fuzzy inventory model with two warehouses under possibility constraints a multi item inventory model with two storage facilities is developed with advertisement price and displayed inventory level dependent demand in a fuzzy environment purchase cost investment amount and storehouse capacity are imprecise the model is formulated as a single multi objective programming problem under fuzzy constraint constraints are satisfied with some pre defined necessity and the problem is solved via the goal programming method gpm when crisp equivalents of the constraints are available and by a fuzzy simulation based single multi objective genetic algorithm fsga fsmoga otherwise the model is illustrated with some numerical examples and results from different methods are compared in some particular cases

coupled cell networks semigroups lie algebras and normal forms we introduce the concept of a semigroup coupled cell network and show that the collection of semigroup network vector fields forms a lie algebra this implies that near a dynamical equilibrium the local normal form of a semigroup network is a semigroup network itself networks without the semigroup property will support normal forms with a more general network architecture but these normal forms nevertheless possess the same symmetries and synchronous solutions as the original network we explain how to compute lie brackets and normal forms of coupled cell networks and we characterize the sn decomposition that determines the normal form symmetry this paper concludes with a generalization to nonhomogeneous networks with the structure of a semigroupoid

reducibility of steady state bifurcations in coupled cell systems abstract a general theory for coupled cell systems was formulated recently by i stewart m golubitsky and their collaborators in their theory a coupled cell system is a network of interacting dynamical systems whose coupling architecture is expressed by a directed graph called a coupled cell network an equivalence relation on cells in a regular network a coupled cell network with identical nodes and identical edges determines a new network called quotient network by identifying cells in the same equivalence class and determines a quotient system as well in this paper we develop an idea of reducibility of bifurcations in coupled cell systems associated with regular networks a bifurcation of equilibria from subspace where states of all cells are equal is called a synchrony breaking bifurcation we say that a synchrony breaking steady state bifurcation is reducible in a coupled cell system if any bifurcation branch for the system is lifted from those for some quotient system first we give the complete classification of codimension one synchrony breaking steady state bifurcations in 1 input regular networks where each cell receives only one edge second we show that under a mild condition on the multiplicity of critical eigenvalues codimension one synchrony breaking steady state bifurcations in generic coupled cell systems associated with an n cell coupled cell network with d n symmetry a regular network is reducible for n 2

symmetry and phaselocking in chains of weakly coupled oscillators weakly coupled chains of oscillators with nearest neighbor interactions are analyzed for phaselocked solutions it is shown that the symmetry properties of the coupling affect the qualitative form of the phaselocked solutions and the scaling behavior of the system as the number of oscillators grows without bound it is also shown that qualitative behavior of these solutions depends on whether the coupling is diffusive or i synaptic terms defined in the paper the methods include the demonstration that the equations for phaselocked solutions can be approximated by a singularly perturbed two point continuum boundary value problem that is easier to analyze the issue of convergence of the phaselocked solutions to solutions of the continuum equation is closely related to questions involving numerical entropy in computation schemes for a conservation law an application to the neurophysiology of motor behavior is discussed briefly

random fuzzy dependent chance programming and its hybrid intelligent algorithm abstract a fuzzy random variable is a measurable function from a probability space to a collection of fuzzy sets while a random fuzzy variable is a function from a collection of random variables to 0 1 this paper provides a spectrum of random fuzzy dependent chance programming in which the underlying philosophy is based on selecting the decision with maximal chance to meet the event in order to speed up the solution process we train a neural network to approximate chance functions based on the training data generated by the random fuzzy simulation finally we integrate random fuzzy simulation neural network and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving random fuzzy dependent chance programming models and illustrate its effectiveness by some numerical examples

neural activity measures and their dynamics we provide an asymptotically justified derivation of activity measure evolution equations amees for a finite size neural network the approach takes into account the dynamics for each isolated neuron in the network being modeled by a biophysical model i e hodgkin huxley equations or their reductions by representing the interacting network as self and pairwise interactions we propose a general definition of spatial projections of the network called activity measures that quantify the activity of a network we show that the evolution equations that govern the dynamics of the activity measure shadow the activity measure of the network i e the two quantities stay close to each other for all times for general interactions and various asymptotic dynamics the amees effectively serve as a dimensionality reduction technique for the complex network when spatial synchrony and coherence are present and allow us to a priori predict network dynamics that would not be guessed from individual neuron behav

