t norm based addition of fuzzy intervals abstract the aim of this paper is to provide new results regarding the effective practical computation of t norm based additions of lr fuzzy intervals

integral input to state stable systems in cascade the integral input to state stability iiss property is studied in the context of nonlinear time invariant systems in cascade some sufficient conditions for the preservation of the iiss property under a cascade interconnection are presented these are first given as growth restrictions on the supply functions of the storage function associated with each subsystem and are then expressed as solutions based requirements a lyapunov based condition guaranteeing that the cascade composed of an iiss system driven by a globally asymptotically stable gas one remains gas is also provided we also show that some of these results extend to cascades composed of more than two subsystems

multidimensional probability density function approximations for detection classification and model order selection this paper addresses the problem of calculating the multidimensional probability density functions pdfs of statistics derived from known many to one transformations of independent random variables rvs with known distributions the statistics covered in the paper include reflection coefficients autocorrelation estimates cepstral coefficients and general linear functions of independent rvs through pdf transformation these results can be used for general pdf approximation detection classification and model order selection a model order selection example that shows significantly better performance than the akaike and mdl method is included

stochastic teams with nonclassical information revisited when is an affine law optimal in this note we consider a parameterized family of two stage stochastic control problems with nonclassical information patterns which includes the well known 1968 counterexample of witsenhausen we show that whenever the performance index does not contain a product term between the decision variables the optimal solution is linear in the observation variables the parameter space can be partitioned into two regions in one of which the optimal solution is linear whereas in the other it is inherently nonlinear extensive computations using two point piecewise constant policies and linear plus piecewise constant policies provide numerical evidence that nonlinear policies may indeed outperform linear policies when the product term is present

computational aspects of fuzzy arithmetics based on archimedean t norms for fuzzy multiplication and division of l r numbers we derive approximation formulas by including the exact results using l r numbers this permits an error control and meets user s ideas on tractable solutions better than the level sets approach does as potential application the resolution of linear systems is considered

shape preserving additions of fuzzy intervals abstract triangular norm based additions preserving the lr shape of lr fuzzy intervals are studied the connection between t norm based additions preserving the linearity of fuzzy intervals and additions preserving lr shape for invertible shapes l and r is given a possibility of controlling the growth of the spread during the calculations with lr fuzzy intervals is shown

on the compositional rule of inference under triangular norms abstract the aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under archimedean t norm where both the observation and the relation parts are given by hellendoorn s function 1980 in particular if the left and right spreads of the observation part is the same as those of the relation part then this upper bound is the exact membership function which generalizes the earlier result by fuller and zimmermann 1982 in that assumption of twice differentiability is deleted

class specific feature sets in classification in this correspondence we present a new approach to the design of probabilistic classifiers that circumvents the dimensionality problem rather than working with a common high dimensional feature set the classifier is written in terms of likelihood ratios with respect to a common class using sufficient statistics chosen specifically for each class

t sum of l r fuzzy numbers abstract the sum of l r fuzzy numbers based on a given archimedian continuous t norm t is studied a series of improving sufficient conditions of several authors ensuring an analytical form of the output sum is completed by a sufficient and necessary condition i e the best sufficient condition some applications are indicated

suboptimal decentralized control over noisy communication channels a b s t r a c t in this paper we present a technique for the design of decentralized controllers for mean square stability of a large scale system with cascaded clusters of subsystems each subsystem is linear and time invariant and both system and measurement are subject to gaussian noise for stability analysis of this system we consider the effects of additive white gaussian noise awgn channels used for exchanging information between subsystems

twenty one ml estimators for model selection classical approaches to determine a suitable model structure from observed input output data are based on hypothesis tests and information based criteria recently the model structure has been considered as a stochastic variable and standard estimation techniques have been proposed the resulting estimators are closely related to the aforementioned methods however it turns out that there are a number of prior choices in the problem formulation which are crucial for the estimators behavior the contribution of this paper is to clarify the role of the prior choices to examine a number of possibilities and to show which estimators are consistent this is done in a linear regression framework for autoregressive models we also investigate a novel prior assumption on stability and give the estimator for the model order and the parameters themselves

