comparison of fuzzy numbers based on the probability measure of fuzzy events abstract most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only and suffer from lack of discrimination and occasionally conflict with intuition it is true that fuzzy numbers are frequently partial order and cannot be compared however this does not alleviate the need for comparison in practical applications in this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to zadeh it considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions the approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number it is shown that several comparison indices in the literature can be obtained based on the probability present measure approach finally some typical examples are used to compare the various different approaches the different interpretations of the dispersion index under different physical situations are emphasized

a fuzzy compromise approach to water resource systems planning under uncertainty abstract a fuzzy compromise approach to decision analysis is described within the context of water resource systems planning under uncertainty the approach allows various sources of uncertainty and is intended to provide a flexible form of group decision support the example compares the electre method with the fuzzy compromise approach the comparison is intended to demonstrate the benefits of adopting a multicriteria decision analysis technique which presents subjectivity within its proper context while maintaining an intuitive and transparent technique for ranking alternatives the fuzzy compromise approach allows a family of possible conditions to be reviewed and supports group decisions through fuzzy sets designed to reflect collective opinions and conflicting judgements ranking of alternatives is accomplished with fuzzy ranking measures designed to illustrate the effect of risk tolerance differences among decision makers two distinct ranking measures are used a centroid measure and a fuzzy comparison measure based on a fuzzy goal

weighted pseudo almost periodic mild solutions of semilinear evolution equations with nonlocal conditions in this paper applying the theory of semigroups of operators to evolution families and banach fixed point theorem we prove the existence and uniqueness of the weighted pseudo almost periodic mild solution of the semilinear evolution equation x t a t x t f t x t with nonlocal conditions x 0 x 0 g x in banach space x under some suitable hypotheses

weighted pseudo almost periodic solutions of a class of abstract differential equations abstract for abstract linear functional differential equations with a weighted pseudo almost periodic forcing term we prove that the existence of a bounded solution on r implies the existence of a weighted pseudo almost periodic solution our results extend the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations to illustrate the results we consider the lotka volterra model with diffusion

optimal revenue for fuzzy demand quantity in this paper we consider the linear demand function in which the demand quantity is a triangular fuzzy number we use the extension principle to find the membership function of the revenue function in a fuzzy sense and its centroid finally we give an example to compute the estimate of the total revenue in a fuzzy sense

consumer surplus and producer surplus for fuzzy demand and fuzzy supply we shall extend consumer surplus and producer surplus of the linear demand function and linear supply function in crisp case to the fuzzy sense

weighted pseudo antiperiodic solutions for fractional integro differential equations in banach spaces in this paper we prove the existence of weighted pseudo antiperiodic mild solutions for fractional integro differential equations in the form d u t au t t a t s au s ds f t u t t r where f u is stepanov like weighted pseudo antiperiodic and a generates a resolvent family of bounded and linear operators on a banach space x a l loc 1 r and 0 here the fractional derivative is considered in the sense of weyl also we give a short proof to show that the vector valued space of stepanov like weighted pseudo antiperiodic functions is a banach space

fuzzy inventory with backorder for fuzzy order quantity and fuzzy shortage quantity abstract in the problem of inventory with backorder the total cost is f q s in section 2 2 1 0 0 let kq s f q s 0 g q s a a b q where q q 1 q 0 q 2 is a triangular fuzzy number also we will have the membership function g q z of the fuzzy cost g q and its centroid

existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time varying coefficients and mixed delays this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to recurrent delayed neural networks several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain furthermore several methods are applied to establish sufficient criteria for the globally exponential stability of this system the approaches are based on constructing suitable lyapunov functionals and the well known banach contraction mapping principle moreover the attractivity and exponential stability of the pseudo almost periodic solution are also considered for the system a numerical example is given to illustrate the effectiveness of our results

pseudo almost periodic solutions of neutral integral and differential equations with applications abstract the existence and uniqueness of pseudo almost periodic solutions to general neutral integral equations with deviations are obtained for this pseudo almost periodic functions in two variables are considered the results extend the corresponding ones to the convolution type integral equations they are used to study pseudo almost periodic solutions of general neutral differential equations and to the so called scalar neutral logistic equation version

