Mahdi Ranjbar | Ferdowsi University of Mashhad (original) (raw)
Papers by Mahdi Ranjbar
Scientific Reports, Dec 9, 2023
Soft Computing, Mar 17, 2022
Applied Mathematical Modelling, Apr 1, 2011
This paper presents a new neural network for solving quadratic programming problems. The new mode... more This paper presents a new neural network for solving quadratic programming problems. The new model has a simple form, furthermore it has a good convergence rate with a less number calculation operation than the old models. It converges very fast to exact solution of the dual problem and by substituting in a formulation, the optimal solution of the original problem is obtained. Neural network model with one of numerical method is solved. Finally, simple numerical examples are provided for more illustration.
Applied Soft Computing, 2018
Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applica... more Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applications. In this paper, we used two comparative operators for expressing monotonicity of the T-operators on hesitant fuzzy elements (HFEs). Hence, properties of some T-operators for Xu-Xia partial order (≤ H (m)) and Xia-Xu order (⪯) are studied on typical hesitant fuzzy elements (THFEs). Finally, an application of T-operators on HFEs has been explained in fuzzy rulebased systems for a practical problem in economics. Also, for a conceptual comparison, a benchmark data under a hesitant fuzzy information environment has been used.
Neural Computing and Applications, Dec 2, 2010
This paper is concentrated on two types of fuzzy linear programming problems. First type with fuz... more This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it’s simple implementation.
IEEE Transactions on Fuzzy Systems, Feb 1, 2020
Fuzzy set theory has been extensively employed in mathematical programming, especially in linear ... more Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places, where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems; therefore in this paper, we have studied such problems. For this purpose, at first the motivation of the paper is explained, then types of hesitant fuzzy linear programming models are introduced. Since it is not easy to take all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to describe symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach, and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.
Expert Systems With Applications, Aug 1, 2020
Abstract In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study so... more Abstract In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study some essential properties of these numbers. We show (α, k)-cuts that were discussed in the recent literature for hesitant fuzzy sets (HFSs), on HFNs have resulted in compact intervals. In the following, we propose a new binary operation on these numbers. It has shown that the outcome of the proposed operation is a HFN. In addition, a new hesitant fuzzy relationship for comparing two HFNs is given. Finally, some applications of these numbers are presented in two examples. For this purpose, we propose a new approach to solve linear programming with hesitant fuzzy parameters.
Engineering Applications of Artificial Intelligence, Sep 1, 2022
Neurocomputing, Apr 1, 2017
This paper presents an artificial neural network to solve the quadratic zero-one programming prob... more This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zeroone programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time.
Applied Intelligence, Apr 27, 2020
In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the ev... more In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.
Hesitant fuzzy numbers have been presented as an extension of the fuzzy numbers to take a better... more Hesitant fuzzy numbers have been presented as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. In this paper, we use a triangular hesitant fuzzy numbers in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the hesitant fuzzy numbers and a new method of comparing hesitant fuzzy numbers to get the hesitant fuzzy performance score. Finally, a practical example is provided to show the the effectiveness of this study.
Engineering Applications of Artificial Intelligence
Iranian Journal of Fuzzy Systems, 2021
A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant f... more A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a newlattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems.
Applied Intelligence
In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the ev... more In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.
Applied Soft Computing
Abstract Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory an... more Abstract Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applications. In this paper, we used two comparative operators for expressing monotonicity of the T-operators on hesitant fuzzy elements (HFEs). Hence, properties of some T-operators for Xu-Xia partial order ( ≤ ℍ ( m ) ) and Xia-Xu order (⪯) are studied on typical hesitant fuzzy elements (THFEs). Finally, an application of T-operators on HFEs has been explained in fuzzy rule-based systems for a practical problem in economics. Also, for a conceptual comparison, a benchmark data under a hesitant fuzzy information environment has been used.
Neurocomputing
This paper presents an artificial neural network to solve the quadratic zero-one programming prob... more This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zero-one programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time.
This paper is concentrated on two types of fuzzy linear programming problems. First type with fuz... more This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it’s simple implementation.
In this paper, we present a one-layer recurrent neural network (NN) for solving convex optimizati... more In this paper, we present a one-layer recurrent neural network (NN) for solving convex optimization problems by using the Mangasarian and Solodov (MS) implicit Lagrangian function. In this paper by using Krush–Kuhn–Tucker conditions and MS function the NN model was derived from an unconstrained minimization problem. The proposed NN model is one layer and compared to the available NNs for solving convex optimization problems, which has a better performance in convergence time. The proposed NN model is stable in the sense of Lyapunov and globally convergent to optimal solution of the original problem. Finally, simulation results on several numerical examples are presented and the validity of the proposed NN model is demonstrated.
Expert Systems with Applications
Scientific Reports, Dec 9, 2023
Soft Computing, Mar 17, 2022
Applied Mathematical Modelling, Apr 1, 2011
This paper presents a new neural network for solving quadratic programming problems. The new mode... more This paper presents a new neural network for solving quadratic programming problems. The new model has a simple form, furthermore it has a good convergence rate with a less number calculation operation than the old models. It converges very fast to exact solution of the dual problem and by substituting in a formulation, the optimal solution of the original problem is obtained. Neural network model with one of numerical method is solved. Finally, simple numerical examples are provided for more illustration.
Applied Soft Computing, 2018
Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applica... more Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applications. In this paper, we used two comparative operators for expressing monotonicity of the T-operators on hesitant fuzzy elements (HFEs). Hence, properties of some T-operators for Xu-Xia partial order (≤ H (m)) and Xia-Xu order (⪯) are studied on typical hesitant fuzzy elements (THFEs). Finally, an application of T-operators on HFEs has been explained in fuzzy rulebased systems for a practical problem in economics. Also, for a conceptual comparison, a benchmark data under a hesitant fuzzy information environment has been used.
