fuzzy process control construction of control charts with fuzzy numbers this paper presents the construction of fuzzy control charts for a process with fuzzy outcomes derived from the subjective quality ratings provided by a group of experts the proposed fuzzy process control fpc methodology comprises an off line stage and an on line stage in the off line stage experts assign quality ratings to products based on a numerical scale the individual numerical ratings are then aggregated to form collective opinions expressed in the form of fuzzy numbers the collective knowledge applied by the experts when conducting the quality rating process is acquired through a process of fuzzy regression analysis performed by a neural network in the on line stage the product dimensions are measured and the fuzzy regression model is employed to automate the experts judgments by mapping the measured dimensions to appropriate fuzzy quality ratings the fuzzy quality ratings are then plotted on fuzzy control charts whose construction and out of control conditions are developed using possibility theory the developed control charts not only monitor the central tendency of the process but also indicate its degree of fuzziness

a theoretical investigation into the performance of the hopfield model an analysis is made of the behavior of the hopfield model as a content addressable memory cam and as a method of solving the traveling salesman problem tsp the analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix the dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace in the case of content addressable memory it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function with these expressions the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more

joint data and channel estimation using blind trellis search techniques a novel method of maximum likelihood sequence estimation is proposed for data that are transmitted over unknown linear channels this procedure does not require a startup sequence for estimating the channel impulse response rather the data and the channel are simultaneously estimated it is implemented without any loss of optimality by a trellis search algorithm which searches for the best data sequence from among a number of hypothesized trellises which are constructed from the observed sequence the number of states in each trellis and the number of trellises grow exponentially with the channel memory a suboptimal trellis search algorithm is proposed whose complexity at best is slightly higher than that of the adaptive viterbi algorithm operating with a known channel response a simplified channel estimation algorithm when the number of data alphabets is greater than 2 is also proposed fast convergence of the algorithm in estimating the channel is demonstrated for binary pulse amplitude modulation over a variety of channels convergence over a wide range of snr occurs within 100 symbols the channel estimation algorithm for multi level signals converges within 500 1000 symbols we finally present an application of this algorithm to the problem of sequence estimation in the presence of rapidly time varying intersymbol interference the algorithm provides reliable zero delay decisions which results in a better channel tracking algorithm when compared to previously proposed schemes

fuzzy linear regression with fuzzy intervals abstract in this paper we introduce a new class of fuzzy linear regression models based on tanaka s approach unlike in the tanaka model here all training data influence the estimated interval the crisp lp of tanaka s approach is generalized to a fuzzy linear programming problem with the proposed model an adaptation of the fuzzy regression equation to new data becomes possible

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

blind equalization of digital communication channels using high order moments the authors describe algorithms for blind equalization of digital communication channels of the quadrature amplitude modulation qam type these algorithms are based on the fourth order statistical moments of the received data sequence the first of the two is a linear least squares type algorithm the second algorithm is of the nonlinear least squares type the algorithms use the fourth order statistical moments of the symbol sequence to explicitly estimate the channel impulse response the estimated impulse response is used in turn to construct a linear mean square error equalizer the performance of this equalizer is not optimal in any sense but it is adequate for channels with mild intersymbol interference or when the number of data points available for estimating the channel response is very large

construction of p charts using degree of nonconformity control charts are among the simplest of on line statistical process control techniques when the quality characteristic is a variable the p chart takes time to react to shifts in the production process because of its weak response to small variations in the process mean and variance in this paper instead of considering an item to be either conforming or nonconforming the degree of nonconformity based on fuzzy concepts is defined and a fuzzy p chart based on the mean degree of nonconformity is constructed it is shown that this chart has a better response to variations in both the mean and the variance of the process

constructing fuzzy measures in expert systems abstract this paper is an overview of results regarding various representations of fuzzy measures and methods for constructing fuzzy measures in the context of expert systems which were obtained by the authors and their associates during the last three years included are methods for constructing fuzzy measures by various transformations by extension by statistical inference and by various data driven methods based either on the sugeno integral or the choquet integral and using neural networks genetic algorithms or fuzzy relation equations