the optimum output quantity of a duopoly market under a fuzzy decision environment the main purpose of this paper is to develop a new optimum output quantity decision analysis of a duopoly market under a fuzzy decision environment to efficiently handle the fuzziness of the decision variables the linguistic values subjectively represented by the trapezoidal fuzzy numbers are used to act as the evaluation tool of decision variables such as fixed cost and unit variable cost this paper will apply fuzzy set theory to construct an optimum output quantity decision model based on aiming for the maximum profit of a duopoly market by using this decision model the decision makers fuzzy assessments with various variables can be considered in the decision process to assure more convincing and accurate decision making

composition of pseudo almost automorphic and asymptotically almost automorphic functions this paper is concerned with pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions new results concerning the composition of pseudo almost automorphic functions are established

matrices of operators and regularized cosine functions this paper is concerned with matrices of abstract differential operators which are parabolic in the sense of shilov or correct in the sense of petrovskij we show that they generate regularized cosine functions with suitable regularizing operators under sharper conditions the results then are applied to matrices of partial differential operators on many function spaces finally the wellposedness of the associated second order systems is discussed

optimal revenue for demand function in fuzzy sense abstract in this paper we consider the linear or quadratic demand function such that its coefficients are triangular fuzzy numbers then we use the extension principle to find the membership function of the revenue function in fuzzy sense and their centroid finally we obtain the optimal demand quantity x in the fuzzy sense and the estimate of the maximum revenue in fuzzy sense

weighted pseudo almost periodic solutions to some differential equations abstract the paper considers some new classes of functions called weighted pseudo almost periodic functions which implement in a natural fashion the classical pseudo almost periodic functions due to zhang properties of these weighted pseudo almost periodic functions are discussed including a composition result for weighted pseudo almost periodic functions the results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo almost periodic solution to the heat equation with dirichlet conditions

backorder fuzzy inventory model under function principle in this paper the fuzzy inventory model is discussed especially in the case of permitting backorder under the fuzzy environment of fuzzy demand fuzzy order cost fuzzy inventory cost and fuzzy backorder cost we use the function principle instead of the extension principle to calculate the total fuzzy inventory cost we also apply the median rule to find the optimal economic order quantity eoq and shortage quantity

stepanov like pseudo almost periodic mild solutions to perturbed nonautonomous evolution equations with infinite delay abstract in this paper we prove the invariance of stepanov like pseudo almost periodic functions under bounded linear operators furthermore we obtain existence and uniqueness theorems of pseudo almost periodic mild solutions to evolution equations u t a t u t h t and u t a t u t f t b u t t c t s u s d s f t on r assuming that a t satisfy acquistapace terreni conditions that the evolution family generated by a t has exponential dichotomy that r 0 a is almost periodic that b c t s t s are bounded linear operators that f is lipschitz with respect to the second argument uniformly in the first argument and that h f f are stepanov like pseudo almost periodic for p 1 and continuous to illustrate our abstract result a concrete example is given

weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type abstract this paper studies suitable sufficient conditions to ensure the existence and uniqueness of weighted pseudo almost periodic solutions to a neutral delay integral equation of advanced type introduced by t a burton in the literature the abstract results are then utilized to characterize weighted pseudo almost periodic solutions to the well known logistic equation

economic principle on profit in the fuzzy sense for the economic principle on profit in the crisp sense the profit is maximum when the marginal revenue equals the marginal cost for the linear or quadratic demand and cost functions we consider the case when their coefficients are fuzzy numbers then we use the extension principle to explain this principle used in the fuzzy sense these results are extensions of the crisp case

consumer surplus and producer surplus in fuzzy sense abstract in economics we extend the concept of consumer surplus of demand function and producer surplus of supply function to cover the fuzzy sense here we deal with the following four sets of types of demand and supply functions 1 i both demand and supply functions are linear 2 ii both demand and supply functions are quadratic 3 iii demand function is quadratic and supply function is linear 4 iv demand function is linear and supply function is quadratic

exponential stability for nonautonomous impulsive neutral partial stochastic evolution equations with delay abstractin this paper we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic ev

weighted pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with weighted pseudo almost automorphic functions which are more general and complicated than weighted pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space which extends known results

