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Mehdi Ghatee
  • Department of Computer Science, Amirkabir University of Technology, Tehran, Iran
  • +9821 64542531
  • Mehdi Ghatee (مهدی قطعی) is a Full Professor of Computer Science at the Amirkabir University of Technology, Tehran, I... moreedit
  • Professor S. Mehdi Hashemiedit
Driver identification is an important research area in intelligent transportation systems, with applications in commercial freight transport and usage-based insurance. One way to perform the identification is to use smartphones as sensor... more
Driver identification is an important research area in intelligent transportation systems, with applications in commercial freight transport and usage-based insurance. One way to perform the identification is to use smartphones as sensor devices. By extracting features from smartphone-embedded sensors, various machine learning methods can identify the driver. The identification becomes particularly challenging when the number of drivers increases. In this situation, there is often not enough data for successful driver identification. This paper uses a Generative Adversarial Network (GAN) for data augmentation to solve the problem of lacking data. Since GAN diversifies the drivers' data, it extends the applicability of the driver identification. Although GANs are commonly used in image processing for image augmentation, their use for driving signal augmentation is novel. Our experiments prove their utility in generating driving signals emanating from the Discrete Wavelet Transform (DWT) on smartphones' accelerometer and gyroscope signals. After collecting the augmented data, their histograms along the overlapped windows are fed to machine learning methods covered by a Stacked Generalization Method (SGM). The presented hybrid GAN-SGM approach identifies drivers with 97% accuracy, 98% precision, 97% recall, and 97% F1-measure that outperforms standard machine learning methods that process features extracted by the statistical, spectral, and temporal approaches.
To real-time management of the bridges under dynamic conditions, this paper develops a rule-based decision support framework to extract the necessary rules from simulation results made by Aimsun. In this rule-based system, the supervised... more
To real-time management of the bridges under dynamic conditions, this paper develops a rule-based decision support framework to extract the necessary rules from simulation results made by Aimsun. In this rule-based system, the supervised and the unsupervised learning algorithms are applied to generalize the rules where the initial set of rules are provided by the aid of fuzzy rule generation algorithms on the results of Aimsun traffic micro-simulation software. As a pilot case study, Nasr Bridge in Tehran is simulated in Aimsun7 and WEKA data mining software is used to execute the learning algorithms. Based on this experiment, the accuracy of the supervised algorithms to generalize the rules is greater than 80%. In addition, CART decision tree and sequential minimal optimization (SMO) provides 100% accuracy for normal data and so these algorithms are so reliable for crisis management on bridge. This means that, it is possible to use such machine learning methods to manage bridges in...
Various feature selection methods have been recently proposed on different applications to reduce the computational burden of machine learning algorithms as well as the complexity of learned models. Preserving sample similarities and... more
Various feature selection methods have been recently proposed on different applications to reduce the computational burden of machine learning algorithms as well as the complexity of learned models. Preserving sample similarities and selecting discriminative features are two major factors should be satisfied, especially by unsupervised feature selection methods. This paper aims to propose a novel unsupervised feature selection approach which employs an $\ell_{2,1}$-norm regularization model to preserve global and local similarities by minimizing an objective function. Cluster analysis is also incorporated in this framework to take the inherent structure of the data into account. The experimental results show the strength of the proposed approach as compared with the earlier well-known methods on a variety of standard datasets.
In this paper, we will present a Hopfield Neural Network (HNN) model to tackle the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW). The rationale of the proposed HNN model is to derive a new form of energy function to... more
In this paper, we will present a Hopfield Neural Network (HNN) model to tackle the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW). The rationale of the proposed HNN model is to derive a new form of energy function to describe vehicle routing costs in the VRPFTW. In order to achieve a minimum total cost, we first study a standard mathematical model which contains all constraints in the VRPFTW. Then, a Hopfield Neural Network (HNN) model is designed to rapidly find the satisfactory solution of VRPFTW. Finally, we evaluate the proposed HNN by a number of Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances. Our computational results show that the proposed HNN significantly reduces the computational time compared to standard mathematical methods.