k means clustering based data detection and symbol timing recovery for burst mode optical receiver burst mode receivers are key components of optical transmission systems including passive optical networks and have received much attention in recent years we present new efficient methods for burst optical signal detection in burst mode data transmission using a modified k means clustering technique we also develop a data aided feedforward symbol timing recovery method based on a polynomial interpolation and maximum likelihood estimation theory a performance criterion considering the error caused by the interpolation approximation is derived for this method the proposed detection and timing recovery approaches can be implemented effectively and rapidly therefore they are very suitable for burst mode receivers we also provide some numerical examples to demonstrate the performance of the proposed methods

least squares quantization in pcm it has long been realized that in pulse code modulation pcm with a given ensemble of signals to handle the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall it has been shown by panter and dite that in the limit as the number of quanta becomes infinite the asymptotic fractional density of quanta per unit voltage should vary as the one third power of the probability density per unit voltage of signal amplitudes in this paper the corresponding result for any finite number of quanta is derived that is necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy the optimization criterion used is that the average quantization noise power be a minimum it is shown that the result obtained here goes over into the panter and dite result as the number of quanta become large the optimum quautization schemes for 2 b quanta b 1 2 cdots 7 are given numerically for gaussian and for laplacian distribution of signal amplitudes

fuzzy least squares linear regression analysis for fuzzy input output data a fuzzy regression model is used in evaluating the functional relationship between the dependent and independent variables in a fuzzy environment most fuzzy regression models are considered to be fuzzy outputs and parameters but non fuzzy crisp inputs in general there are two approaches in the analysis of fuzzy regression models linear programming based methods and fuzzy least squares methods in 1992 sakawa and yano considered fuzzy linear regression models with fuzzy outputs fuzzy parameters and also fuzzy inputs they formulated multiobjective programming methods for the model estimation along with a linear programming based approach in this paper two estimation methods along with a fuzzy least squares approach are proposed these proposed methods can be effectively used for the parameter estimation comparisons are also made between them

linear regression analysis for fuzzy input and output data using the extension principle abstract the method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed the membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators in order to obtain the membership value of any given value taken from the fuzzy least squares estimator optimization problems have to be solved we also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data

a parametric approach to description of linguistic values of variables and hedges abstract an experimental approach is described to obtaining membership functions which describe the values of linhuistic estimates of variables and mathematical tools for description of hedges and computation of composite linguistic estimates applied aspects of using the proposed approach are discussed

cluster based blind nonlinear channel estimation a cluster based maximum likelihood sequence estimator mlse for nonlinear channels was described which consists of a clustering network and an mlse implemented by the viterbi algorithm the cluster based mlse can be used for digital communication through nonlinear finite length channels because channel mapping estimation is used instead of channel estimation in the conventional mlse the clustering network of the cluster based mlse which estimates the channel mapping between the signal input vectors and the noiseless channel outputs is a supervised network and requires a training sequence we propose a blind channel mapping estimator to estimate the channel mapping without using the training sequence the blind channel mapping estimator has a clustering block and a mapping block the clustering block estimates the channel outputs which represent the channel mapping subject to an unknown permutation operation because no training sequence is utilized that permutation operation is resolved by the mapping block and therefore the channel mapping is obtained introducing the blind channel mapping estimator into the cluster based mlse a blind cluster based mlse for nonlinear channels can be done computer simulations of the blind channel mapping estimator and the blind mlse for nonlinear channels are presented

least squares estimates in fuzzy regression analysis abstract regression is a very powerful methodology for forecasting which is considered as an essential component of successful or applications in this paper an idea stemmed from the classical least squares is proposed to handle fuzzy observations in regression analysis based on the extension principle the membership function of the sum of squared errors is constructed the fuzzy sum of squared errors is a function of the regression coefficients to be determined which can be minimized via a nonlinear program formulated under the structure of the chen klein method for ranking fuzzy numbers to illustrate how the proposed method is applied three cases one crisp input fuzzy output one fuzzy input fuzzy output and one non triangular fuzzy observations are exemplified the results show that the least squares method of this paper is able to determine the regression coefficients with better explanatory power most important it works for all types of fuzzy observations not restricted to the triangular one