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

c semigroups and almost periodic solutions of evolution equations abstract the paper is concerned with the existence of almost periodic mild solutions to evolution equations of the form u t au t f t where a generates a c semigroup and f is almost periodic using the evolution c semigroup associated with the equation under consideration we obtain various sufficient conditions for the existence of almost periodic solutions to which extend previous ones to a more general class of ill posed equations involving c semigroups

existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations abstract in this paper under acquistapace terreni conditions we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients

an incremental multivariate regression method for function approximation from noisy data abstract in this paper we consider the problem of approximating functions from noisy data we propose an incremental supervised learning algorithm for rbf networks hidden gaussian nodes are added in an iterative manner during the training process for each new node added the activation function center and the output connection weight are settled according to an extended chained version of the nadaraja watson estimator then the variances of the activation functions are determined by an empirical risk driven rule based on a genetic like optimization technique

ranking fuzzy numbers based on decomposition principle and signed distance by using the decomposition principle and the crisp ranking system on r we construct a new ranking system for fuzzy numbers which is very realistic and also matching our intuition as in r

existence of weighted pseudo anti periodic solutions to some non autonomous differential equations abstract in this paper we first introduce two new concepts called respectively weighted pseudo periodicity and weighted pseudo anti periodicity which generalize respectively the well known notions of periodicity and that of anti periodicity basic properties of these new functions are discussed furthermore the existence of weighted pseudo anti periodic solutions to some damped non autonomous second order differential equations will be investigated to illustrate our abstract results the existence of weighted pseudo anti periodic solutions to a plate like equation is discussed

new approach for the existence of pseudo almost periodic solutions for some second order differential equation with piecewise constant argument abstract the following equation d 2 d t 2 x t px t 1 qx 2 t 1 2 f t is considered and necessary and sufficient conditions are given in order to ensure the existence and uniqueness of pseudo almost periodic solutions

a class of semigroups regularized in space and time we consider times integrated c regularized semigroups which are a hybrid between semigroups regularized in space c semigroups and integrated semigroups regularized in time we study the basic properties of these objects also in absence of exponential boundedness we discuss their generators and establish an equivalence theorem between existence of integrated regularized semigroups and well posedness of certain cauchy problems we investigate the effect of smoothing regularized semigroups by fractional integration

fuzzy linear programming models to solve fuzzy matrix games abstract in this paper a zero sum two person game with imprecise values in its matrix of payoffs is considered we propose a method for its solution based on the establishment of a fuzzy linear programming f l p problem for each player the method is shown as a generalization of that conventionally used in the solution of a classical game to solve such f l p problems we propose the auxiliary models resulting from the application of some of the methods for ranking fuzzy numbers hence according to the kind of ranking method that players want to use different solutions to the former game can be obtained we show that these solutions are of the same nature as the parameters defining the game and corresponding to a fuzzy predicate that can be established as the value of the game is around

existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations this paper is concerned with the study of weighted pseudo almost periodic solutions to some classes of hyperbolic differential equations upon making some suitable assumptions the existence and uniqueness of a weighted pseudo almost periodic solution is obtained to illustrate our main result we study the existence of a weighted pseudo almost periodic solution to a system of partial differential equations arising in control systems described by abstract retarded functional differential equations with feedback control

multivariate classification through adaptive delaunay based c spl deg spline approximation this paper introduces a new method for adaptively building a multivariate c spl deg spline approximation from scattered samples of an unknown function the central feature of the method is a means for adaptively tesselating an approximation space to form a multidimensional mesh over which the spline fitting then occurs the mesh used is a delaunay tesselation of the approximation space whose vertices lie at a subset of the scattered sample locations the specific subset of sample locations used is adaptively determined by repeated overfitting and simplification of the resulting spline approximation overfitting and simplification is an attractive paradigm for high dimensional approximation problems because it provides a means for forming an approximation that is complex only in regions where the scattered sample data provide sufficient evidence of complexity in the underlying unknown function overfitting and simplification is effectively exploited in this new approach as the function representation used is not subject to certain recursive dependencies the properties of the new technique are demonstrated in the context of an easily visualized bivariate classification problem the technique is then applied to a 10 dimensional clinical ecg classification problem and the results are compared to those obtained with a perceptron based neural network

existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional differential equations and applications the paper considers the existence and uniqueness of pseudo almost periodic mild solutions to some classes of first order partial neutral functional differential equations upon making some suitable assumptions existence and uniqueness results are obtained applications include both a partial integro differential equation arising in control systems and the scalar reaction diffusion equation with delay

composition of pseudo almost periodic functions and semilinear differential equations under the assumption of uniformly continuity we establish a composition theorem of pseudo almost periodic functions in general banach spaces as an application we give some existence theorems of pseudo almost periodic solutions and mild pseudo almost periodic solutions for some differential equations

a single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints abstract this paper develops a mathematical model for a single period multi product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints after calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness particular expressions for those density functions are considered here the constraints are of three types i both are stochastic ii one stochastic and other one imprecise fuzzy and iii both imprecise the stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility necessity constraints stochastic and fuzzy constraints are transformed to equivalent deterministic ones using here and now approach and fuzzy relations respectively the deterministic problems are solved using a non linear optimization technique generalized reduced gradient method the model is illustrated through numerical examples sensitivity analyses on profit functions due to different permitted aspiration and confidence levels are presented

the best prices of three mutually complementary merchandises in the fuzzy sense abstract let the demand functions of three mutually complementary merchandises x 1 x 2 x 3 be x 1 a 1 a 2 p 1 a 3 p 2 a 4 p 3 x 2 b 1 b 2 p 1 b 3 p 2 b 4 p 3 x 3 c 1 c 2 p 1 c 3 p 2 c 4 p 3 0 p 1 a 1 a 2 0 p 2 b 1 b 3 0 p 3 c 1 c 4 with a j 0 b j 0 c j 0 j 1 2 3 4 known the total revenue is r p 1 p 2 p 3 x 1 p 1 x 2 p 2 x 3 p 3 the monopolists can find the best prices p 1 p 2 p 3 for x 1 x 2 x 3 that make r p 1 p 2 p 3 reach its maximum in this paper we deal with a perfect competitive market and find out the best prices in the fuzzy sense to get the maximum revenue

characterization of the equilibrium strategy of the bimatrix game with fuzzy payoff in this paper we consider fuzzy bimatrix games which mean bimatrix games with fuzzy payoff matrices we define two types of concepts of equilibrium strategy and investigate their relationships moreover we prove that these nash equilibrium strategies exist in any fuzzy bimatrix games

a numerical approach to a multi objective optimal inventory control problem for deteriorating multi items under fuzzy inflation and discounting the optimal production and advertising policies for an inventory control system of deteriorating multi items under a single management are formulated with resource constraints under inflation and discounting in fuzzy environment here the deterioration of the items and depreciation of sales are at a constant rate deteriorated items are salvaged and the effect of inflation and time value of money are taken into consideration the inflation and discount rates are assumed to be imprecise and represented by fuzzy numbers these imprecise quantities are first transformed to corresponding intervals and then following interval mathematics the related objective function is changed to respective multi objective functions using utility function method ufm the multi objective problem is changed to a single objective problem here the production and advertisement rates are unknown and considered as control decision variables the production advertisement and demand rates are functions of time t the total profit which consists of the sales proceeds production cost inventory holding cost and advertisement cost is formulated as an optimal control problem and evaluated numerically using ufm and generalized reduced gradient grg technique finally numerical experiment sensitivity analysis and graphical representation are provided to illustrate the system for the present model expressions and graphical results are presented when the rates of advertisement are constant

converse problems of fourier expansion and their applications abstract let f c r h have a countable frequency set freq f and satisfy parseval s equality we show that if f satisfies one of the following conditions a uniformly continuous and freq f has a unique limit point at infinity b indefinite integral is lipschitz freq f converges fast in some sense c in the case of euclidean space h all the coefficients are positive then f is pseudo almost periodic example is given to show that the conclusion cannot be improved the results are applied to the theory of riesz fischer and the optimal control theory

