appraisal of the generalized likelihood uncertainty estimation glue method 1 recent research documents that the widely accepted generalized likelihood uncertainty estimation glue method for describing forecasting precision and the impact of parameter uncertainty in rainfall runoff watershed models fails to achieve the intended purpose when used with an informal likelihood measure in particular glue generally fails to produce intervals that capture the precision of estimated parameters and the difference between predictions and future observations this paper illustrates these problems with glue using a simple linear rainfall runoff model so that model calibration is a linear regression problem for which exact expressions for prediction precision and parameter uncertainty are well known and understood the simple regression example enables us to clearly and simply illustrate glue deficiencies beven and others have suggested that the choice of the likelihood measure used in a glue computation is subjective and may be selected to reflect the goals of the modeler if an arbitrary likelihood is adopted that does not reasonably reflect the sampling distribution of the model errors then glue generates arbitrary results without statistical validity that should not be used in scientific work the traditional subjective likelihood measures that have been used with glue also fail to reflect the nonnormality heteroscedasticity and serial correlation among the residual errors generally found in real problems and hence are poor metrics for even simple sensitivity analyses and model calibration most previous applications of glue only produce uncertainty intervals for the average model prediction which by construction should not be expected to include future observations with the prescribed probability we show how the glue methodology when properly implemented with a statistically valid likelihood function can provide prediction intervals for future observations which will agree with widely accepted and statistically valid analyses

on fuzzy random linear programming abstract the fuzzy random linear programming having fuzzy random variable coefficients and the decision vector of fuzzy pseudorandom variables is studied the first results show the fact that a fuzzy pseudorandom resp fuzzy random optimization solution of a fuzzy random linear programmings the subsequent conclusions present methods random optimization solutions of relative random linear programmings the subsequent conclusions present methods that a fuzzy pseudorandom resp fuzzy random optimization solution of a fuzzy random linear programming is structured by a class of pseudorandom resp random optimization solutions of relative random linear programmings finally some theorems are proved which solve the problems finding the fuzzy probability distribution function and fuzzy mathematical expectation of optimization value for a fuzzy random linear programming these results reveal properties of a fuzzy random linear programming and give the solution for a fuzzy random linear programming

a locking free scheme for the lqr control of a timoshenko beam in this paper we analyze a locking free numerical scheme for the lqr control of a timoshenko beam we consider a non conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension to solve the lqr problem we seek a feedback control which depends on the solution of an algebraic riccati equation an optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems this estimate is valid with constants that do not depend on the thickness of the beam which leads to the conclusion that the method is locking free in order to assess the performance of the method numerical tests are reported and discussed

the theory of fuzzy stochastic processes abstract in this paper we deal with the general theory of fuzzy stochastic processes we give the suitable definitions of fuzzy random function fuzzy stochastic process and their fall shadow distribution functions the concepts of separability and measurability of a fuzzy random function are introduced and some properties of these new concepts are derived we investigate the continuity of fuzzy sample function of a fuzzy stochastic process

vertex method for computing functions of fuzzy variables abstract this paper is to introduce a new approach the vertex method for computing functions of fuzzy variables the method is based on the cut concept and interval analysis the vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi occurrence of variables in the functional expression by conventional interval analysis methods the algorithm is very easy to implement and can be applied to many practical problems some examples are given to illustrate the applications

complexity classes without machines on complete languages for up this paper develops techniques for studying complexity classes that are not covered by known recursive enumerations of machines often counting classes probabilistic classes and intersection classes lack such enumerations concentrating on the counting class up we show that there are relativizations for which upa has no complete languages and other relativizations for which pb upb npb and upb has complete languages among other results we show that p up if and only if there exists a set s in p of boolean formulas with at most one satisfying assignment such that s sat is not in p p up coup if and only if there exists a set s in p of uniquely satisfiable boolean formulas such that no polynomial time machine can compute the solutions for the formulas in s if up has complete languages then there exists a set r in p of boolean formulas with at most one satisfying assignment so that sat r is complete for up finally we indicate the wide applicability of our techniques to counting and probabilistic classes by using them to examine the probabilistic class bpp there is a relativized world where bppa has no complete languages if bpp has complete languages then it has a complete language of the form b majority where b p and majority f f is true for at least half of all assignments is the canonical pp complete set