on the convergence of the tau method for nonlinear differential equations of riccati s type on considere l equation differentielle non lineaire de type riccati y x y 2 x 1 y 0 1 0 x a a 0 et la suite y n x des fonctions y n x telles que pour n 0 y n 1 x y n 1 x y n x 1 y n 1 0 1 0 x a 0 a a on demontre que la suite y n x n 0 converge uniformement vers la solution unique y x dans l intervalle 0 x a

redundancy optimization problems with uncertainty of combining randomness and fuzziness by using random fuzzy lifetimes as basic parameters three types of system performance expected system lifetime system lifetime and system reliability are presented some random fuzzy simulations are employed to estimate the system performance furthermore a spectrum of random fuzzy models are constructed for redundancy optimization problems in order to solve these models a hybrid intelligent algorithm is used finally some numerical examples are provided for the sake of illustration

the maximum fuzzy weighted matching models and hybrid genetic algorithm a matching of a graph is an independent subset of the edges set and a maximum matching is a matching with as many edges in it as possible the maximum weighted matching problem is to find a maximum matching in a given graph such that the sum of the weights of the edges in it is maximum in this paper the concepts of expected maximum fuzzy weighted matching the maximum fuzzy weighted matching and the most maximum fuzzy weighted matching are initialized according to various decision criteria the maximum fuzzy weighted matching problem is formulated as expected value model chance constrained programming and dependent chance programming by using the credibility theory and the crisp equivalents are also given furthermore a hybrid genetic algorithm is designed for solving the proposed fuzzy programming models finally a numerical example is given

fuzzy random programming with equilibrium chance constraints to model fuzzy random decision systems this paper first defines three kinds of equilibrium chances via fuzzy integrals in the sense of sugeno then a new class of fuzzy random programming problems is presented based on equilibrium chances also some convex theorems about fuzzy random linear programming problems are proved the results provide us methods to convert primal fuzzy random programming problems to their equivalent stochastic convex programming ones so that both the primal problems and their equivalent problems have the same optimal solutions and the techniques developed for stochastic convex programming can apply after that a solution approach which integrates simulations neural network and genetic algorithm is suggested to solve general fuzzy random programming problems at the end of this paper three numerical examples are provided since the equivalent stochastic programming problems of the three examples are very complex and nonconvex the techniques of stochastic programming cannot apply in this paper we solve them by the proposed hybrid intelligent algorithm the results show that the algorithm is feasible and effectiveness

structure of resonances and formation of stationary points in symmetrical chains of bilinear oscillators abstract dynamics of strongly nonlinear systems can in many cases be modelled by bilinear oscillators which are the oscillators whose springs have different stiffnesses in compression and tension this underpins the analysis of a wide range of phenomena from oscillations of fragmented structures connections and mooring lines to deformation of geological media single bilinear oscillators were studied previously and the presence of multiple resonances both super and sub harmonic was found less attention was paid to systems of multiple bilinear oscillators that describe many natural and engineering processes such as for example the behaviour of fragmented solids here we fill this gap concentrating on the simplest case 1d symmetrical chains of bilinear oscillators we show that the presence and structure of resonances in a symmetric chain of bilinear oscillators with fixed ends depends upon the number of oscillating masses two elementary chains act as the basic ones a single mass bilinear chain a mass connected to the fixed points by two bilinear springs that behaves as a linear oscillator with a single resonance and a two mass chain that is a coupled bilinear oscillator two masses connected by three bilinear springs the latter has multiple resonances we demonstrate that longer chains either do not have resonances or get decomposed in the resonance into either the single mass or two mass elementary chains with stationary masses in between the resonance frequencies are inherited from the basic chains of decomposition we show that if the number of masses is odd the chain can be decomposed into the single mass bilinear chains separated by stationary masses it then inherits the resonances of the single mass bilinear chain the chains with the number of masses minus 2 divisible by 3 can be decomposed into the two mass bilinear chains separated by stationary masses and inherit the resonances of the two mass chains the chains whose lengths satisfy both criteria such as chains with 5 11 17 masses allow both types of resonances

