Nesar Ahmad

Structure identification of generalized adaptive neuro-fuzzy inference systems

This paper presents a method to identify the structure of generalized adaptive neuro-fuzzy inference systems (GANFISs). The structure of GANFIS consists of a number of generalized radial basis function (GRBF) units. The radial basis functions are irregularly distributed in the form of hyper-patches in the input-output space. The minimum number of GRBF units is selected based on a heuristic using the fuzzy curve. For structure identification, a new criterion called structure identification criterion (SIC) is proposed. SIC deals with a trade off between performance and computational complexity of the GANFIS model. The computational complexity of gradient descent learning is formulated based on simulation study. Three methods of initialization of GANFIS, viz., fuzzy curve, fuzzy C-means in x/spl times/y space and modified mountain clustering have been compared in terms of cluster validity measure, Akaikes information criterion (AIC) and the proposed SIC.

Generalization of adaptive neuro-fuzzy inference systems

The paper aims at several objectives. The adaptive network-based fuzzy inference systems (ANFIS) of Jang is extended to the generalized ANFIS (GANFIS) by proposing a generalized fuzzy model (GFM) and considering a generalized radial basis function (GRBF) network. The GFM encompasses both the Takagi-Sugeno (TS)-model and the compositional rule of inference (CRI)-model. A local model, a property of TS-model, and the index of fuzziness, a property of CRI-model define the consequent part of a rule of GFM. The conditions by which the proposed GFM converts to TS-model or the CRI-model are presented. The basis function in GRBF is a generalized Gaussian function of three parameters. The architecture of the GRBF network is devised to learn the parameters of GFM, since it has been proved in this paper that GRBF network and GFM are functionally equivalent. It is shown that GRBF network can be reduced to either the standard RBF or the Hunts RBF network. The issue of the normalized versus the nonnormalized GRBF networks is investigated in the context of GANFIS. An interesting property of symmetry on the error surface of GRBF network is investigated in the present work. The proposed GANFIS is applied for the modeling of a multivariable system like stock market.

Soft Computing Techniques for Rank Aggregation on the World Wide Web

Rank aggregation is the problem of generating a near-“consensus” ranking for a given set of rankings. When applied to the web, this finds applications in meta-searching, search engine comparison, spam fighting and word association techniques. The rank aggregation obtained by optimizing the Spearman footrule distance is called footrule optimal aggregation (FOA), and it also satisfies the Condorcet property. We find in literature a polynomial time algorithm to compute FOA for full lists. However, when collating the results of the search engines, the lists are almost invariably always the partial ones, as different search engines usually return non-overlapping lists of documents. The FOA for partial lists, however, is NP-hard. This NP-hard nature of partial footrule optimal aggregation problem (PFOA) motivates us to apply genetic algorithm (GA) for the PFOA problem. The GA based technique may take long to compute, but we propose to decide upon the number of generations of GA based on the time limit allowed by the user. We have also considered some “positional” methods, as they are linear in complexity. A classical positional method is the Bordas method. Since, fuzzy logic has been extensively studied in literature for arriving at consensus in group decision making, the adoption of some fuzzy techniques is also being investigated here for getting an improvement over the Bordas method. We have not only adopted and compared the classical fuzzy rank ordering techniques for web applications, but also proposed three novel techniques that outshine the existing techniques.

Genetic-Fuzzy Systems for Financial Decision Making

This paper describes the use of genetic algorithms for inducing fuzzy rulebases within the context of decision support systems for financial trading. The genetic algorithm part of the procedure is based on Packards algorithm for complex data analysis. The fuzzy pre-processing of the data is achieved by using a Single Linkage clustering algorithm in conjunction with an heuristic cluster selection mechanism. We believe that this hybrid approach has advantages over other ‘black-box’ machine learning procedures in that it produces transparent decision models that are easily understood by decision-makers. Further, the induced decision models lend themselves naturally to judgmental revisions by decision-makers.