conditional model order estimation a new approach to model order selection is proposed based on the theory of sufficient statistics the method does not require any prior knowledge of the model parameters it is able to discriminate between models by basing the decision on the part of the data that is independent of the model parameters this is accomplished conceptually by transforming the data into a sufficient statistic and an ancillary statistic with respect to the model parameters it is the probability density function of the ancillary statistic when adjusted for its dimensionality that is used to estimate the order furthermore the rule is directly tied to the goal of minimizing the probability of error and does not employ any asymptotic approximations the estimator can be shown to be consistent and via computer simulation is found to outperform the minimum description length estimator

analytical expressions for the addition of fuzzy intervals abstract the addition of fuzzy quantities is undeniably the most important operation in fuzzy arithmetic in this paper we consider the general case of the addition of fuzzy intervals based on a continuous triangular norm we start our discussion with an extensive literature review in which we recall explicit formulae for the addition based on the strongest and the weakest triangular norm for the addition based on the algebraic product and several recent results for the addition based on a continuous archimedean triangular norm including specific theorems for strict and nilpotent triangular norms subsequently the addition based on an ordinal sum is studied and it is shown how this addition can be transformed into a series of additions based on the summands of this ordinal sum this important observation implies that the addition based on an arbitrary continuous triangular norm can be practically performed provided the summands of the corresponding ordinal sum representation and the fuzzy intervals involved fulfil the appropriate conditions mentioned in the overview this is illustrated by means of several examples

on the proper forms of bic for model order selection the bayesian information criterion bic is often presented in a form that is only valid in large samples and under a certain condition on the rate at which the fisher information matrix fim increases with the sample length this form has been improperly used previously in situations in which the conditions mentioned above do not hold in this correspondence we describe the proper forms of bic in several practically relevant cases that do not satisfy the above assumptions in particular we present a new form of bic for high signal to noise ratio snr cases the conclusion of this study is that bic remains one of the most successful existing rules for model order selection if properly used

on the convergence of product sum series of l r fuzzy numbers we study series a1 a2 an of l r fuzzy numbers where addition is defined via the sup product norm convulation and obtain some convergence theorems which generalize earlier results by fuller cf 2

asymptotic map criteria for model selection the two most popular model selection rules in signal processing literature have been akaike s 1974 criterion aic and rissanen s 1978 principle of minimum description length mdl these rules are similar in form in that they both consist of data and penalty terms their data terms are identical but the penalties are different mdl being more stringent toward overparameterization aic penalizes for each additional model parameter with an equal incremental amount of penalty regardless of the parameter s role in the model in most of the literature on model selection mdl appears in a form that also suggests equal penalty for every unknown parameter this mdl criterion we refer to as naive mdl in this paper we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters the approach to showing this is bayesian and it relies on large sample theory we derive maximum a posteriori map rules for several different families of competing models and obtain forms that are similar to aic and naive mdl for some families however we find that the derived penalties are different in those cases our extensive simulations show that the map rule outperforms aic and naive mdl

solutions to a class of linear quadratic gaussian lqg stochastic team problems with nonclassical information abstract we consider a stochastic dynamic team problem with two controllers and nonclassical information which can be viewed as the transmission of a garbled version of a gaussian message over a number of noisy channels under a fidelity criterion we show that the optimum solution under a quadratic loss functional consists of linearly transforming the garbled message to a certain optimum power level p and then optimally decoding it by using a linear transformation at the receiving end the power level p is determined by the solution of a fifth order algebraic equation the paper also discusses an extension of this result to the case when the channel noise is correlated with the input random variable and shows that for the single channel case the optimum solution is again linear

a note to the t sum of l r fuzzy numbers abstract we generalize the results of hong and hwang 1994 for the membership function of finite infinite sum of l r fuzzy numbers where the sum is based on some continuous archimedean t norm t

a note to the addition of fuzzy numbers based on a continuous archimedean t norm abstract a simple method of computing the t sum of special types of fuzzy numbers is introduced for the lukasiewicz t norm tl the proposed method can be applied to the addition of fuzzy numbers with convex membership functions the classes of fuzzy numbers leading to t idempotents are studied for continuous t norms