channel dependent constrained combinatorial clustering constrained combinatorial clustering ccc is a new approach for grouping multiple features where the clustering metric depends on an unknown communication channel assignment features assigned to the same channel cannot be from the same source and conversely channels assigned to the same source must be distinct while the number of sources and their states are unknown the channels are assumed to be known except for additive noise potential clustering assignments are checked for compatibility with the constraints in a structured way that results in significant computational savings with respect to exhaustive enumeration especially when combined with a k best channel assignment algorithm that has polynomial complexity by combining two channel assignment methods exhaustive and k best with two clustering techniques ccc and greedy four new algorithms are presented to solve this novel problem along with detailed computational complexity analyses the main algorithm ccc is a top down clustering strategy based on assignment aggregation in a channel constrained environment the approaches are compared on a one dimensional simulation significant performance differences in source estimation accuracy and estimated number of sources are observed at low signal to noise ratios snrs and for low values of k some novel permutation symmetry properties arising from the study which lead to a new type of self affine set or discrete fractal are also presented

fuzzy approaches for multiple objective linear fractional optimization abstract the problem of finding a solution to a multiple objective linear fractional program arises in several real world situations in this paper we advocate that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness after representing imprecise aspirations of the decision maker by structured linguistic variables or converting the original problem via approximations or change of variables into a multiple objective linear program techniques of fuzzy linear programming may be used to reach a satisfactory solution it is shown that under reasonable restrictions this solution is efficient pareto optimal for the original problem numerical examples are also included for illustration

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

l metric on the space of l fuzzy numbers abstract in this article a natural l topology is constructed on the set of l fuzzy numbers which is called the standard l topology it is proved that the standard l topology can be induced by an l metric the space of trapezoidal fuzzy numbers can be regarded as a subspace of the space of l fuzzy numbers an l metric on the set of trapezoidal fuzzy numbers is presented

an interactive fuzzy satisficing method for multiobjective linear fractional programming problems abstract we present a new interactive fuzzy decision making method for solving multiobjective linear fractional programming problems by assuming that the decision maker dm has fuzzy goals for each of the objective functions through the interaction with the dm the fuzzy goals of the dm are quantified by eliciting the corresponding membership functions including nonlinear functions after determining the membership functions if the dm specifies reference membership values the minimax problem is solved by combined use of the bisection method and the linear programming method and the dm is supplied with the corresponding pareto optimal solution together with the trade off rates between the membership functions then by considering the current values of the membership functions as well as the trade off rates the dm responds by updating his her reference membership values in this way the compromise or satisficing solution for the dm can be derived efficiently from among a pareto optimal solution set by updating his her reference membership values on the basis of the proposed method a time sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

l fuzzy numbers and their properties in this paper the notions of l fuzzy convex sets and l fuzzy numbers are introduced where l is a completely distributive lattice the notions of 0 1 fuzzy convex sets and 0 1 fuzzy numbers are generalized furthermore their properties and characterizations are presented in terms of cut sets of l fuzzy sets

identification of membership functions based on fuzzy observation data abstract for the classification problem of which categories having vague or verbal definition okuda et al proc 3rd ifsa congr 1989 755 proposed a model in which each category is defined by fuzzy sets and each appearance frequency is explained by the probability of zadeh s fuzzy event they called this model fuzzy observation membership functions are usually given directly by the user s subjectivity but these membership functions cannot be used in the fuzzy observation model because they have no assurance to meet the restriction as the fuzzy event in this paper we propose a method to obtain the membership functions which satisfy the restriction as the fuzzy event against to given probability density function and discuss the effectiveness of the method

multiple objective linear fractional programming a fuzzy set theoretic approach abstract a method for optimizing a multiobjective linear fractional programming problem is developed which yields always an efficient solution