models for a fuzzy inventory of two replaceable merchandises without backorder based on the signed distance of fuzzy sets abstract this paper investigates the inventory problems for two mutually complementary merchandises we first consider the merchandises in a monopoly market and then in a perfect competitive market with the fuzzy sets concept we discuss how to determine the optimal ordering policy for the aforementioned inventory problem such that the total related cost is minimum three results are obtained and the numerical examples are provided to illustrate these results in contrast with the previous studies that employed the extension principle and centroid method to derive the estimate of the total cost in the fuzzy sense we show that using the decomposition principle and the signed distance can attain it easier

the existence of pseudo almost periodic solutions for some nonlinear differential equations in banach spaces abstract let e be a real banach where x h denotes the limit of the quotient x x t h t as 0 t 0 consider the differential equation d x d t a t x f t where we assume amongst other properties that a is strongly dissipative in the following sense x y a t x a t y p t x y x y where is a function of the type u 0 and p is a function majorized by an almost periodic function with negative mean value first we show that this equation has a unique pseudo almost periodic solution then we apply this result to the class of the following equations d x d t q t x x f t 0 where q is a pseudo almost periodic function with positive mean value

solving fuzzy equations in economics and finance abstract in this paper we apply our new solution procedure for solving fuzzy equations linear non linear differential to three problems in economics and finance the three applications are 1 leontief s input output model 2 the internal rate of return and 3 a dynamic supply demand model where price and supply are governed by a system of differential equations

linear codes interpolation from noisy patterns by means of a vector quantization process abstract an algorithm inferring a boolean linear code from noisy patterns received by a noisy channel under the assumption of uniform occurrence distribution over the codewords and an upper bound to the amount of data are presented a vector quantizer is designed from the noisy patterns choosing the obtained codebook as code approximation it is shown both theoretically and experimentally that when the data are affected by independent random errors this strategy requires a small number of patterns to obtain a good identification with high probability of the code from the noisy data

economic order quantity in fuzzy sense for inventory without backorder model abstract this paper investigates a group of computing schemas for economic order quantity as fuzzy values of the inventory without backorder we express the fuzzy order quantity as the normal triangular fuzzy number q 1 q 0 q 2 and then solve the aforementioned optimization problem we find that after defuzzification the total cost is slightly higher than in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders deliveries and sales

stepanov like pseudo almost periodicity and its applications to some nonautonomous differential equations abstract the paper revisits the concept of s p pseudo almost periodicity recently introduced by the author in particular we study the existence of pseudo almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and s p pseudo almost periodic for p 1 applications include the existence of pseudo almost periodic solutions to the heat equation with a forcing term which is s p pseudo almost periodic and jointly continuous

regularity of mild solutions for a class of fractional order differential equations in this article we show sufficient conditions ensuring the existence and uniqueness of a mild solution to the equation d au t au t d a 1f t u t 1 a 2 email protected r in the same space where f belongs here a is a sectorial operator defined in a banach space x d a is the fractional derivative in the riemann liouville sense and f x email protected x for each email protected x where w x is a vector valued subspace of the space of continuous and bounded functions the subspaces w x that we will consider in this article are the space of periodic almost periodic almost automorphic and compact almost automorphic vector valued functions among others in particular we extend and unify recent results established for the equation in the papers agarwal et al 2010 cuevas et al 2010 and cuevas and lizama 2008

weighted pseudo almost periodic solutions for some partial functional differential equations abstract in this work we give sufficient conditions for the existence and uniqueness of a weighted pseudo almost periodic solution for some partial functional differential equations to illustrate our main result we study the existence of a weighted pseudo almost periodic solution for some diffusion equation with delay

stepanov like pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations abstract we obtain new existence and uniqueness theorems of pseudo almost periodic mild solutions to nonautonomous neutral partial evolution equations d d t u t f t u t a t u t f t u t g t u t t r d d t u t f t b u t a t u t f t b u t g t c u t t r assuming that a t satisfy acquistapace terreni conditions the evolution family generated by a t has exponential dichotomy r 0 a is almost periodic b c are densely defined closed linear operators f g are lipschitz with respect to the second argument uniformly in the first argument f is pseudo almost periodic in the first argument g is stepanov like pseudo almost periodic in the first argument for p 1 and jointly continuous to illustrate our abstract results two examples are given