generalized connection graph method for synchronization in asymmetrical networks we present a general framework for studying global complete synchronization in networks of dynamical systems with asymmetrical connections we extend the connection graph stability method originally developed for symmetrically coupled networks to the general asymmetrical case the principal new component of the method is the transformation of the directed connection graph into an undirected graph in our method for symmetrically coupled networks we have to choose a path between each pair of nodes the extension of the method to asymmetrical coupling consists in symmetrizing the graph and associating a weight to each path this weight involves the node unbalance of the two nodes this quantity is defined to be the difference between the sum of connection coefficients of the outgoing edges and the sum of the connection coefficients of the incoming edges to the node the synchronization condition for this symmetrized and weighted network then also guarantees synchronization in the original asymmetrical network

parallel strategies for the step by step tau method we propose some computational strategies for a parallel implementation of the step by step tau method of ortiz this type of piecewise polynomial approximation is an extension of the well known lanczos tau method preliminary numerical experimentation showed promising results with respect to cpu time and accuracy of the solution in particular we apply this approach in parallel to the order zero airy s generalized function significant improvements have been obtained when compared with the numerical results of the sequential version of the segmented approximation which has been reported in previous research

numerical solution of systems of ordinary differential equations with the tau method an error analysis the recursive formulation of the tau method is extended to the case of systems of ordinary differential equations and an error analysis is given upper and lower error bounds are given in one of the examples considered the asymptotic behavior of the error compares in this case with that of the best approximant by algebraic polynomials for each of the components of the vector solution 1 introduction interest in the tau method see 2 3 5 for a long time regarded only as a tool for the construction of accurate approximations of a very restricted class of functions has been enhanced by the availability of software for its computer implementation and by the possibility of using it in the numerical solution of complex nonlinear differential equations over extended intervals the approxima tion of the solution of such type of equations is achieved as a result of finding tau approximants of a sequence of problems defined by linear differential equations details of this technique are given in 6 the subject of this paper is the extension of ortiz recursive formulation of lanczos tau method 5 to the case of systems of differential equations and more particularly to its error analysis for such systems our error estimation technique is applied to three model examples for which the exact solution is readily available it is discussed in general and with more detail when applied to the first of these examples for the second example we show how to get upper and lower error bounds we then compare these bounds with those given by meinardus 4 for the best uniform approximation of each of the components of the vector solution by algebraic polynomials to find that they are asymptotically equivalent the third example is a differential equation with variable coefficients and a nonempty subspace of residuals see 5 results of numerical experiments on the use of the tau method for the approxi mate solution of systems of ordinary differential equations with particular reference to stiff systems are reported in 8 the problems discussed in this paper can also be considered in the framework of simultaneous approximation of a function and its derivatives with the tau method see 1

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

analytical and numerical investigation of mixed type functional differential equations this paper is concerned with the approximate solution of a linear non autonomous functional differential equation with both advanced and delayed arguments we search for a solution x t defined for t 1 k k n that satisfies this equation almost everywhere on 0 k 1 and assumes specified values on the intervals 1 0 and k 1 k we provide a discussion of existence and uniqueness theory for the problems under consideration and describe numerical algorithms for their solution giving an analysis of their convergence

network architecture and spatio temporally symmetric dynamics we examine the relation between the structure of a network and the spatio temporally symmetric periodic dynamics it can support for solutions in which no cell is stationary we show that only networks in which all cells interact with each other or which contain a single group of interacting cells which drive the remainder of the network can exhibit such dynamics robustly these characteristics of network architecture are not captured by the typical statistical quantities used to describe network structure we illustrate the existence of spatio temporally periodic solutions through a direct construction using ideas from coupled cell theory and the theory of weakly coupled oscillators and show that these solutions can be stable in a very large region of parameter space while we consider only a special type of network behavior these ideas extend to more general architectures and dynamics

stability switches bifurcation and multi stability of coupled networks with time delays abstract this paper reveals the dynamical behaviors of a network consisting of a pair of ring sub networks and two way couplings of neurons between the individual sub networks time delays are introduced into the internal connections within the individual sub networks and the couplings between the individual sub networks the stability and instability of the trivial equilibrium of the network are analyzed and the conditions for the existence of hopf bifurcation are obtained by discussing the associated characteristic equation the criterion for the global stability of the trivial equilibrium of the network is given by constructing a suitable lyapunov functional numerical simulations are performed to validate the theoretical results and rich dynamical behaviors are observed such as multiple stability switches of the network equilibrium synchronous asynchronous oscillations and multi stability