Various feature selection methods have been recently proposed on different applications to reduce the computational burden of machine learning algorithms as well as the complexity of learned models. Preserving sample similarities and... more
Various feature selection methods have been recently proposed on different applications to reduce the computational burden of machine learning algorithms as well as the complexity of learned models. Preserving sample similarities and selecting discriminative features are two major factors should be satisfied, especially by unsupervised feature selection methods. This paper aims to propose a novel unsupervised feature selection approach which employs an $\ell_{2,1}$-norm regularization model to preserve global and local similarities by minimizing an objective function. Cluster analysis is also incorporated in this framework to take the inherent structure of the data into account. The experimental results show the strength of the proposed approach as compared with the earlier well-known methods on a variety of standard datasets.
The aim of this paper is to develop an activity-based travel demand model by receiving cellular network data. Our contribution is to model the uncertainty of human behaviors and also the ambiguity in features affecting users’ activities.... more
The aim of this paper is to develop an activity-based travel demand model by receiving cellular network data. Our contribution is to model the uncertainty of human behaviors and also the ambiguity in features affecting users’ activities. We used probabilities to model the first aspect and fuzzy theory to treat with the second; therefore, a hybrid model is proposed based on the Hidden Markov Model (HMM) and Fuzzy Inference System (FIS) such that FIS is used in the emission model of HMM. To show the efficiency of this model, we applied the model to the data collected by Irancell operator and validated the results with four different data sources; labeled data collected from volunteers, ground truth data labeled by an expert, activity-based number of trips generated from/attracted to different regions and reported traffic volume of highways. We have shown that the activity recognition accuracy of the model is 83% and an average error of 5% is obtained when comparing the statistics of t...
In this paper, we will present a Hopfield Neural Network (HNN) model to tackle the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW). The rationale of the proposed HNN model is to derive a new form of energy function to... more
In this paper, we will present a Hopfield Neural Network (HNN) model to tackle the Vehicle Routing Problem with Flexible Time Windows (VRPFlexTW). The rationale of the proposed HNN model is to derive a new form of energy function to describe vehicle routing costs in the VRPFTW. In order to achieve a minimum total cost, we first study a standard mathematical model which contains all constraints in the VRPFTW. Then, a Hopfield Neural Network (HNN) model is designed to rapidly find the satisfactory solution of VRPFTW. Finally, we evaluate the proposed HNN by a number of Vehicle Routing Problem with Time Windows (VRPTW) benchmark instances. Our computational results show that the proposed HNN significantly reduces the computational time compared to standard mathematical methods.
The aim of this paper is to develop an activity-based travel demand model by receiving cellular network data. Our contribution is to model the uncertainty of human behaviors and also the ambiguity in features affecting users’ activities.... more
The aim of this paper is to develop an activity-based travel demand model by receiving cellular network data. Our contribution is to model the uncertainty of human behaviors and also the ambiguity in features affecting users’ activities. We used probabilities to model the first aspect and fuzzy theory to treat with the second; therefore, a hybrid model is proposed based on the Hidden Markov Model (HMM) and Fuzzy Inference System (FIS) such that FIS is used in the emission model of HMM. To show the efficiency of this model, we applied the model to the data collected by Irancell operator and validated the results with four different data sources; labeled data collected from volunteers, ground truth data labeled by an expert, activity-based number of trips generated from/attracted to different regions and reported traffic volume of highways. We have shown that the activity recognition accuracy of the model is 83% and an average error of 5% is obtained when comparing the statistics of t...
This paper tries to minimize the sum of a linear and a linear fractional function over a closed convex set defined by some linear and conic quadratic constraints. At first, we represent some necessary and sufficient conditions for the... more
This paper tries to minimize the sum of a linear and a linear fractional function over a closed convex set defined by some linear and conic quadratic constraints. At first, we represent some necessary and sufficient conditions for the pseudoconvexity of the problem. For each of the conditions, under some reasonable assumptions, an appropriate second-order cone programming (SOCP) reformulation of the problem is stated and a new applicable solution procedure is proposed. Efficiency of the proposed reformulations is demonstrated by numerical experiments. Secondly, we limit our attention to binary variables and derive a sufficient condition for SOCP representability. Using the experimental results on random instances, we show that the proposed conic reformulation is more efficient in comparison with the well-known linearization technique and it produces more eligible cuts for the branch and bound algorithm.