galerkin approximation in modeling of controlled distributed parameter flexible systems abstract numerical study of control problems for linear distributed parameter flexible mechanical systems requires finite dimensional modeling of the system we study the conditions for h covergence of the transfer functions of finite dimensional galerkin approximations this convergence ensures that control problems can be solved by using a galerkin model a stabilization problem for the angular position of a bernoulli euler beam illustrates the theoretical consideration the beam with an inertial drive represents a flexible manipulator link

randomized boolean decision trees several remarks abstract assume we want to show that a the cost of any randomized decision tree computing a given boolean function is at least c to this end it suffices to prove that b there is a probability distribution over the set of all assignments to variables of that function with respect to which the average cost of any deterministic decision tree computing that function is at least c yao 1977 showed that this method is universal for proving lower bounds for randomized errorless decision trees that is that a is equivalent to b in the present paper we prove that this is the case also for randomized decision trees which are allowed to make errors this gives the positive answer to the question posed in yao 1977 in the second part of the paper we exhibit an example when randomized directional decision trees defined in yao 1977 to evaluate read once formulae are not optimal we construct a formula fn of n boolean variables such that the cost of the optimal directional decision tree computing fn is n and there is an undirectional randomized decision tree computing fn of cost o n for some

fuzzy weighted averages and implementation of the extension principle abstract this paper addresses the computational aspect of the extension principle when the principle is applied to algebraic mappings and in particular to weighted average operations in risk and decision analysis a computational algorithm based on the cut representation of fuzzy sets and interval analysis is described the method provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner examples are given to illustrate the method and its relation to other discrete methods and the exact approach by non linear programming the algorithm has been implemented in a computer program which can handle very general extended algebraic operations on fuzzy numbers

on solutions and distribution problems of the linear programming with fuzzy random variable coefficients abstract this paper studies the solution method and distribution problems for two kinds of linear programming with fuzzy random variable coefficients some concepts of solutions for example the fuzzy pseudo random optimization solution are introduced for these new programming problems we prove some equivalent theorems that transform the fuzzy random programming problems into a series of random programming problems by using the simplex method of linear programming with random variable coefficients we give the solution method of linear programming with fuzzy random variable coefficients the formulas of probability distribution function projective distribution function and expectation on these new programmings are presented

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

the general theory for response analysis of fuzzy stochastic dynamical systems abstract most real life structural mechanical systems have complex geometrical and material properties and operate under complex fuzzy environmental conditions these systems are certainly subjected to fuzzy random excitations induced by the environment for an analytical treatment of such a system subjected to fuzzy random excitations it becomes necessary to establish the general theory of fuzzy stochastic dynamical systems in the first part of this paper on the dynamic response of fuzzy stochastic systems we construct the mathematical models of fuzzy random algebraic equation dynamic systems nth order fuzzy random differential equation dynamic systems and a system of first order fuzzy random differential equations the theory of the response fuzzy mean response and fuzzy covariance response of fuzzy random algebraic equation dynamic systems in time domain and frequency domain is brought forward in the second part the theory of the response fuzzy mean response and fuzzy covariance response of the nth order fuzzy random differential equation dynamic systems in time domain and frequency domain is put forward the theory of the response analysis of a system to both stationary and nonstationary fuzzy random excitations is established the method of the response analysis of a system to nonstationary fuzzy random excitation with evolutionary spectra is brought forward and two examples are considered in the third part the theory of the response fuzzy mean response and fuzzy covariance response of a system of the first order fuzzy random differential equations with constant coefficients and variable coefficients in time domain and frequency domain is put forward an example is given to show the rationality and validity of the theory

extension principles for fuzzy set theory in several cases we show that it is possible to extend a notion in classical mathematics by identifying each fuzzy subset with the continuous chain of its closed cuts and by applying this notion to these cuts in particular this idea is applied to extend functions from subsets into subsets for instance closure operators and functions from sets into real numbers for instance measures

lower bounds on probabilistic linear decision trees abstract the power of probabilistic linear decision trees is examined it is shown that the standard arguments used to prove lower bounds on deterministic linear decision trees apply to probabilistic linear decision trees as well examples are next given of problems which randomization helps solving

