Statistical limit inferior and limit superior for sequences of fuzzy numbers
- Authors: Aytar, Salih , Mammadov, Musa , Pehlivan, Serpil
- Date: 2006
- Type: Text , Journal article
- Relation: Fuzzy Sets and Systems Vol. 157, no. 7 (2006), p. 976-985
- Full Text: false
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- Description: In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers. © 2005 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003001832
The core of a sequence of fuzzy numbers
- Authors: Aytar, Salih , Pehlivan, Serpil , Mammadov, Musa
- Date: 2008
- Type: Text , Journal article
- Relation: Fuzzy Sets and Systems Vol. 159, no. 24 (2008), p. 3369-3379
- Full Text: false
- Reviewed:
- Description: In this paper, based on level sets we define the limit inferior and limit superior of a bounded sequence of fuzzy numbers and prove some properties. We extend the concept of the core of a sequence of complex numbers, first introduced by Knopp in 1930, to a bounded sequence of fuzzy numbers and prove that the core of a sequence of fuzzy numbers is the interval [ν, μ] where ν and μ are extreme limit points of the sequence. © 2008 Elsevier B.V. All rights reserved.
A global optimization method for solving integer systems of equation
- Authors: Bai, Fusheng , Wu, Zhiyou , Yang, Y. J. , Mammadov, Musa
- Date: 2007
- Type: Text , Conference paper
- Relation: Paper presented at 7th International Conference on Optimization: Techniques and Applications, ICOTA7, Kobe International Conference Center, Japan : 12th-15th December 2007
- Full Text: false
- Description: 2003005717
A filled function method for constrained nonlinear equations
- Authors: Bai, Fusheng , Mammadov, Musa , Wu, Zhiyou , Yang, Yongjian
- Date: 2008
- Type: Text , Journal article
- Relation: Pacific Journal of Optimization Vol. 4, no. 1 (Jan 2008), p. 9-18
- Full Text: false
- Reviewed:
- Description: We consider the problem of solving a constrained system of nonlinear equations. After reformulating the system into an equivalent constrained global optimization problems, we construct a filled function based on a special property of the reformulated problem. A filled function method is then proposed to solve the constrained system of nonlinear equations. Some numerical examples are presented to illustrate the usefulness of the present techniques.
- Description: C1
An inexact modified subgradient algorithm for nonconvex optimization
- Authors: Burachik, Regina , Kaya, Yalcin , Mammadov, Musa
- Date: 2008
- Type: Text , Journal article
- Relation: Computational Optimization and Applications Vol. , no. (2008), p. 1-24
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- Description: We propose and analyze an inexact version of the modified subgradient (MSG) algorithm, which we call the IMSG algorithm, for nonsmooth and nonconvex optimization over a compact set. We prove that under an approximate, i.e. inexact, minimization of the sharp augmented Lagrangian, the main convergence properties of the MSG algorithm are preserved for the IMSG algorithm. Inexact minimization may allow to solve problems with less computational effort. We illustrate this through test problems, including an optimal bang-bang control problem, under several different inexactness schemes. © 2008 Springer Science+Business Media, LLC.
- Description: C1
An ensemble technique for multi class imbalanced problem using probabilistic neural networks
- Authors: Chandrasekara, N. , Tilakaratne, Chandima , Mammadov, Musa
- Date: 2018
- Type: Text , Journal article
- Relation: Advances and Applications in Statistics Vol. 53, no. 6 (2018), p. 647-658
- Full Text: false
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- Description: The class imbalanced problem is one of the major difficulties encountered by many researchers when using classification tools. Multi class problems are especially severe in this regard. The main objective of this study is to propose a suitable technique to handle multi class imbalanced problem. Probabilistic neural network (PNN) is used as the classification tool and the directional prediction of Australian, United States and Srilankan stock market indices is considered as the application. We propose an ensemble technique to handle multi class imbalanced problem that is called multi class undersampling based bagging (MCUB) technique. This is a new initiative that has not been considered in the literature to handle multi class imbalanced problem by employing PNN. The results obtained demonstrate that the proposed MCUB technique is capable of handling multi class imbalanced problem. Therefore, the PNN with the proposed ensemble technique can be used effectively in data classification. As a further study, other classification tools can be used to investigate the performance of the proposed MCUB technique in solving class imbalanced problems.