This paper tries to minimize the sum of a linear and a linear fractional function over a closed convex set defined by some linear and conic quadratic constraints. At first, we represent some necessary and sufficient conditions for the... more
This paper tries to minimize the sum of a linear and a linear fractional function over a closed convex set defined by some linear and conic quadratic constraints. At first, we represent some necessary and sufficient conditions for the pseudoconvexity of the problem. For each of the conditions, under some reasonable assumptions, an appropriate second-order cone programming (SOCP) reformulation of the problem is stated and a new applicable solution procedure is proposed. Efficiency of the proposed reformulations is demonstrated by numerical experiments. Secondly, we limit our attention to binary variables and derive a sufficient condition for SOCP representability. Using the experimental results on random instances, we show that the proposed conic reformulation is more efficient in comparison with the well-known linearization technique and it produces more eligible cuts for the branch and bound algorithm.
Vehicular communication systems are developed not only to increase safety but also for mobility of road transportation. Roadside units (RSU) are the prominent elements of this technology. This equipment is installed in roadside and... more
Vehicular communication systems are developed not only to increase safety but also for mobility of road transportation. Roadside units (RSU) are the prominent elements of this technology. This equipment is installed in roadside and intersections to gather traffic information from vehicles and to send messages and alarms to vehicles. Due to costly implementation and maintenance of this equipment, determining the number of RSUs and placement of them is an important problem. In this paper, we proposed a novel binary programming (BP) model to a placement of RSUs beside a road for maximizing information dissemination to vehicles. This approach makes decisions based on the number of curves, the number of on-ramps, accident rate, weather condition, and cost limitations. The proposed model is applied on Tehran to Pardis freeway. According to computational experiments, four operational phases to equip the whole road for information dissemination is obtained.
This paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations. This main fuzzy problem is efficiently decomposed and... more
This paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations. This main fuzzy problem is efficiently decomposed and is solved by a branch-and-price algorithm. In the nodes of the branch-and-price tree, the linear relaxation of the problem is solved by applying a column generation method. Also, the relationship between the optimal solutions of this problem under possibility and necessity relations is derived. To show the validation of the proposed algorithm, some results are proved. In addition, the application of this algorithm is illustrated on fuzzy multicommodity flow problem. For this case, a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method. Some examples are solved and their results are compared with the previous works. Also, the results of the proposed algorithm are reported on some large-scale benchmark instances.
This paper develops a new rule-based decision support system (RB-DSS) to find the safest solutions for routing, scheduling, and assignment in Hazmat transportation management. To define the safe program in RB-DSS, the accident frequency... more
This paper develops a new rule-based decision support system (RB-DSS) to find the safest solutions for routing, scheduling, and assignment in Hazmat transportation management. To define the safe program in RB-DSS, the accident frequency and severity are estimated for different scenarios of transportation, and they are used to classify the scenarios by a new structure of decision tree (DT), which is proposed to select branching variables at the primary levels according to the experts' perception. The outputs of the DT are stated in the form of if-then rules trained by a multilayer perceptron neural network to generalize the safe programs for Hazmat transportation. To illustrate the performance of this approach, the UK road accident data set is used.
Abstract: The multi-modal network has a great role in urban transportation networks in which travelers apply several modes such as subway, bus, feeder, walking and etc. Some of the most applicable problems in multi-modal transportation... more
Abstract: The multi-modal network has a great role in urban transportation networks in which travelers apply several modes such as subway, bus, feeder, walking and etc. Some of the most applicable problems in multi-modal transportation networks are network design, scheduling and routing. This paper briefly introduces these problems and their applications in traffic management systems such as ATMS and ATIS. Almost all of these problems are known as Np-hard so intelligent algorithms such as neural networks, ant colony or genetic ...
In this paper, a multi-perspective decision support system (MP-DSS) to design hierarchical public transportation network is developed. Since this problem depends on different perspectives , MP-DSS consists of two subsystems with macro and... more
In this paper, a multi-perspective decision support system (MP-DSS) to design hierarchical public transportation network is developed. Since this problem depends on different perspectives , MP-DSS consists of two subsystems with macro and micro subsystems based on travel information , land use and expert knowledge. In the micro subsystem , two sub-modules are developed considering origin-destination demand matrix and attractive places to travel. In the first subsystem , based on traffic assignment models , the bus corridors can be extended and by the second approach , connectivity between attractive places can be provided by new bus lanes. Multi-commodity flow problem and spanning tree problem are used in these two sub-modules to assign the public services to the corresponding networks. The corridors obtained from these sub-modules are evaluated by experts board module. These corridors are used to extend bus rapid transit (BRT) , exclusive bus lanes between multiple districts and sh...