detecting change points for shifts in mean and variance using fuzzy classification maximum likelihood change point algorithms knowing the time of changes called change point cp in a process is crucial for engineers to recognize the root cause fast and accurately since special causes may induce simultaneous changes in mean and variance detecting changes in both at once is required many methodologies in quality control were developed for detecting changes in either mean or variance only and process parameters were assumed known often however they are rarely known exactly and a small estimation error may lead to unfavorable cp estimates fuzzy partitioning is better suited to cases of vague boundaries between two segments which appear very often in reality a new mechanism called fuzzy classification maximum likelihood change point fcml cp algorithm is proposed to detect shifts in mean and variance simultaneously a cp framework is transferred into a mixture model and then a fcml cp algorithm is created through fuzzy classification maximum likelihood procedures the proposed fcml cp can be applied to phase i and ii processes without knowledge of in control process parameters it can estimate multiple cps of process mean or and variance simultaneously the effectiveness and superiority of fcml cp are shown by extensive experiments with numerical and real data sets specifically the proposed fcml cp is superior to the commonly used statistical mixture likelihood approach using expectation maximization em algorithm it is much more time saving especially the remarkable performance of fcml cp in detecting cps for small changes is particularly important and helpful for engineers to recognize the special cause fast and correctly since an out of control signal resulted from small changes is usually delayed long we propose a new algorithm fcml cp to detect change points in a statistical process the mixture likelihood embedded fuzzy c partition is utilized to estimate the change points the method outperforms statistical likelihood approaches various experiments show the effectiveness and practicability of the proposed method excellent performance in detecting small changes is helpful for root cause analyses

evaluation of fuzzy linear regression models abstract fuzzy linear regression provides means for tackling regression problems lacking a significant amount of data for determining regression models and with vague relationships between the dependent variable and independent variables in the paper a two stage construction of a linear regression model is proposed using an enhancement of a minimal vagueness criterion already discussed in fuzzy regression analysis two different experiments are set up and used for evaluating both models the choice of the fuzzy regression model should be made in the context of a practical application

fuzzy regression in hydrology a general methodology for fuzzy regression is developed and illustrated by an actual hydrological case study fuzzy regression may be used whenever a relationship between variables is imprecise and or data are inaccurate and or sample sizes are insufficient in such cases fuzzy regression may be used as a complement or an alternative to statistical regression analysis in fuzzy regression several goodness of fit criteria may be used such as the maximum average vagueness criterion and the prediction vagueness criterion the technique is illustrated by means of a case study involving the relationship between soil electrical resistivity and hydraulic permeability this relationship is imprecise and based on only a few data points in the present case a curvilinear relationship is fitted using fuzzy regression with six calculated resistivities and six measured permeabilities prediction vagueness criteria appears to yield a more robust fuzzy regression than the maximum average vagueness criteria potential application areas of fuzzy regression in hydrology are discussed further the methodology is relatively simple and the results can be interpreted to provide a valuable hydrological decision making aid

new processing techniques based on the constant modulus adaptive algorithm this paper presents three extensions of the constant modulus algorithm cma introduced in an earlier paper as a means of correcting degradations in constant enyelope waveforms as originally formulated the cma employs an fir filter with complex coefficients and accepts complex quadrature input data in this paper first a real input real coefficient version of the algorithm is shown to perform arbitrarily close to the fully complex version secondly the algorithm is extended for the enhancement of signals having a nonconstant but known envelope as might arise in data signals with pulse shaping lastly a multichannel version of cma wherein several observations are linearly combined is presented for joint adaptation of multiple filters this approach can be used for example as a means of spatial or polarization beamsteering to reject additive interferers and compensate for channel induced polarization rotation

compensatory operators in fuzzy linear programming with multiple objectives previously h j zimmermann 11 presented a fuzzy approach to solve the linear vectormaximum problem in the mentioned approach the author uses the minimum or the product operators to translate the semantic meaning of the and the aim of this paper is to reconsider this approach by using operators which allow some degree of compensation between aggregated membership functions firstly the c operator already defined in 12 is used to combine our fuzzy objectives it is shown that solutions obtained by this way are always efficient unfortunately the substitute problem is not generally computationally feasible we suggest then the min bounded sum operator which is a compensatory one has some desired properties and is supported by empirical arguments it allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand point of efficiency

fuzzy regression wiht radial basis function network radial basis function network is used in fuzzy regression analysis without predefined functional relationship between the input and the output the proposed approach is a fuzzification of the connection weights between the hidden and the output layers this fuzzy network is trained by a hybrid learning algorithm where self organized learning is used for training the parameters of the hidden units and supervised learning is used for updating the weights between the hidden and the output layers the c mean clustering method and the k nearest neighbor heuristics are used for the self organized learning the supervised learning is carried out by solving a linear possibilistic programming problem techniques for the generalization of the network are also proposed numerical examples are used to illustrate and to test the performances of the approach