the best prices of two mutual complements in the fuzzy sense abstract let the demand functions of two mutual complements be i x 1 a 1 a 2 p 1 a 3 p 2 x 2 b 1 b 2 p 1 b 3 p 2 0 p 1 a 1 a 2 0 p 2 b 1 b 3 where a j 0 b j 0 j 1 2 3 are known ii x 1 a 1 a 2 p 1 a 3 p 1 2 a 4 p 2 x 2 b 1 b 2 p 1 b 3 p 2 0 p 1 x 1c 0 p 2 b 1 b 3 with a j 0 j 1 2 3 4 b j 0 j 1 2 3 are known the best prices p 1 p 2 in a fuzzy sense are described in this report

pseudo almost periodic solutions of some differential equations ii we first present some results about pseudo almost periodic functions then we use these results to show some theorems about existence and uniqueness of the pseudo almost periodic solutions of the linear and the quasi linear nonautonomous equations finally we set up some theorems of the existence of pseudo almost periodic solutions implying the existence of almost periodic solutions of general ordinary differential equation systems

existence and uniqueness of pseudo almost periodic solutions to semilinear differential equations and applications abstract this paper deals with the existence and uniqueness of pseudo almost periodic solutions to the semilinear differential equations of the form u t a u t b u t f t u t where a b are densely defined closed linear operators on a hilbert space h and f r h h is a jointly continuous function using both the so called method of the invariant subspaces for unbounded linear operators and the classical banach fixed point principle the existence of a pseudo almost periodic solution to is obtained under some suitable assumptions as applications we examine the existence and uniqueness of pseudo almost periodic solutions to some second order hyperbolic equations

almost periodic solutions of neutral functional differential equations in this paper we study a non autonomous neutral functional differential equation in a banach space applying the theory of semigroups of operators to evolution equations and krasnoselskii s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under consideration

mappings of higher order and nonlinear equations in some spaces of almost periodic functions abstract in the first part of the paper we examine mappings of higher order from a general point of view that is in normed spaces of bounded real valued functions defined on r particular attention is paid to the relation of such mappings with the so called autonomous superposition operators next we investigate mappings of higher order in banach spaces of almost periodic functions and their perturbations we also give necessary and sufficient conditions guaranteeing that a nonautonomous superposition operator acts in the space of almost periodic functions in the sense of levitan and is uniformly continuous in the banach space of bounded almost periodic functions in the sense of levitan we discuss mappings of higher order and a convolution operator some applications to nonlinear differential and integral equations are given

antiperiodic solutions of semilinear integrodifferential equations in banach spaces abstract we are concerned in this paper with the existence of antiperiodic mild solutions of some semilinear integrodifferential equations in a banach space we study further properties of antiperiodic functions including a new composition theorem and introduce the new concept of asymptotically antiperiodic functions

existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations abstract some sufficient conditions for the existence and uniqueness of pseudo almost periodic mild solutions to some classes of partial evolution equations are given we then make use of our abstract results to discuss the existence of pseudo almost periodic solutions to some partial differential equations

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

the cournot game under a fuzzy decision environment the conventional precision based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist this paper considers the cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers our model utilizes the weighted center of gravity wcog method to defuzzify the fuzzy profit function into a crisp value we derive the equilibrium cournot quantity of each firm by simultaneously solving the first order condition of each firm our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method in addition we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm s cost and market demand functions we conduct sensitivity analysis to investigate the effect of parameter perturbations on firms outcomes the results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters

on the relationship between generalization error hypothesis complexity and sample complexity for radial basis functions feedforward networks together with their training algorithms are a class of regression techniques that can be used to learn to perform some task from a set of examples the question of generalization of network performance from a finite training set to unseen data is clearly of crucial importance in this article we first show that the generalization error can be decomposed into two terms the approximation error due to the insufficient representational capacity of a finite sized network and the estimation error due to insufficient information about the target function because of the finite number of samples we then consider the problem of learning functions belonging to certain sobolev spaces with gaussian radial basis functions using the above mentioned decomposition we bound the generalization error in terms of the number of basis functions and number of examples while the bound that we derive is specific for radial basis functions a number of observations deriving from it apply to any approximation technique our result also sheds light on ways to choose an appropriate network architecture for a particular problem and the kinds of problems that can be effectively solved with finite resources i e with a finite number of parameters and finite amounts of data