Abstract Model selection is a challenge, and a popular Convolutional Neural Networks (CNN) usually takes extra-need parameters. It causes overfitting in real applications. Besides, the extracted hidden features would be lost when the... more
Abstract Model selection is a challenge, and a popular Convolutional Neural Networks (CNN) usually takes extra-need parameters. It causes overfitting in real applications. Besides, the extracted hidden features would be lost when the number of convolution layers increases. We use the least auxiliary loss-functions to solve both of these problems. To this end, an optimization problem is stated to select a set of layers with the highest contributions in the training process. Also, an impact growth adaptation procedure adjusts the weights of losses. The constructed Least Auxiliary Loss-functions with Impact Growth Adaptation (Laliga) is a professional forum to select the best settings of auxiliary loss functions for CNNs training. Laliga memorizes the hidden features carefully and better represents the space by using non-redundant and more relevant features. Also, it uses singular value decomposition to regularize the weights. The theoretical results show that Laliga decreases overfitting substantially. Although this algorithm is useful for all CNN models, its results are auspicious for Visual Geometry Group (VGG) networks. The testing accuracies of Laliga for different VGG models on MNIST, CIFAR-10, and CIFAR-100 datasets are 99.7 % , 92.3 % , and 73.4 % , indicating Laliga overcomes many regularization methods in the dropout family. Besides, on more complicated datasets Caltech-101 and Caltech-256, its accuracies raise than 66.1 % and 33.2 % , which are better than dropout and close to Adaptive Spectral Regularization (ASR) results, although Laliga converges rapidly than ASR. Finally, we analyze the results of Laliga in a transportation case study.
Abstract Classification of the high-dimensional data by a new expert system is followed in the current paper. The proposed system defines some non-disjoint clusters of highly relevant features with the least inner-redundancy. For each... more
Abstract Classification of the high-dimensional data by a new expert system is followed in the current paper. The proposed system defines some non-disjoint clusters of highly relevant features with the least inner-redundancy. For each cluster, a neural tree is implemented exploiting an Extreme Learning Machine (ELM) together an inference engine in any node. The derived classification rules from ELM are stored in the rule-base of the inference engine to recognize the classes. A majority voting is used to unify the results of the different neural trees. This structure is refereed as the Forest of Extreme Learning Machines with Rule-base Transferring (FELM-RT). The contribution of FELM-RT is to decrease the duplicated computations by using two novel interaction models between the neural trees. In the first interaction model, namely Peer-to-Peer (P2P) model, each node can share its rule-base with the other nodes of the various neural trees. In the second that is referred as Server-to-Client (S2C) model, a neural tree that works on a cluster with the best relevancy and redundancy, shares the rules with the other neural trees. In both of the models, a fuzzy aggregation technique is used to adjust the certainty of the rules. The processing time of FELM-RT decreases essentially and it improves the classification accuracy. The high results of F-measure and G-mean, show that FELM-RT classifies the high-dimensional datasets without over-fitting. The comparison between FELM-RT and some state-of-the-art classifiers reveals that FELM-RT overcomes them specially on the datasets with more than 3 million features.
The future of transportation is driven by the use of artificial intelligence to improve living and transportation. This paper presents a neural network-based system for driver identification using data collected by a smartphone. This... more
The future of transportation is driven by the use of artificial intelligence to improve living and transportation. This paper presents a neural network-based system for driver identification using data collected by a smartphone. This system identifies the driver automatically, reliably and in real-time without the need for facial recognition and also does not violate privacy. The system architecture consists of three modules data collection, preprocessing and identification. In the data collection module, the data of the accelerometer and gyroscope sensors are collected using a smartphone. The preprocessing module includes noise removal, data cleaning, and segmentation. In this module, lost values will be retrieved and data of stopped vehicle will be deleted. Finally, effective statistical properties are extracted from data-windows. In the identification module, machine learning algorithms are used to identify drivers' patterns. According to experiments, the best algorithm for d...