neural gas network for vector quantization and its application to time series prediction a neural network algorithm based on a soft max adaptation rule is presented this algorithm exhibits good performance in reaching the optimum minimization of a cost function for vector quantization data compression the soft max rule employed is an extension of the standard k means clustering procedure and takes into account a neighborhood ranking of the reference weight vectors it is shown that the dynamics of the reference weight vectors during the input driven adaptation procedure are determined by the gradient of an energy function whose shape can be modulated through a neighborhood determining parameter and resemble the dynamics of brownian particles moving in a potential determined by the data point density the network is used to represent the attractor of the mackey glass equation and to predict the mackey glass time series with additional local linear mappings for generating output values the results obtained for the time series prediction compare favorably with the results achieved by backpropagation and radial basis function networks

fuzzy linear fractional goal programming applied to refinery operations planning abstract chemical process plant operations planning in an oil refinery has been modelled as fuzzy linear fractional multiple goal programming problem a variant of the fuzzy linear fractional goal programming model of dutta et al fuzzy sets and systems 52 1992 39 45 has been developed and used in the present study to solve the problem which has two fuzzy fractional goals and 22 crisp constraints linear membership functions have been assumed and min operator has been used as the aggregator linguistic variable has been taken as close throughout the paper following dutta et al 1992 a software has been developed in turbo c to implement the model the software takes the parameters defining the fuzziness and crisp data from the input field and solves the crisp equivalent to the fuzzy linear fractional goal programming problem the parameters defining fuzziness are subjectively chosen by the user decision maker the software finally outputs satisfying decision variables satisfying fuzzy fractional goal values optimal values of the profit numerator and the capacities of the primary unit and cracker denominators which are involved in the fuzzy fractional goals the results indicate that the present model yielded a more efficient solution compared to the crisp solution of allen british chem eng 16 1971 685 691 as far as the fractional objectives are concerned this demonstrates the efficacy of the present model however a paltry decrement of 1 3 in the profit is noticed in the present study in comparison to the crisp solution of allen 1971

on a fuzzy set approach to solving multiple objective linear fractional programming problem in 1984 luhandjula used a linguistic variable approach in order to present a procedure for solving multiple objective linear fractional programming problem molfpp in 1992 dutta et al fuzzy sets and systems 52 1 1992 39 45 modified the linguistic approach of luhandjula such as to obtain efficient solution to problem molfpp the aim of this paper is to point out certain shortcomings in the work of dutta et al and give the correct proof of theorem which validates the obtaining of the efficient solutions we notice that the method presented there as a general one does only work efficiently if certain hypotheses restrictive enough and hardly verified are satisfied the example considered by dutta et al is again used to illustrate the approach

a hybrid fuzzy statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts control charts are the most popular statistical process control spc tools used to monitor process changes when a control chart produces an out of control signal it means that the process has changed however control chart signals do not indicate the real time of the process changes which is essential for identifying and removing assignable causes and ultimately improving the process identifying the real time of the process change is known as change point estimation problem most of the traditional change point methods are based on maximum likelihood estimators mle which need strict statistical assumptions in this paper first we introduce clustering as a potential tool for change point estimation next we discuss the challenges of employing clustering methods for change point estimation afterwards based on the concepts of fuzzy clustering and statistical methods we develop a novel hybrid approach which is able to effectively estimate change points in processes with either fixed or variable sample size using extensive simulation studies we also show that the proposed approach performs considerably well in all considered conditions in comparison to powerful statistical methods and popular fuzzy clustering techniques the proposed approach can be employed for processes with either normal or non normal distributions it is also applicable to both phase i and phase ii finally it can estimate the true values of both in and out of control states parameters

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

fuzzy goal programming an additive model abstract an additive model to solve fuzzy goal programming fgp is formulated the method uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function cardinal and ordinal weights for nonequivalent fuzzy goals are also incorporated in the method the solution procedure is illustrated with a numerical example

a compromise procedure for the multiple objective linear fractional programming problem abstract a generalization of a well known multiple objective linear fractional programming molfp problem the multiple objective fractional programming mofp problem is formulated a concept of multiple objective programming mop problem corresponding to mofp is introduced and some relations between those problems are examined based on these results a compromise procedure for molfp problem is proposed a numerical example is given to show how the procedure works