equitable random graphs random graph models have played a dominant role in the theoretical study of networked systems the poisson random graph of erd s and renyi in particular as well as the so called configuration model have served as the starting point for numerous calculations in this paper we describe another large class of random graph models which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure including community structure bipartite structure degree correlations stratification and others yet are exactly solvable for a wide range of properties in the limit of large graph size including percolation properties complete spectral density and the behavior of homogeneous dynamical systems such as coupled oscillators or epidemic models

segmented tau approximation for test neutral functional differential equations we use the segmented formulation of the tau method to approximate the solutions of the neutral delay differential equationy t ay t by email protected cy email protected f t t 0 y t email protected t t 0 which represents for different values of a b c and t a family of functional differential equations that some authors have considered as test equations in different numerical experimentations the tau method introduced by lanczos is an important example of how to get approximations of functions defined by a differential equation in the formulation of a step by step tau version is expected that the error is minimized at the matching points of successive steps through the study of recent papers it seems to be demonstrated that the step by step tau method is a natural and promising strategy for the numerical solution of functional differential equations in preliminary experimentation significant improvements have been obtained when compared with the numerical results obtained elsewhere

tau method treatment of a delayed negative feedback equation the step by step tau method is applied to find polynomial approximations to the solution of the nonlinear functional equation email protected t email protected t 1 1 x t t 0 which arises in population dynamics the behavior of the approximate solutions is consistent with the theoretical results obtained elsewhere

the fuzzy quadratic assignment problem with penalty new models and genetic algorithm the assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers and each worker receives exactly just one job such that the total cost is optimal the quadratic assignment problem with penalty takes three types of costs into consideration direct cost interactive cost an penalty in this paper the fuzzy quadratic assignment problem with penalty is formulated as expected value model chance constrained programming and dependent chance programming according to various decision criteria and the crisp equivalents are given furthermore hybrid genetic algorithm is designed for solving the proposed fuzzy programming models

entropy maximization model for the trip distribution problem with fuzzy and random parameters many trip distribution problems can be modeled as entropy maximization models with quadratic cost constraints in this paper the travel costs per unit flow between different zones are assumed to be given fuzzy variables and the trip productions at origins and trip attractions at destinations are assumed to be given random variables for this case an entropy maximization model with chance constraint is proposed and is proved to be convex in order to solve this model fuzzy simulation stochastic simulation and a genetic algorithm are integrated to produce a hybrid intelligent algorithm finally a numerical example is presented to demonstrate the application of the model and the algorithm

fuzzy chance constrained portfolio selection abstract this paper selects the portfolio with fuzzy returns by criteria of chance represented by credibility measure in the paper two types of credibility based portfolio selection model are provided according to two types of chance criteria by one chance criterion the objective is to maximize the investor s return at a given threshold confidence level by another chance criterion the objective is to maximize the credibility of achieving a specified return level subject to the constraints to provide a general method to solve the new models a hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed in the paper two numerical examples with security returns taking different types of membership function are also given to illustrate the modelling idea of the paper and to demonstrate the effectiveness of the proposed algorithm

fuzzy importance sampling method for estimating failure possibility abstract to improve the computational efficiency of the fuzzy simulation in estimating failure possibility of the structure containing fuzzy uncertainty a fuzzy importance sampling method is proposed in this paper in the proposed method the optimal importance sampling density for estimating failure possibility is deduced as the product of the indicator function related to failure domain and the joint membership function of fuzzy model inputs at first subsequently the markov chain simulation and an adaptive kernel sampling method are employed to generate a group of samples asymptotically following the optimal importance sampling density based on this group of samples an approximate expression of the optimal importance sampling density expression is constructed finally the failure possibility can be efficiently estimated by using a small number of samples generated by the approximate optimal importance sampling density results of three examples demonstrate that the proposed method is a more efficient and robust method for estimating the failure possibility estimation compared with the original fuzzy simulation method

graph fibrations and symmetries of network dynamics abstract dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking a methodology for classifying patterns of synchrony in networks was developed by golubitsky and stewart they showed that the robustly synchronous dynamics of a network is determined by its quotient networks this result was recently reformulated by deville and lerman who pointed out that the reduction from a network to a quotient is an example of a graph fibration the current paper exploits this observation and demonstrates the importance of self fibrations of network graphs self fibrations give rise to symmetries in the dynamics of a network we show that every network admits a lift with a semigroup or semigroupoid of self fibrations the resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking also when the network has a trivial symmetry groupoid then every robust synchrony in the lift is determined by symmetry we finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks

patterns in square arrays of coupled cells in recent years it has been observed that reaction diffusion equations with neumann boundary conditions as well as other classes of pdes possess more symmetry than that which may be expected and these hidden symmetries affect the generic types of bifurcation which occur w x w x w x see golubitsky et al 6 field et al 5 armbruster and dangelmayr 1 w x w x crawford et al 2 gomes and stewart 8 9 and others in addition equilibria with more highly developed patterns may exist for these equaw x tions than might otherwise be expected epstein and golubitsky 4 show that these symmetries also affect the discretizations of reaction diffusion equations on an interval in particular equilibria of such systems may have well defined patterns which may be considered as a discrete analog of turing patterns w x in this paper we use an idea similar to the one in 4 to show that the same phenomena occurs in discretizations of reaction diffusion equations on a square satisfying neumann boundary conditions such discretizations lead to n n square arrays of identically coupled cells by embedding the original n n array into a new 2n 2n array we can embed the neumann boundary condition discretization in a periodic boundary condition discretization and increase the symmetry group of the equations from

bifurcations of limit cycles in complex networks of hamiltonian systems and lloyd s conjecture abstract this paper is motivated by hilbert s sixteenth problem concerning the number and distribution of limit cycles in planar polynomial vector fields we propose an original method inspired by the complex systems framework in order to construct a family of hamiltonian systems admitting non degenerate centers located on the vertices of a planar network we introduce two novel polynomial perturbations adapted to those systems with the aim to produce a high number of limit cycles the first one is oriented along the gradient of the unperturbed system and the second one is again constructed with a complex systems approach using the melnikov integral we reach in a small number of particular cases the lower bound of cubical order for the hilbert number h n conjectured by lloyd in 1988

minimax chance constrained programming models for fuzzy decision systems abstract the existing chance constrained programming for fuzzy decision systems is essentially a kind of maximax models optimistic models which maximize the maximum possible return this paper presents a spectrum of minimax models as opposed to maximax models based on chance constrained programming as well as chance constrained multi objective programming and chance constrained goal programming in which the minimax models will select the alternative that provides the best of the worst possible return finally a fuzzy simulation based genetic algorithm will be designed for solving minimax models and illustrated by some numerical examples

error analysis of the tau method dependence of the error on the degree and on the length of the interval of approximation abstract in this paper we discuss the dependence of tau method approximations on i the degree of approximant n and ii the length of the interval of approximation h we shall show that the tau method parameters i i decay exponentially in terms of n and ii for a fixed n they decay in terms of h as h 2 n

multi item eoq model with hybrid cost parameters under fuzzy fuzzy stochastic resource constraints a geometric programming approach in this paper a multi item economic order quantity eoq model is considered in which the cost parameters are of fuzzy hybrid nature under two types of resources a resources as fuzzy quantities b resources as fuzzy and fuzzy random quantities the unit cost depends on demand rate the time horizon is taken to be infinite we find the average cost for the model which is a function of order quantity and demand rate and also of some hybrid parameters when the resources are fuzzy quantities the problem is transformed into its equivalent unconstrained deterministic form by using a surprise function for the constraints the problem involving hybrid number is again equivalently rewritten as a multi objective minimization of the mean of the objective function and variance function of the distribution inventory problem introducing new variables we transform the terms of the functions into signomial types using fuzzy multi objective solution procedure we solve the problem through geometric programming approach sensitivity analysis has been performed to study the effect of different weights considered for mean objective function and variance function

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

fuzzy multi product constraint newsboy problem in this paper we consider the multi product newsboy problem with fuzzy demands under budget constraint since the demands of products are often fuzzy in real life the profit of the newsboy is fuzzy too we develop three types of models under different criteria evm model dcp model and ccp model in these models the objective functions are to maximize the expected profit of newsboy the chance of achieving a target profit and the profit which satisfies some chance constraints with at least some given confidence level respectively furthermore the hybrid intelligent algorithm based on genetic algorithm and fuzzy simulation is designed for these models and some illustrating examples are given in order to show the application of these proposed models and algorithm

a novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty abstract in today s business environments the high importance of economic benefits and environmental impacts of using scrapped products has caused most companies to move to designing the closed loop supply chain network this paper considers the closed loop supply chain network design problem under hybrid uncertainty while there are two sources of uncertainty for most parameters thus require fortifying of the robustness of the decision the first source is that some uncertain parameters may be based on the future scenarios which are considered according to the probability of their occurrence the second source is that the values of these parameters in each scenario are usually imprecise and can be specified by possibilistic distributions in this case the best robust decision has some additional properties in terms of mean value and variability of the objective function we introduced two types of the variability named scenario variability and possibilistic variability possibility theory is used to choose a solution in such a problem and a novel robust fuzzy stochastic programming approach is proposed that has significant advantages the performance of the proposed model is also compared with that of other models in term of the mean cost and variability by simulation

segmented tau approximation for a parametric nonlinear neutral differential equation abstract the segmented formulation of the tau method is used to approximate the solutions of the parametric nonlinear neutral differential equation y t ry t a by t cy t t 0 y t t t 0 which represents for different values of the parameters r a b c and a family of functional differential equations with some of its members arising in areas as different as the number theory mathematical biology and population dynamics for this equation no closed form of analytical solution is available the numerical results obtained are consistent with the theoretical and practical results reported elsewhere

symmetries stability and control in nonlinear systems and networks this paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks specifically it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems this synergy between structural properties symmetries and convergence properties contraction is illustrated in the contexts of network motifs arising for example in genetic networks from invariance to environmental symmetries and from imposing different patterns of synchrony in a network

dependent chance programming with fuzzy decisions dependent chance programming dcp is a new type of stochastic programming and has been extended to the area of fuzzy programming this paper provides a spectrum of dcp and dependent chance multiobjective programming dcmop as well as dependent chance goal programming dcgp models with fuzzy rather than crisp decisions the terms of uncertain environment event chance function and induced constraints are discussed in the case of fuzzy decisions a technique of fuzzy simulation is also designed for computing chance functions finally we present a fuzzy simulation based genetic algorithm for solving these models and illustrate its effectiveness by some numerical examples

a new approach to fuzzy programming abstract a fuzzy program is defined in the usual way as a sequence of statements instruction which are considered as functions possibly fuzzy functions and fuzzy predicates defined on the given input domain the essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs and a new method of evaluating fuzzy predicates the result of the fuzzy program execution is an appropriate fuzzy subset in the output domain

a novel multi stage possibilistic stochastic programming approach with an application in relief distribution planning proposing a novel multi stage possibilistic stochastic programming approach considering fuzzy probabilities in the scenario tree s arcs accounting for deep uncertainty of sdps at the early stages of the scenario tree through random fuzzy variables providing a real post disaster relief distribution planning case study in this paper a novel multi stage possibilistic stochastic programming mspsp approach is developed at the early stages there is little information on how to pursue mspsp the optimal decision while in the course of time new series of information become unfolded which further necessitate the model to be updated compared to other competent uncertainty programming approaches i e the classical two stage stochastic programming tssp and multi stage stochastic programming mssp and enhanced versions of tssp and mssp approaches the proposed mspsp method relaxes the subjectively setting the deterministic occurrence probabilities and allows possible perturbation in their values as fuzzy probabilities it further enables these values to be updated so that the updated values do not conflict with each other and their summation does not exceed one also given the existence of several sources of uncertainty and the deep level of uncertainty in the early stages the scenario dependent variables at such stages are treated as random fuzzy variables finally it takes into account the effect of unfolded information in an on going fashion in the course of time applicability of the proposed approach is tested on a real case study for the post disaster relief distribution planning in tehran finally useful managerial insights are provided through conducting several sensitivity analyses

uncertain programming a unifying optimization theory in various uncertain environments by uncertain programming we mean the optimization theory in generally uncertain random fuzzy fuzzy random grey etc environments three broad classes of uncertain programming are expected value models and chance constrained programming as well as dependent chance programming in order to solve general uncertain programming models a simulation based genetic algorithm is also documented finally some applications and further research problems appearing in this area are posed

