design of a fuzzy finite capacity queuing model based on the degree of customer satisfaction analysis and fuzzy optimization due to uncontrollable factors the parameters in the queuing models may be uncertain and so in this paper we present the design of a fuzzy finite capacity queuing model in which the arrival pattern and the service pattern follow an exponential distribution under uncertain parameter as for the design of the system the criterion of optimization proposed is aimed at the optimum selection of the number of servers with the goal of providing a high degree of satisfaction to clients when they join the system this optimization process will be solved through markov chains with fuzzy state the validity of the procedure proposed to incorporate fuzzy data in this queuing system is confirmed by a fuzzy simulation experiment of the differential equations which govern the behaviour of the model by the bontempi s qua si iii algorithm the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informative results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite capacity queuing models with uncertain data can have a broader range of applications

exact energy and momentum conserving algorithms for general models in nonlinear elasticity implicit time integration schemes that inherit the conservation laws of total energy linear and angular momentum are considered for initial boundary value problems in finite deformation elastodynamics conserving schemes are constructed for general hyperelastic material models both compressible and incompressible and are formulated in a way that is independent of spatial discretization three numerical examples for ogden type material models implemented using a finite element discretization in space are given to illustrate the performance of the proposed schemes these examples show that relative to the standard implicit mid point rule the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy

multi multiplier ambient space formulations of constrained dynamical systems with an application to elastodynamics various formulations of the equations of motion for both finite and infinite dimensional constrained lagrangian dynamical systems are studied the different formulations correspond to different ways of enforcing constraints through multiplier fields all the formulations considered are posed on ambient spaces whose members are unrestricted by the need to satisfy constraint equations but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied the stability properties of the invariant set within its ambient space are shown to be different in each case we use the specific model problem of linearized incompressible elastodynamics to compare properties of three different ambient space formulations we establish the well posedness of one formulation in the particular case of a homogeneous isotropic body subject to specified tractions on its boundary

singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation abstract a short time existence theorem is proven for the initial boundary value problem for a class of quasilinear symmetric hyperbolic systems containing a constant coefficient spatial operator multiplied by a large parameter solutions u are shown to remain bounded independently of for a time independent of provided that u 0 and u l 0 are bounded independently of and certain structural conditions are satisfied this result is applied to the quasigeostrophic approximation of the shallow water equations and the constant pressure approximation in combustion and solutions for these cases are shown to converge to solutions of limiting equations as

optimizing a priority discipline queueing model using fuzzy set theory the aim of this paper is to provide a more realistic description of priority discipline queueing models by using fuzzy set theory it develops and optimizes two fuzzy queueing models with priority discipline a model with nonpreemptive priorities system and a model with preemptive priorities system denoted by m i m i 1 and m i f i 1 the first symbol is for a queueing system where arrivals and services from a single server follow a poisson process with fuzzy parameter and the last symbol is for a queueing model with arrivals follows a poisson process with fuzzy rate and fuzzy deterministic service rate zadeh s extension principle is the basic approach to this research into fuzzy stochastic processes our results are the basis for a discussion of optimal selection of priority discipline two fuzzy queueing systems that are commonly found in real situations are solved and serve as examples that highlight the validity of the procedure we propose fuzzy queueing models are more realistic than the crisp queues that are commonly used in reality furthermore extending queueing models to the fuzzy environment widens their scope of application

on borel mappings and σ ideals generated by closed sets abstract we obtain some results about borel maps with meager fibers on polish spaces the results are related to a recent dichotomy by sabok and zapletal concerning borel maps and ideals generated by closed sets in particular we give a classical proof of this dichotomy we shall also show that for certain natural ideals i generated by closed sets in compact metrizable spaces x every borel map on a borel set in x not in i either has a fiber not in i or else it is injective on a borel set not in i this is the case for the ideal generated by finite dimensional closed sets in the hilbert cube which provides an answer to a question asked by m elekes

on using a cuts to evaluate fuzzy equations abstract consider an equation y f x1 xn where the extension principle is used to find y f x 1 x n when we subtitute fuzzy numbers x i for the xi 1 i n if x i denotes an cut of x i then we argue that for only certain simple equations will one obtain y equal to f x 1 x n where f is evaluated using interval arithmetic

