational output discharge. Comparison between computational hydrograph of output discharge and experimental result show that the effects of objective function on result prediction predominate in the Linear Muskingum model whereas these are virtually negligible in non-Linear Muskingum model.