Optimal accelerated life test designs for Burr Type XII distributions under periodic inspection and Type I censoring

This article develops optimal accelerated life test designs for Burr Type XII distributions under periodic inspection and Type I censoring. It is assumed that the mean lifetime (the Burr XII scale parameter) is a log-linear function of stress and that the shape parameters are independent of stress. For given shape parameters, design stress and high test stress, the test design is optimized with respect to the low test stress and the proportion of test units allocated to the low stress. The optimality criterion is the asymptotic variance of the maximum-likelihood estimator of log mean life at the design stress with the use of equally spaced inspection times. Computational results for various values of the shape parameters show that this criterion is insensitive to the number of inspection times and to misspecification of imputed failure probabilities at the design and high test stresses. Procedures for planning an accelerated life test, including selection of sample size, are also discussed. It is shown that optimal designs previously obtained for exponential and Weibull distributions are similar to those obtained here for the appropriate special cases of the Burr XII distribution. Thus the Burr XII distribution is a useful and widely applicable family of reliability models for ALT design.

A new criteria for input variable identification of dynamical systems

The concept of the approximate fuzzy data model (AFDM) is introduced. An attempt is made for input variable identification for fuzzy modeling of dynamical systems using the fuzzy curve, which is the output of AFDM. An output ratio is defined based on AFDM and system output that gives rise to the proposed criteria whose effectiveness is demonstrated by experimentation on mathematical models as well as by simulation on a few examples of dynamical systems. The proposed criteria thus serve as a significance test for the identification of inputs that actually affect the output.

Parameter determination for a generalized fuzzy model

This paper underlines a way to evolve a generalized fuzzy model (GFM), using the interpolation of CRI and TS models in their consequent parts of fuzzy rules. The GFM possesses the index of fuzziness of CRI model and the local model of the TS model. The parameters of the GFM are estimated by a two-step process. The consequent part of fuzzy rules is reformulated to suit the LSE framework for estimating the associated parameters. By assuming Generalized Gaussian membership function for the premise parts, Gradient descent technique is used to update its parameters. The performance of two classes of GFM has been tested on two systems and it is shown that class II GFM is the best out of all the fuzzy models tested.

Cluster-Weighted Modeling as a Basis for Non-Additive GFM

The cluster-weighted modeling (CWM) is a mixture density estimator around local models. To be specific, the input regions together with output regions are treated to be Gaussian serving as local models. These models are linked by a linear function involving the mixture of densities of local models. A connection between the CWM and generalized fuzzy model (GFM) is established in this work for utilizing the concepts of probability theory in deriving additive and non-additive fuzzy system versions of GFM

Extended dynamic fuzzy logic system (DFLS) based indirect stable adaptive control of non-linear systems

Abstract The dynamic fuzzy logic system (DFLS) consists of static fuzzy logic system added with a dynamic element—the integrator—with a feedback constant α. It was shown to possess the important universal approximation capability. Further, Lee and Vukovich developed DFLS based stable indirect adaptive control scheme via Lyapunov synthesis approach for a class of non-linear systems of the form x =f(X)+bu . In this paper, this is extended so that now, it can be applied to a larger class of non-linear dynamic systems, i.e., of the form x =f(X)+g(X)u . It was successfully investigated on a chaotic system-modified Duffing’s equation.

Fuzzy modeling of fluidized catalytic cracking unit

The paper deals with the fuzzy system identification of reactor-regenerator-stripper-fractionators (RRSF) section of a fluidized catalytic cracking unit (FCCU). The fuzzy system identification based on the data collected from an operating refinery of FCCU of capacity, 1.2MMPTA, with a sample time of 10min. A generalized fuzzy model (GFM) and identification of structure and model parameter for multi-input/single output is presented. The GFM has the capability of representing both the CRI model and TS model under certain conditions. The structure identification and the parameter estimation are carried out using hybrid learning approach comprising modified mountain clustering and gradient descent learning with least square estimation (LSE) for the identification of a fuzzy model. The modified mountain clustering considers every data point as a potential cluster center in xxy hyperspace. The optimum number of clusters, which leads to an optimum number of rules, is determined with the help of validity function that guides the search. The obtained result from the modified mountain clustering initializes the GFM. Further hybrid of the gradient descent technique and LSE is aimed at learning of the GFM parameters in two phases. In the first phase of an epoch of learning gradient descent tunes the premise parameter and index of fuzziness of each rule. In second phase, LSE utilizes the results of first phase for evaluating the coefficient of local linear model of corresponding rules.