Neural Computing and Applications, Dec 2, 2010
This paper is concentrated on two types of fuzzy linear programming problems. First type with fuz... more This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it’s simple implementation.
IEEE Transactions on Fuzzy Systems, Feb 1, 2020
Fuzzy set theory has been extensively employed in mathematical programming, especially in linear ... more Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places, where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems; therefore in this paper, we have studied such problems. For this purpose, at first the motivation of the paper is explained, then types of hesitant fuzzy linear programming models are introduced. Since it is not easy to take all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to describe symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach, and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.
Expert Systems With Applications, Aug 1, 2020
Abstract In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study so... more Abstract In this paper, we propose a new definition of hesitant fuzzy numbers (HFNs) and study some essential properties of these numbers. We show (α, k)-cuts that were discussed in the recent literature for hesitant fuzzy sets (HFSs), on HFNs have resulted in compact intervals. In the following, we propose a new binary operation on these numbers. It has shown that the outcome of the proposed operation is a HFN. In addition, a new hesitant fuzzy relationship for comparing two HFNs is given. Finally, some applications of these numbers are presented in two examples. For this purpose, we propose a new approach to solve linear programming with hesitant fuzzy parameters.
Engineering Applications of Artificial Intelligence, Sep 1, 2022
Neurocomputing, Apr 1, 2017
This paper presents an artificial neural network to solve the quadratic zero-one programming prob... more This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zeroone programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time.
Applied Intelligence, Apr 27, 2020
In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the ev... more In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.
Hesitant fuzzy numbers have been presented as an extension of the fuzzy numbers to take a better... more Hesitant fuzzy numbers have been presented as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. In this paper, we use a triangular hesitant fuzzy numbers in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the hesitant fuzzy numbers and a new method of comparing hesitant fuzzy numbers to get the hesitant fuzzy performance score. Finally, a practical example is provided to show the the effectiveness of this study.
Engineering Applications of Artificial Intelligence
Iranian Journal of Fuzzy Systems, 2021
A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant f... more A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a newlattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems.
Applied Intelligence
In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the ev... more In this paper, we introduce a hesitant fuzzy multi-objective programming problem, in which the evaluation information provided by the decision makers is expressed in a hesitant fuzzy environment. For this purpose a new solution concept, namely hesitant fuzzy Pareto optimal solution to the problem is introduced, and two methods are proposed to obtain it. Then it is shown that the optimal solutions of these methods are the hesitant fuzzy Pareto optimal solutions. Finally, these methods are implemented on some illustrative examples and comparative analysis of our methodology is taken with other extensions of fuzzy sets.
Applied Soft Computing
Abstract Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory an... more Abstract Extending of the T-operators on hesitant fuzzy sets (HFSs) is important in the theory and applications. In this paper, we used two comparative operators for expressing monotonicity of the T-operators on hesitant fuzzy elements (HFEs). Hence, properties of some T-operators for Xu-Xia partial order ( ≤ ℍ ( m ) ) and Xia-Xu order (⪯) are studied on typical hesitant fuzzy elements (THFEs). Finally, an application of T-operators on HFEs has been explained in fuzzy rule-based systems for a practical problem in economics. Also, for a conceptual comparison, a benchmark data under a hesitant fuzzy information environment has been used.
Neurocomputing
This paper presents an artificial neural network to solve the quadratic zero-one programming prob... more This paper presents an artificial neural network to solve the quadratic zero-one programming problems under linear constraints. In this paper, by using the connection between integer and nonlinear programming, the quadratic zero-one programming problem is transformed into the quadratic programming problem with nonlinear constraints. Then, by using the nonlinear complementarity problem (NCP) function and penalty method this problem is transformed into an unconstrained optimization problem. It is shown that the Hessian matrix of the associated function in the unconstrained optimization problem is positive definite in the optimal point. To solve the unconstrained optimization problem an artificial neural network is used. The proposed neural network has a simple structure and a low complexity of implementation. It is shown here that the proposed artificial neural network is stable in the sense of Lyapunov. Finally, some numerical examples are given to show that the proposed model finds the optimal solution of this problem in the low convergence time.
This paper is concentrated on two types of fuzzy linear programming problems. First type with fuz... more This paper is concentrated on two types of fuzzy linear programming problems. First type with fuzzy coefficients in the objective function and the second type with fuzzy right-hand side values and fuzzy variables. Considering fuzzy derivative and fuzzy differential equations, these kinds of problems are solved using a fuzzy neural network model. To show the applicability of the method, it is applied to solve the fuzzy shortest path problem and the fuzzy maximum flow problem. Numerical results illustrate the method accuracy and it’s simple implementation.
In this paper, we present a one-layer recurrent neural network (NN) for solving convex optimizati... more In this paper, we present a one-layer recurrent neural network (NN) for solving convex optimization problems by using the Mangasarian and Solodov (MS) implicit Lagrangian function. In this paper by using Krush–Kuhn–Tucker conditions and MS function the NN model was derived from an unconstrained minimization problem. The proposed NN model is one layer and compared to the available NNs for solving convex optimization problems, which has a better performance in convergence time. The proposed NN model is stable in the sense of Lyapunov and globally convergent to optimal solution of the original problem. Finally, simulation results on several numerical examples are presented and the validity of the proposed NN model is demonstrated.
Expert Systems with Applications