optimal selection of the service rate for a finite input source fuzzy queuing system finite input source queuing models have a wide range of applications in many practical situations and are frequently found in machine maintenance and repair operations owing to uncontrollable factors finite input source queuing problems parameters may contain uncertainty that is why to begin with in this paper it is proposed the analysis development and design of a fuzzy queuing model with finite input source in which the arrival pattern as well as the service pattern follow an exponential distribution under uncertain parameter in order to design the system the established optimization criterion consists in determining the optimal number of servers so as to minimize the expected total cost function per unit time to choose among uncertain alternatives three techniques to make decisions under uncertainty are proposed this type of systems has a finite waiting line as a result the system of differential equations that governs the model s behaviour consists of a finite number of equations in the second place this feature of the finite input source queuing systems enables us to bring forward in this paper two new contributions i in the first one the following doubt has been raised and solved if the convergence of the probabilities email protected i t obtained from the fuzzy differential equations that govern the behaviour of the finite source system is worked out does the result match the steady state fuzzy probabilities obtained by applying zadeh s extension principle to the classic queuing model and ii it has been performed a fuzzy simulation experiment on the differential equations using bontempi s qua si iii algorithm this enables us to know the time evolution of the probabilities email protected i t and its convergence on the one hand on the other we can compare the results of the simulation to those analytically obtained by applying zadeh s extension principle this way the validity of the proposed procedure for the simulation is verified by means of the theoretical results the extension of queuing decision models to fuzzy environments enables the decision maker to obtain more informing results and wider knowledge on the behaviour of the system since the results obtained in the fuzzy queuing model are fuzzy subsets containing the whole initial information that is why the finite input source queuing models with uncertain data can be of more use and can have a broader range of applications

elementary queueing theory based on possibility theory abstract we consider a queueing system with multiple parallel servers finite or infinite system capacity and calling source but whose arrivals and service completions are governed by a possibility distribution changes in the number of customers in the system is modeled by a transition matrix and powers of under max min product produce if it converges the steady state possibility distribution results are applied to the machine servicing problem to determine the most economical size of the repair crew

time value of delays in unreliable production systems with mixed uncertainties of fuzziness and randomness abstract this paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed random and fuzzy uncertainties that result from unreliable systems to consider different types of delay time values the system states are appropriately and carefully identified and defined and a cost based fuzzy decision model that incorporates several unreliability factors is constructed then the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level to identify the lower and upper bounds on the minimal total cost per unit time at and thus construct the membership function to provide analytical expressions a special case with analytical results is also presented in contrast to existing studies the results derived from the proposed solution procedure conserve the fuzziness of the input information representing a significant difference from the crisp results obtained using approaches based on probability theory the results indicate that the proposed approach can provide more precise information to managers and improve decision making in practical system design

a characterization of the extension principle abstract we provide an alternative characterization of the extension principle of fuzzy sets this characterization is based upon using relations to represent mappings we apply this new characterization to develop an extension for non deterministic mappings

a stochastic approximation algorithm with varying bounds many optimization problems that are intractable with conventional approaches will yield to stochastic approximation algorithms this is because these algorithms can be used to optimize functions that cannot be evaluated analytically but have to be estimated for instance through simulation or measured thus stochastic approximation algorithms can be used for optimization in simulation unfortunately the classical stochastic approximation algorithm sometimes diverges because of unboundedness problems we study the convergence of a variant of stochastic approximation defined over a growing sequence of compact sets we show that this variant converges under more general conditions on the objective function than the classical algorithm while maintaining the same asymptotic convergence rate we also present empirical evidence that shows that this algorithm sometimes converges much faster than the classical algorithm

ranking and defuzzification methods based on area compensation abstract we present some interesting properties related to the area compensation procedure to compare fuzzy numbers it has been proved that this method produces more than a fuzzy interval order it induces a ranking of fuzzy numbers some further results are given about the transitivity property and about computational aspects extensions to non normal fuzzy numbers and fuzzy quantities are also proposed

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

the compressible euler equations in a bounded domain existence of solutions and the incompressible limit a short time existence theorem is proven for the euler equations for nonisentropic compressible fluid flow in a bounded domain and solutions with low mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

global existence for three dimensional incompressible isotropic elastodynamics via the incompressible limit the existence of global in time classical solutions to the cauchy problem for incompressible nonlinear isotropic elastodynamics for small initial displacements is proved solutions are constructed via approximation by slightly compressible materials the energy for the approximate solutions remains uniformly bounded on a time scale that goes to infinity as the material approaches incompressibility a necessary component to the long time existence of the approximating solution is a null or linear degeneracy condition inherent in the isotropic case which limits the quadratic interaction of the shear waves the proof combines energy and decay estimates based on commuting vector fields and a compactness argument 2004 wiley periodicals inc

an index for ordering fuzzy numbers abstract a new index that is useful for ordering ranking of fuzzy numbers is proposed to use this index the membership functions of fuzzy numbers need not be normal or convex properties of this index and its relationship to the 1981 yager s index are explained a numerical comparison between the proposed and four other ordering procedures is presented

the incompressible limit in nonlinear elasticity the incompressible limit in nonlinear elasticity is shown to fall under the theory of singular limits of quasilinear symmetric hyperbolic systems developed by klainerman and majda specifically initial value problems for a family of hyperelastic materials with stored energy functions w left frac partial x partial x right w infty left frac partial x partial x right lambda 2 w left det frac partial x partial x right are considered wherex andx are reference and deformed coordinates respectively under the assumption that the elasticity tensor a kl ij equiv frac partial 2 w infty partial left frac partial x i partial x k right partial left frac partial x j partial x l right is positive definite near the identity matrix and thatw 1 0 the following results are proven for appropriate initial data