Driver identification is an important research area in intelligent transportation systems, with applications in commercial freight transport and usage-based insurance. One way to perform the identification is to use smartphones as sensor... more
Driver identification is an important research area in intelligent transportation systems, with applications in commercial freight transport and usage-based insurance. One way to perform the identification is to use smartphones as sensor devices. By extracting features from smartphone-embedded sensors, various machine learning methods can identify the driver. The identification becomes particularly challenging when the number of drivers increases. In this situation, there is often not enough data for successful driver identification. This paper uses a Generative Adversarial Network (GAN) for data augmentation to solve the problem of lacking data. Since GAN diversifies the drivers' data, it extends the applicability of the driver identification. Although GANs are commonly used in image processing for image augmentation, their use for driving signal augmentation is novel. Our experiments prove their utility in generating driving signals emanating from the Discrete Wavelet Transfor...
Abstract Classification of the high-dimensional data by a new expert system is followed in the current paper. The proposed system defines some non-disjoint clusters of highly relevant features with the least inner-redundancy. For each... more
Abstract Classification of the high-dimensional data by a new expert system is followed in the current paper. The proposed system defines some non-disjoint clusters of highly relevant features with the least inner-redundancy. For each cluster, a neural tree is implemented exploiting an Extreme Learning Machine (ELM) together an inference engine in any node. The derived classification rules from ELM are stored in the rule-base of the inference engine to recognize the classes. A majority voting is used to unify the results of the different neural trees. This structure is refereed as the Forest of Extreme Learning Machines with Rule-base Transferring (FELM-RT). The contribution of FELM-RT is to decrease the duplicated computations by using two novel interaction models between the neural trees. In the first interaction model, namely Peer-to-Peer (P2P) model, each node can share its rule-base with the other nodes of the various neural trees. In the second that is referred as Server-to-Client (S2C) model, a neural tree that works on a cluster with the best relevancy and redundancy, shares the rules with the other neural trees. In both of the models, a fuzzy aggregation technique is used to adjust the certainty of the rules. The processing time of FELM-RT decreases essentially and it improves the classification accuracy. The high results of F-measure and G-mean, show that FELM-RT classifies the high-dimensional datasets without over-fitting. The comparison between FELM-RT and some state-of-the-art classifiers reveals that FELM-RT overcomes them specially on the datasets with more than 3 million features.
Abstract Monitoring and evaluating of driving behavior is the main goal of this paper that encourage us to develop a new system based on Inertial Measurement Unit (IMU) sensors of smartphones. In this system, a hybrid of Discrete Wavelet... more
Abstract Monitoring and evaluating of driving behavior is the main goal of this paper that encourage us to develop a new system based on Inertial Measurement Unit (IMU) sensors of smartphones. In this system, a hybrid of Discrete Wavelet Transformation (DWT) and Adaptive Neuro Fuzzy Inference System (ANFIS) is used to recognize overall driving behaviors. The behaviors are classified into the safe, the semi-aggressive, and the aggressive classes that are adopted with Driver Anger Scale (DAS) self-reported questionnaire results. The proposed system extracts four features from IMU sensors in the forms of time series. They are decomposed by DWT in two levels and their energies are sent to six ANFISs. Each ANFIS models the different perception about driving behavior under uncertain knowledge and returns the similarity or dissimilarity between driving behaviors. The results of these six ANFISs are combined by three different decision fusion approaches. Results show that Coiflet-2 is the most suitable mother wavelet for driving behavior analysis. In addition, the proposed system recognizes the overall driving behavior patterns with 92% accuracy without necessity to evaluate the maneuvers one by one. We show that without longitude acceleration data, the driver behavior cannot be recognized successfully while the results do not disturb substantially when the gyroscope is not available.
We design a new ensemble system based on mixture of experts.The anti-correlation measure is augmented to error function of mixture of experts.The gating network assigns the weights to all of the ou...
ABSTRACT This paper proposes a new hybrid method namely SA-IP including simulated annealing and interior point algorithms to find the optimal toll prices based on level of service (LOS) in order to maximize the mobility in urban network.... more
ABSTRACT This paper proposes a new hybrid method namely SA-IP including simulated annealing and interior point algorithms to find the optimal toll prices based on level of service (LOS) in order to maximize the mobility in urban network. By considering six fuzzy LOS for flows, the tolls of congested links can be derived by a bi-level fuzzy programming problem. The objective function of the upper level problem is to minimize the difference between current LOS and desired LOS of links. In this level, to find optimal toll, a simulated annealing algorithm is used. The lower level problem is a fuzzy flow estimator model with fuzzy link costs. Applying a famous defuzzification function, a real-valued multi-commodity flow problem can be obtained. Then a polynomial time interior point algorithm is proposed to find the optimal solution regarding to the estimated flows. In pricing process, by imposing cost on some links with LOS F or E, users incline to use other links with better LOS and less cost. During the iteration of SA algorithm, the LOS of a lot of links gradually closes to their desired values and so the algorithm decreases the number of links with LOS worse than desirable LOS. Sioux Falls network is considered to illustrate the performance of SA-IP method on congestion pricing based on different LOS. In this pilot, after toll pricing, the number of links with LOS D, E and F are reduced and LOS of a great number of links becomes C. Also the value of objective function improves 65.97% after toll pricing process. It is shown optimal toll for considerable network is 5 dollar and by imposing higher toll, objective function will be worse.