entropy variation on the fuzzy numbers with arithmetic operations entropy is always the measure of the fuzziness degree for a fuzzy set this paper studies the entropy variation on the fuzzy numbers or fuzzy sets under the following several cases i two fuzzy sets on the same type but different support size ii the addition of finite number of fuzzy numbers on the same type iii the subtraction of finite number of fuzzy numbers on the same type iv the multiplication of a constant and a fuzzy number it is shown that through the above arithmetic operations the resultant fuzzy number is the same type as the original fuzzy numbers and the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number

nonlinear feedback control of slewing beams abstract this paper is concerned with feedback control of slewing beams it allows for the hub to have finite rotation which leads to a fully nonlinear system it uses the method of state dependent riccati equation sdre to obtain feedback control laws the model assumes finite rigid body rotations and infinitesimal small elastic displacements it considers both the classical euler bermoulli model and the timoshenko model for the beam it uses finite element method to obtain approximate equations that can be used to construct feedback control laws

uncertainty assessment of hydrological models with fuzzy extension principle evaluation of a new arithmetic operator the most important drawback of standard fuzzy arithmetic is unrealistic accumulation of input uncertainties which results in divergence of fuzzy outputs some of the currently available methods of simulating fuzzy systems provide the results which tend to naive large values after several time steps of the system simulation in this paper a new fuzzy arithmetic operator based on fuzzy extension principle has been proposed for simulation and assessment of uncertainty in hydrological systems implementing the concept of fuzzy approximate reasoning in the proposed approach in this study represents acceptable behavior in uncertainty propagation from the parameters and structures of the models to the outputs to show the efficiency of the proposed fuzzy arithmetic operator in the context of hydrologic modeling two nonlinear monthly water balance models have been examined and their outputs have been compared with the results obtained by standard fuzzy arithmetic and the vertex method one small humid basin in france and a middle size basin in a semiarid region in iran have been the case studies of this research in this paper the lower and upper bounds and the most frequent values of the model parameters inferred from the sampling simulation procedure have been used to define triangular fuzzy membership functions three statistical indicators have been used to evaluate efficiency of the methods based on the bracket observations and coverage of the uncertainty bounds the estimated values of these indicators have shown that both vertex and the proposed methods outperform standard fuzzy arithmetic also the proposed method has provided better or roughly equal efficiencies compared with vertex method over both basins

operations on fuzzy numbers via fuzzy reasoning abstract the paper discusses the issue of arithmetic operations on fuzzy numbers from the point of view of fuzzy reasoning it shows that the binary operations on fuzzy numbers via the extension principle can be represented in the spirit of fuzzy reasoning this approach provides a link between the techniques used in fuzzy systems modeling and fuzzy arithmetic operations

approximation theory for linear quadratic guassian optimal control of flexible structures this paper presents approximation theory for the linear quadratic gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators the main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator which is infinite dimensional design of the optimal compensator separates into an optimal linear quadratic control problem and a dual optimal state estimation problem the solution to each problem lies in the solution to an infinite dimensional riccati operator equation the approximation scheme in the paper approximates the infinite dimensional lqg problem with a sequence of finite dimensional lqg problems defined for a sequence of finite dimensional usually finite element or modal approximations of the distributed model of the structure two riccati matrix equations determine the solution to each approximating problem the finite dimensional equations for numerical approximation

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

the transformation method for the simulation and analysis of systems with uncertain parameters in this paper the transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of cuts the method represents a special implementation of fuzzy arithmetic that avoids the well known effect of overestimation which usually arises when fuzzy arithmetic is reduced to interval computation systems with uncertain model parameters can thus be simulated without any artificial widening of the simulation results as a by product of the implementation scheme the transformation method also provides a measure of influence to quantitatively analyze the uncertain system with respect to the effect of each uncertain model parameter on the overall uncertainty of the model output by this a special kind of sensitivity analysis can be defined on the basis of fuzzy arithmetic finally to show the efficiency of the transformation method the method is applied to the simulation and analysis of a model for the friction interface between the sliding surfaces of a bolted joint connection

computational algorithm for controlling a timoshenko beam abstract this paper is concerned with computational algorithms for lqr control of a timoshenko slewing beam problem the algorithm make use of a conforming finite element scheme that is shown to produce convergent control laws it is shown that the closed loop feedback can effectively control the vibrations due to an initial displacement it is also shown that when the system parameters are such that an euler bernoulli model is adequate to describe the dynamics of the beam the functional gains using the full timoshenko model are qualitatively similar to the ones using an euler bernoulli model