zadeh s extension principle for continuous functions of non interactive variables a parallel optimization approach there is a growing interest in the use of fuzzy intervals in many engineering applications however a direct implementation of zadeh s extension principle which forms the basis for computing with fuzzy intervals is still computationally too demanding for practical use in the case of a continuous function and fuzzy intervals that describe non interactive variables as inputs the output is a fuzzy interval as well and can be determined for each cut separately the problem thus reduces to finding the endpoints of these cuts which amounts to a number of interwoven optimization problems in the case of a non monotone continuous function however these optimization problems are non trivial in this paper different optimization algorithms are applied for that purpose gradient descent based on sequential quadratic programming simplex simulated annealing particle swarm optimization and particle swarm optimization combined with gradient descent in addition two approaches are followed to determine a suitable number of cuts either a fixed predetermined number is used or an initially very small number is chosen that is subsequently increased according to a linearity criterion both a non parallel and a parallel implementation are designed the parallel version is restricted to work with particle swarm optimization and employs communication to optimize its internal performance by exploiting the dependence between the various optimization problems different configurations are evaluated on a set of benchmark functions in terms of the mean area under the output fuzzy interval and the number of function evaluations particle swarm optimization combined with gradient descent starting from a small number of cuts leads to the most accurate fuzzy intervals at the cost of a relatively large number of function evaluations

a note on product sum of l r fuzzy numbers abstract triesch 1993 provided a partial answer to fuller s 1991 question about the membership function of the finite sum defined via the sup product norm convolution of l r fuzzy numbers in this short note we prove the other half

model estimation and classification via model structure determination in model estimation we often face problems with unknown parameters in the candidate models this paper proposes the model structure determination msd for model estimation with unknown parameters we start with the problem of model order selection and decompose the probability density function pdf into the information provided by the data about the model parameters and that of the model structure the factor that depends on the model parameters is approximated using a minimax procedure and the msd depends on the model structure only it is shown that the msd is equivalent to the exponentially embedded family eef for model order selection under some conditions finally we apply the msd to a classification problem where we have partial knowledge about the parameters and simulation results show that it outperforms the pseudo maximum likelihood pseudo ml rule

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a t norm embedding theorem for fuzzy sets it is well known that the class of upper semicontinuous normal convex fuzzy sets with compact supports can be embedded isometrically as a complete convex cone in a banach space we prove an analogous result for a subclass of fuzzy sets that is free from the normality limitation by exchanging the standard algebraic operations on fuzzy sets with operations based on strict t norms this allows us to investigate a new notion of fuzzy convexity that we call t convexity we show that the class of upper semicontinuous fuzzy t convex sets with nonempty compact supports can be embedded as a closed convex cone in a banach space this implies that fuzzy t convex sets satisfy the cancellation law we discuss a possible application of the embedding theorem in mathematical morphology

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

generalized pseudo convolution in the theory of probabilistic metric spaces information fuzzy numbers optimization system theory a notion of the generalized pseudo convolution of functions based on pseudo operations is introduced it is proved that such general pseudo convolution is commutative associative operation that in some cases has a unit element we present that the generalized pseudo convolution occurs as a basic notion in many different theories as probabilistic metric spaces information theory fuzzy numbers optimization system theory

fuzzy outranking for environmental assessment case study iron and steel making industry recent years have seen a world wide change in the environmental policy towards integrated pollution prevention taking into account all environmental media consequently the environmental assessment of production techniques has to consider multiple criteria which cannot be aggregated to one single index the concepts of multi criteria decision making mcdm seem a suitable means in order to implement life cycle assessment lca into integrated decision processes the outranking methods as a special subgroup of mcdm methods are particularly suitable for integral decision making through the notion of weak preference and incomparability which better represent the real decision situation as demonstrated in this paper especially the outranking method promethee brings together flexibility and simplicity for the user and is therefore chosen for the enhancement towards the evaluation of fuzzy data on preferences scores and weights