Research Interests:
Research Interests:
We treat with the Minimal Cost Multicommodity Flow Problem (MCMFP) in the setting of fuzzy sets, by forming a coherent algorithmic framework referred to as a fuzzy MCMFP. Given the character of granular information captured by fuzzy sets,... more
We treat with the Minimal Cost Multicommodity Flow Problem (MCMFP) in the setting of fuzzy sets, by forming a coherent algorithmic framework referred to as a fuzzy MCMFP. Given the character of granular information captured by fuzzy sets, the objective is to find multiple flows satisfying the demands of commodities, by using available supplies consuming the least possible cost. With this regard, the supply and demand of nodes may be presented linguistically; the travel cost and capacity of links can be defined under ...
Research Interests:
ABSTRACT This paper deals with a new decision support system (DSS) for intelligent tunnel. This DSS includes two subsystems. In the first, the rules are extracted from incident severity database and micro-simulation results. Then simple... more
ABSTRACT This paper deals with a new decision support system (DSS) for intelligent tunnel. This DSS includes two subsystems. In the first, the rules are extracted from incident severity database and micro-simulation results. Then simple fuzzy grid technique is applied to generate the rules. The accuracy degree of this subsystem is 63% in the presented experiment. In the second subsystem, these rules are trained by DSS with two modules. In the first module unsupervised learning methods such as K-mean, farthest first, self-organizing map (SOM), learning vector quantization (LVQ), hierarchical clustering and filtered clustering are implemented. The best performance in this module corresponds to hierarchical clustering with 70% accuracy on normal data. Also learning vector quantization (LVQ) provides 74% accuracy on discrete data in this module. In the second module feed forward neural network, Naïve Bayes tree, classification and regression tree (CART), and support vector machine (SVM) are applied. In this module the most accuracy is 87% on normal data regarding to feed forward neural network and also Naïve Bayes tree provides 89.3% accuracy on discrete data. To illustrate the performance of the proposed learning DSS, we use two sources of data. The first is UK road safety data bank which is applied to estimate severity of real incidents in tunnel. The second one is simulation results of Niayesh tunnel in Tehran which is implemented on Aimsun 7. Although only incident management in tunnel is focused by this paper, it is possible to find similar results on learning DSS for other user services of intelligent tunnel.
Fuzzy mathematics is a generalization in which fuzzy numbers replace real numbers and fuzzy arithmetic replaces real arithmetic. It is an excellent scope for modeling vague and uncertain aspects of the actual environments. In this... more
Fuzzy mathematics is a generalization in which fuzzy numbers replace real numbers and fuzzy arithmetic replaces real arithmetic. It is an excellent scope for modeling vague and uncertain aspects of the actual environments. In this important area, Dubois and Prade1 defined a fuzzy matrix as a rectangular array of fuzzy numbers. They have also defined the LR type fuzzy numbers with some useful approximate arithmetic operators. The aim of this paper is to extend some useful aspects of linear algebra e.g. determinant, norm and eigenvalue for fuzzy matrices with LR fuzzy number entries by the use of fuzzy arithmetic. Finally, applications in fuzzy analytical hierarchy process (AHP) are investigated.
The aim of minimal cost flow problem (MCFP) is to find the least transportation cost of a single commodity through a capacitated network. This paper presents a model to deal with one particular group of such problems in which the supply... more
The aim of minimal cost flow problem (MCFP) is to find the least transportation cost of a single commodity through a capacitated network. This paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers. For easier reference, hereafter, we refer to this group of problems as fully fuzzified MCFP. To represent our model, Hukuhara's difference and approximated multiplication are used. Thereafter, we sort fuzzy ...

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