Sharif Digital Repository

In this paper, we propose two new algorithms for transductive multi-label learning from missing data. In transductive matrix completion (MC), the challenge is prediction while the data matrix is partially observed. The joint MC and prediction tasks are addressed simultaneously to enhance accuracy in comparison with separate tackling of each. In this setting, the labels to be predicted are modeled as missing entries inside a stacked matrix along the feature-instance data. Assuming the data matrix is of low rank, we propose a new recommendation method for transductive MC by posing the problem as a minimization of the smoothed rank function with non-affine constraints, rather than its convex... 

We explore some duality properties in fuzzy number linear programming problems. By use of a linear ranking function we introduce the dual of fuzzy number linear programming primal problems. We then present several duality results. © 2006 Elsevier Inc. All rights reserved  

Recently, fuzzy variable linear programming problems have attracted some interests. We introduce the dual of fuzzy variable linear programming problem, and then deduce some important duality results. COPYRIGHT © ENFORMATIKA  

We propose an approach for computing the general compromised solution of an LR fuzzy linear system by use of a ranking function when the coefficient matrix is a crisp m×n matrix. The solution is so that mean values of a compromised solution satisfies the corresponding crisp linear system. We show that if the corresponding crisp system is incompatible, then the fuzzy linear system lacks any solution. Otherwise, we solve a constrained least squares problem to compute a compromised solution. If the optimal value of the constrained least squares problem is zero, then we obtain the LR solution, namely the exact solution, of the system with respect to a ranking function. On the other hand, if the... 

We discuss how to solve bipolar fuzzy quadratic programming problems, where the parameters are bipolar triangular fuzzy numbers, making use of linear ranking functions. Also, we explore some duality properties of bipolar triangular fuzzy number quadratic programming problem (BTFNQPP). © 2017 IEEE  

To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search (VNS) algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a... 

To solve a fuzzy optimization problem, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre’s method as an effective approach for comparison of LR fuzzy numbers. Using our new results on LR fuzzy numbers, we show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. We propose a new variable neighborhood search approach for solving fuzzy number quadratic programming problems by using the modified Kerre’s method. In our algorithm, a local search is performed using descent directions, found by solving five crisp mathematical programming problems. In several available methods, a fuzzy optimization... 

Recently, Ghanbari and Mahdavi-Amiri (Appl Math Model 34:3363–3375, 2010) gave the general compromised solution of an LR fuzzy linear system using ABS algorithm. Here, using this general solution, we solve quadratic programming problems with fuzzy LR variables. We convert fuzzy quadratic programming problem to a crisp quadratic problem by using general solution of fuzzy linear system. By using this method, the crisp optimization problem has fewer variables in comparison with other methods, specially when rank of the coefficient matrix is full. Thus, solving the fuzzy quadratic programming problem by using our proposed method is computationally easier than the solving fuzzy quadratic... 

We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently,... 

In this paper, we introduce a novel and robust approach to quantized matrix completion. First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to control the violation from quantization bounds due to two properties: first, it is differentiable; and second, it is less sensitive to outliers than the quadratic loss. A smooth rank approximation is utilized to endorse lower rank on the genuine data matrix. Thus, an unconstrained optimization problem with differentiable objective function is obtained allowing us to advantage from... 

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally,... 

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach... 

To solve a fuzzy linear program, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method for comparison of LR fuzzy numbers. We give some new results on LR fuzzy numbers and show that to compare two LR fuzzy numbers, it is not necessary to compute the fuzzy maximum of two numbers directly. Using the modified Kerre's method, we propose a new variable neighborhood search algorithm for solving fuzzy number linear programming problems. In our algorithm, the local search is defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy optimization problem is converted to a... 

In this paper, we address the matrix completion problem and propose a novel algorithm based on a smoothed rank function (SRF) approximation. Among available algorithms like FPCA and OptSpace, there is no solution that can simultaneously cover wide range of easy and hard problems. This new algorithm provides accurate results in almost all scenarios with a reasonable run time. It especially has low execution time in hard problems where other methods need long time to converge. Furthermore, when the rank is known in advance and is high, our method is very faster than previous methods for the same accuracy. The main idea of the algorithm is based on a continuous and differentiable approximation... 

Bus network design is an important problem in public transportation. In practice, some parameters of this problem are uncertain. We propose two models for the bus terminal location problem with fuzzy parameters. In the first formulation, the number of passengers corresponding to each node is a fuzzy number. In the second formulation, an additional assumption of fuzzy neighborhood is considered. These problems being NP-hard, we use a genetic algorithm (GA) and a simulated annealing (SA) algorithm for solving them. We also propose an idea to hybridize these algorithms. In our hybrid algorithm, SA is applied as a neighborhood search procedure of GA on the best individual of the population,...