Optimization of multiple classifiers in data mining based on string rewriting systems
- Authors: Dazeley, Richard , Kelarev, Andrei , Yearwood, John , Mammadov, Musa
- Date: 2009
- Type: Text , Journal article
- Relation: Asian-European Journal of Mathematics Vol. 2, no. 1 (2009), p. 41-56
- Relation: https://purl.org/au-research/grants/arc/DP0211866
- Relation: https://purl.org/au-research/grants/arc/LP0669752
- Full Text:
- Description: Optimization of multiple classifiers is an important problem in data mining. We introduce additional structure on the class sets of the classifiers using string rewriting systems with a convenient matrix representation. The aim of the present paper is to develop an efficient algorithm for the optimization of the number of errors of individual classifiers, which can be corrected by these multiple classifiers.
Application of optimisation-based data mining techniques to tobacco control dataset
- Authors: Dzalilov, Zari , Zhang, J , Bagirov, Adil , Mammadov, Musa
- Date: 2010
- Type: Text , Journal article
- Relation: International Journal of Lean Thinking Vol. 1, no. 1 (2010), p. 27-41
- Full Text: false
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- Description: Tobacco smoking is one of the leading causes of death around the world. Consequently, control of tobacco use is an important global public health issue. Tobacco control may be aided by development of theoretical and methodological frameworks for describing and understanding complex tobacco control systems. Linear regression and logistic regression are currently very popular statistical techniques for modeling and analyzing complex data in tobacco control systems. However, in tobacco markets, numerous interrelated factors nontrivially interact with tobacco control policies, such that policies and control outcomes are nonlinearly related.
Application of optimisation-based data mining techniques to medical data sets: A comparative analysis
- Authors: Dzalilov, Zari , Bagirov, Adil , Mammadov, Musa
- Date: 2012
- Type: Text , Conference paper
- Relation: IMMM 2102: The Second International Conference on Advances in Information Mining and Management p. 41-46
- Full Text: false
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- Description: Abstract - Computational methods have become an important tool in the analysis of medical data sets. In this paper, we apply three optimisation-based data mining methods to the following data sets: (i) a cystic fibrosis data set and (ii) a tobacco control data set. Three algorithms used in the analysis of these data sets include: the modified linear least square fit, an optimization based heuristic algorithm for feature selection and an optimization based clustering algorithm. All these methods explore the relationship between features and classes, with the aim of determining contribution of specific features to the class outcome. However, the three algorithms are based on completely different approaches. We apply these methods to solve feature selection and classification problems. We also present comparative analysis of the algorithms using computational results. Results obtained confirm that these algorithms may be effectively applied to the analysis of other (bio)medical data sets
Predicting and controlling the dynamics of infectious diseases
- Authors: Evans, Robin , Mammadov, Musa
- Date: 2015
- Type: Text , Conference proceedings
- Relation: 54th IEEE Conference on Decision and Control, CDC 2015; Osaka, Japan; 15th-18th December 2015; Published in Proceedings of the IEEE Conference on Decision and Control; p. 5378-5383
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- Description: This paper introduces a new optimal control model to describe and control the dynamics of infectious diseases. In the present model, the average time to isolation (i.e. hospitalization) of infectious population is the main time-dependent parameter that defines the spread of infection. All the preventive measures aim to decrease the average time to isolation under given constraints. The model suggested allows one to generate a small number of possible future scenarios and to determine corresponding trajectories of infected population in different regions. Then, this information is used to find an optimal distribution of bed capabilities across countries/regions according to each scenario. © 2015 IEEE.