a composition theorem for weighted pseudo almost automorphic functions and applications abstract in this paper we establish a composition theorem for weighted pseudo almost automorphic functions under a weaker lipschitz condition our composition theorem generalizes some known results moreover the existence and uniqueness of pseudo almost automorphic solutions for abstract semilinear evolution equations are studied

optimal fuzzy profit for price in fuzzy sense the fuzzy price function can be derived from a linear or a quadratic demand function and a linear cost function in this article we find the optimal fuzzy profit using the fuzzy price function and linear cost function the results are identical when the fuzzy case was reduced to the crisp case

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

a new composition theorem for square mean almost automorphic functions and applications to stochastic differential equations abstract in this paper we establish a new composition theorem for square mean almost automorphic functions under conditions which are different from lipschitz conditions in the literature we apply this new composition theorem together with schauder s fixed point theorem to investigate the existence of square mean almost automorphic mild solutions for a stochastic differential equation in a real separable hilbert space finally an interesting corollary is also given for the sub linear growth cases

existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications this paper is concerned with the existence and uniqueness of pseudo almost periodic solutions to the class of semilinear differential equations of the form u t au t f t bu t where a is the infinitesimal generator of an analytic semigroup acting on a complex banach space x b d b x x is a densely defined closed linear operator and f r x x is a jointly continuous function under some suitable assumptions on a b and f the existence and uniqueness of a pseudoalmost periodic solution to is obtained

fuzzy inventory with or without backorder for fuzzy order quantity with trapezoid fuzzy number abstract the purpose of this paper is to investigate a group of computing schemas for the economic order quantity as fuzzy values of the inventory with without backorder we express the fuzzy order quantity as the normal trapezoid fuzzy number q 1 q 2 q 3 q 4 and then we solve the aforementioned optimization problem we find that after defuzzification the total cost is slightly higher than in the crisp model however it permits better use of the economic fuzzy quantities arising with changes in orders and deliveries

the use of fuzzy set theory for forecasting corporate tax revenues the system based on the fuzzy set theory for forecasting the florida corporate income tax revenue was developed in response to several years of unsuccessful forecasts generated by the conventional econometric methods the system consists of two parts 1 a the first part utilizes time series of revenue and of the real per capita gnp both time series are transformed into trend vectors through the utilization of moving average technique both vectors are divided into strings of growth patterns such as accelerating growth decelerating growth and negative growth the system checks for several indications of systematic relationship between the gnp vector and the tax revenue vector based on that relationship the forecast of the corporate tax revenues is generated in fuzzy such as very rapid growth slightly negative growth etc 2 b the fuzzy forecast from the first part of the system constitutes input into the second part which in turn generates the range of forecasted revenue in millions of dollars a control mechanism which is built into the system continously checks forecasted rates of change in tax revenues against the actuals throughout the history of the time series to make sure that the cumulative forecasting error will not reach unacceptable magnitude

pseudo almost periodicity of some nonautonomous evolution equations with delay abstract this paper is concerned with pseudo almost periodicity of the solutions to the nonautonomous evolution equation with delay u t a t u t f t u t h some sufficient conditions which ensure the existence and uniqueness of pseudo almost periodic mild solutions to the evolution equation with delay are given an example is shown to illustrate our results

estimating a fuzzy term structure of interest rates using fuzzy regression techniques abstract several papers in the financial literature propose using fuzzy numbers fns to model interest rate uncertainty however in our opinion the first problem to be solved is how to estimate these rates with fns in this paper we attempt to provide a solution to this question with a method for adjusting the temporal structure of interest rates tsir that is based on fuzzy regression techniques this method will enable to quantify the anticipated rates in the fixed income markets for the future with fns in particular we discuss how to estimate the tsir with triangular fuzzy numbers because of their desirable properties