a scaled stochastic approximation algorithm consider a stochastic system of such complexity that its performance can only be evaluated by using simulation or direct experimentation to optimize the expected performance of such systems as a function of several continuous input parameters decision variables we present a scaled stochastic approximation algorithm for finding the zero root of the gradient of the response function in each iteration of the scaled algorithm two independent gradient estimates are sampled at the current estimate of the optimal input parameter vector to compute a scale free estimate of the next search direction we establish sufficient conditions to ensure strong consistency and asymptotic normality of the resulting estimator of the optimal input parameter vector strong consistency is also established for a variant of the scaled algorithm with kesten s acceleration an experimental performance comparison of the scaled algorithm and the classical robbins monro algorithm in two simple queueing systems reveals some of the practical advantages of the scaled algorithm

forcing games and families of closed sets we propose a new game theoretic approach to the idealized forcing in terms of fusion games we provide a tree representation of such forcings which generalizes the classical approach to sacks and miller forcing we show that if a ideal is de nable 1 on 1 1 and generated by closed sets then it is generated by closed sets in all forcing extensions this implies that the countable support iteration of forcings associated with such ideals is proper we use it to prove an in nite dimensional version of the solecki theorem about inscribing positive g set into positive analytic sets among the examples we investigate the ideal e generated by closed null sets and ideals connected with not piecewise continuous functions for the rst one we show that the associated forcing extensions are of minimal degree for the second one we show that the associated forcing notion is equivalent to miller forcing

on boolean algebras related to σ ideals generated by compact sets abstract let h g be hausdorff measures on compact metric spaces x y and let b o r x j h and b o r y j 0 g be the boolean algebras of borel sets modulo ideals of borel sets that can be covered by countably many compact sets of finite h measure or g measure null respectively we shall show that if h is not finite and one of the quotient boolean algebras embeds densely in the other then for some borel b with h b h takes on borel subsets of b only values 0 or this is a particular instance of some more general results concerning boolean algebras b o r x j where j is a ideal of borel sets generated by compact sets

cauchy born rule and the stability of crystalline solids static problems we study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature we prove under certain sharp stability conditions that the correct nonlinear elasticity model is given by the classical cauchy born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the cauchy born rule the analysis is carried out for both simple and complex lattices and for this purpose we develop the necessary tools for performing asymptotic analysis on such lattices our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids

solving fuzzy queueing decision problems via a parametric mixed integer nonlinear programming method abstract this paper proposes a mathematical programming method to construct the membership functions of the fuzzy objective value of the cost based queueing decision problem with the cost coefficients and the arrival rate being fuzzy numbers on the basis of zadeh s extension principle three pairs of mixed integer nonlinear programs minlp parameterized by the possibility level are formulated to calculate the lower and upper bounds of the minimal expected total cost per unit time at through which the membership function of the minimal expected total cost per unit time of the fuzzy objective value is constructed to provide a suitable optimal service rate for designing queueing systems the yager s ranking index method is adopted two numerical examples are solved successfully to demonstrate the validity of the proposed method since the objective value is completely expressed by a membership function rather than by a crisp value it conserves the fuzziness of the input information thus more information is provided for designing queueing systems the successful extension of queueing decision models to fuzzy environments permits queueing decision models to have wider applications in practice

stochastic optimization by simulation numerical experiments with the m m 1 queue in steady state this paper gives numerical illustrations of the behavior of stochastic approximation combined with different derivative estimation techniques to optimize a steady state system it is a companion paper to l ecuyer and glynn 1993 which gives convergence proofs for most of the variants experimented here the numerical experiments are made with a simple m m 1 queue which while simple serves to illustrate the basic convergence properties and possible pitfalls of the various techniques

convergence of powers of s transitive fuzzy matrices abstract natural powers via max min multiplication of s transitive fuzzy matrices are considered it is shown that they oscillate with period equal to 2 this is an extension of the convergence property concerning max min transitive fuzzy matrices

ranking fuzzy numbers with maximizing set and minimizing set abstract up to now these are five methods of ranking n fuzzy numbers in order but these methods contain some confusions and occasionally conflict with intuition this paper introduces the concept of maximizing set and minimizing set to decide the ordering value of each fuzzy number and uses these values to determine the order of the n fuzzy numbers in addition we give a method for calculating the ordering value of each fuzzy number with triangular trapezoidal and two sided drum like shaped membership functions

analysis of fuzzy queues abstract a general approach for queuing systems in a fuzzy environment is proposed based on zadeh s extension principle the possibility concept and fuzzy markov chains to illustrate the approach analytical results for m f 1 and fm fm 1 systems are presented fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations a simple numerical example is also presented