A new reliability analysis method based on the conjugate gradient direction
- Authors: Ezzati, Ghasem , Mammadov, Musa , Kulkarni, Siddhivinayak
- Date: 2015
- Type: Text , Journal article
- Relation: Structural and Multidisciplinary Optimization Vol. 51, no. 1 (2015), p. 89-98
- Full Text: false
- Reviewed:
- Description: Reliability-based design optimization (RBDO) is an important area in structural optimization. A principal step of the RBDO process is to solve a reliability analysis problem. This problem has been considered in inner loop of double-loop RBDO approaches. Although many algorithms have been developed for solving this problem, there are still some challenges. Existing algorithms do not have good convergence rates and often diverge. There is a need to develop more efficient and stable algorithms that can be used for evaluating all performance functions sufficiently. In this paper, a new method, called “Conjugate Gradient Analysis (CGA) Method”, is proposed to apply in the reliability analysis problems. This method is based on the conjugate gradient method. Some mathematical problems are provided in order to demonstrate the advantages of the proposed method compared with the existing methods. © 2014, Springer-Verlag Berlin Heidelberg.
A hybrid clustering algorithm using two level of abstraction
- Authors: Ghosh, Ranadhir , Mammadov, Musa , Ghosh, Moumita , Yearwood, John
- Date: 2005
- Type: Text , Conference paper
- Relation: Paper presented at Fuzzy Logic, Soft Computing, and Computational Intelligence, 11th International Fuzzy Systems Association World Congress, Beijing, China : 28th - 31st July, 2005
- Full Text: false
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- Description: E1
- Description: 2003001360
Two level clustering using SOM and dynamical systems
- Authors: Ghosh, Ranadhir , Mammadov, Musa , Ghosh, Moumita , Yearwood, John
- Date: 2004
- Type: Text , Conference paper
- Relation: Paper presented at ICOTA6: 6th International Conference on Optimization - Techniques and Applications, Ballarat, Victoria : 9th December, 2004
- Full Text: false
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- Description: E1
- Description: 2003000871
Solving a system of nonlinear integral equations by an RBF network
- Authors: Golbabai, A. , Mammadov, Musa , Seifollahi, Sattar
- Date: 2009
- Type: Text , Journal article
- Relation: Computers & Mathematics with Applications Vol. 57, no. 10 (2009), p. 1651-1658
- Full Text: false
- Reviewed:
- Description: In this paper, a novel learning strategy for radial basis function networks (RBFN) is proposed. By adjusting the parameters of the hidden layer, including the RBF centers and widths, the weights of the output layer are adapted by local optimization methods. A new local optimization algorithm based on a combination of the gradient and Newton methods is introduced. The efficiency of some local optimization methods to Update the weights of RBFN is Studied in solving systems of nonlinear integral equations. (C) 2009 Elsevier Ltd. All rights reserved.
Sigma supporting cone and optimality conditions in non-convex problems
- Authors: Hassani, Sara , Mammadov, Musa
- Date: 2014
- Type: Text , Journal article
- Relation: Far East Journal of Mathematical Sciences Vol. 91, no. 2 (2014), p. 169-190
- Full Text: false
- Reviewed:
- Description: In this paper, a new supporting function for characterizing non-convex sets is introduced. The notions of σ-supporting cone and maximal conic gap are proposed and some properties are investigated. By applying these new notions, we establish the optimality conditions considered in [7] for a broader class of finite dimensional normed spaces in terms of weak subdifferentials.
Optimality conditions via weak subdifferentials in reflexive Banach spaces
- Authors: Hassani, Sara , Mammadov, Musa , Jamshidi, Mina
- Date: 2017
- Type: Text , Journal article
- Relation: Turkish Journal of Mathematics Vol. 41, no. 1 (2017), p. 1-8
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- Description: In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are investigated. It partly generalizes several related results obtained for finite dimensional spaces. © Tübitak.
A hybrid wrapper-filter approach to detect the source(s) of out-of-control signals in multivariate manufacturing process
- Authors: Huda, Shamsul , Abdollahian, Mali , Mammadov, Musa , Yearwood, John , Ahmed, Shafiq , Sultan, Ibrahim
- Date: 2014
- Type: Text , Journal article
- Relation: European Journal of Operational Research Vol. 237, no. 3 (2014), p. 857-870
- Full Text: false
- Reviewed:
- Description: With modern data-Acquisition equipment and on-line computers used during production, it is now common to monitor several correlated quality characteristics simultaneously in multivariate processes. Multivariate control charts (MCC) are important tools for monitoring multivariate processes. One difficulty encountered with multivariate control charts is the identification of the variable or group of variables that cause an out-of-control signal. Expert knowledge either in combination with wrapper-based supervised classifier or a pre-filter with wrapper are the standard approaches to detect the sources of out-of-control signal. However gathering expert knowledge in source identification is costly and may introduce human error. Individual univariate control charts (UCC) and decomposition of T2 statistics are also used in many cases simultaneously to identify the sources, but these either ignore the correlations between the sources or may take more time with the increase of dimensions. The aim of this paper is to develop a source identification approach that does not need any expert-knowledge and can detect out-of-control signal in less computational complexity. We propose, a hybrid wrapper-filter based source identification approach that hybridizes a Mutual Information (MI) based Maximum Relevance (MR) filter ranking heuristic with an Artificial Neural Network (ANN) based wrapper. The Artificial Neural Network Input Gain Measurement Approximation (ANNIGMA) has been combined with MR (MR-ANNIGMA) to utilize the knowledge about the intrinsic pattern of the quality characteristics computed by the filter for directing the wrapper search process. To compute optimal ANNIGMA score, we also propose a Global MR-ANNIGMA using non-functional relationship between variables which is independent of the derivative of the objective function and has a potential to overcome the local optimization problem of ANN training. The novelty of the proposed approaches is that they combine the advantages of both filter and wrapper approaches and do not require any expert knowledge about the sources of the out-of-control signals. Heuristic score based subset generation process also reduces the search space into polynomial growth which in turns reduces computational time. The proposed approaches were tested by exhaustive experiments using both simulated and real manufacturing data and compared to existing methods including independent filter, wrapper and Multivariate EWMA (MEWMA) methods. The results indicate that the proposed approaches can identify the sources of out-of-control signals more accurately than existing approaches. © 2014 Elsevier B.V. All rights reserved.
Global asymptotic stability in a class of nonlinear differential delay equations
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2011
- Type: Text , Journal article
- Relation: Discrete and Continuous Dynamical Systems Vol. 2011, no. Supplement 2011 (2011), p.
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- Description: An essentially nonlinear dierential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are de- rived. An application to a physiological model by M.C. Mackey is treated in detail.
- Description: 2003009358
Global stabilization in nonlinear discrete systems with time-delay
- Authors: Ivanov, Anatoli , Mammadov, Musa , Trofimchuk, Sergei
- Date: 2012
- Type: Text , Journal article
- Relation: Journal of Global Optimization Vol.56, no. 2 (2012), p. 1-13
- Full Text: false
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- Description: A class of scalar nonlinear difference equations with delay is considered. Sufficient conditions for the global asymptotic stability of a unique equilibrium are given. Applications in economics and other fields lead to consideration of associated optimal control problems. An optimal control problem of maximizing a consumption functional is stated. The existence of optimal solutions is established and their stability (the turnpike property) is proved. © 2012 Springer Science+Business Media, LLC.
Global stability, periodic solutions and optimal control in a nonlinear differential delay model
- Authors: Ivanov, Anatoli , Mammadov, Musa
- Date: 2010
- Type: Text , Conference proceedings
- Relation: Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations, 2010
- Full Text: false
- Description: A nonlinear differential equation with delay serving as a mathematical model of several applied problmes is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsay. An optimization problem for a maximal consumption is stated and solved for the latter.