nonlinear dynamics of networks the groupoid formalism a formal theory of symmetries of networks of coupled dynamical systems stated in terms of the group of permutations of the nodes that preserve the network topology has existed for some time global network symmetries impose strong constraints on the corresponding dynamical systems which affect equilibria periodic states heteroclinic cycles and even chaotic states in particular the symmetries of the network can lead to synchrony phase relations resonances and synchronous or cycling chaos symmetry is a rather restrictive assumption and a general theory of networks should be more flexible a recent generalization of the group theoretic notion of symmetry replaces global symmetries by bijections between certain subsets of the directed edges of the network the input sets now the symmetry group becomes a groupoid which is an algebraic structure that resembles a group except that the product of two elements may not be defined the groupoid formalism makes it possible to extend group theoretic methods to more general networks and in particular it leads to a complete classification of robust patterns of synchrony in terms of the combinatorial structure of the network many phenomena that would be nongeneric in an arbitrary dynamical system can become generic when constrained by a particular network topology a network of dynamical systems is not just a dynamical system with a high dimensional phase space it is also equipped with a canonical set of observables the states of the individual nodes of the network moreover the form of the underlying ode is constrained by the network topology which variables occur in which component equations and how those equations relate to each other the result is a rich and new range of phenomena only a few of which are yet properly understood

bifurcations from regular quotient networks a first insight abstract we consider regular identical edge identical node networks whose cells can be grouped into classes by an equivalence relation the identification of cells in the same class determines a new network the quotient network in terms of the dynamics this corresponds to restricting the coupled cell systems associated with a network to flow invariant subspaces given by equality of certain cell coordinates assuming a bifurcation occurs for a coupled cell system restricted to the quotient network we ask how that bifurcation lifts to the overall space surprisingly for certain networks new branches of solutions occur besides the ones that occur in the quotient network to investigate this phenomenon we develop a systematic method that enumerates all networks with a given quotient we also prove necessary conditions for the existence of solution branches not predicted by the quotient we then apply our method to two particular quotient networks namely two and three cell bidirectional rings we show there are no additional bifurcating solution branches when the quotient network is a two cell bidirectional ring however two of the 12 five cell networks that have the three cell bidirectional ring as a quotient network exhibit bifurcating solutions that do not occur in the quotient itself thus network architecture sometimes forces the existence of bifurcating branches in addition to the ones determined by the quotient

some remarks on structural relations between the tau method and the finite element method abstract we discuss structural relations between the tau method and the finite element method discrete step h for a dirichlet problem in dimensions one and two we show that the difference between the solution given by each of these methods is bounded by c h in the norm of the sobolev space h 1 0

segmented tau approximation for a forward backward functional differential equation a new approach to numerically solve the forward backward functional differential equation 1 x t ax t bx t 1 cx t 1 is presented where a b and c are constant parameters the step by step version of the tau method is applied to approximate the solution of eq 1 by a piecewise polynomial function a boundary value problem is posed solved with the proposed method and analyzed the numerical results obtained are consistent with those produced by other methods found in the literature

facility location allocation problem in random fuzzy environment using α β cost minimization model under the hurewicz criterion facility location allocation fla which has been proved to be a valuable method in siting service facility is widely used in real life such as emergency service systems telecommunication net works public services etc many researchers have studied the fla problem in a deterministic stochastic or fuzzy environment however those models cannot satisfy various customers demands in some cases thus this paper considers the fla problem under random fuzzy environment using a b cost minimization model under the hurwicz criterion it will be proved that this model can deal with various fla problems in random fuzzy and random fuzzy environments by varying the value l it can balance the optimistic level of the decision makers for solving the random fuzzy model efficiently the simplex algorithm random fuzzy simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm finally a numerical example is presented for illustration

fixed charge transportation problem with type 2 fuzzy variables this paper considers two fixed charge transportation problems with type 2 fuzzy parameters unit transportation costs fixed costs in the first problem and unit transportation costs fixed costs supplies and demands in the second problem are type 2 fuzzy variables for the first problem to get corresponding defuzzified values of the type 2 fuzzy cost parameters first critical value cv based reduction methods are applied to reduce type 2 fuzzy variables into type 1 fuzzy variables and then centroid method is used for complete defuzzification besides this we also apply geometric defuzzification method to the type 2 fuzzy cost parameters in the first problem to provide a comparison of the results coming to the second problem a chance constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the cv based reductions of corresponding type 2 fuzzy parameters next the reduced model is turned into equivalent parametric programming problem the deterministic problems so obtained are then solved by using the standard optimization solver lingo we have provided numerical examples illustrating the proposed models and techniques some sensitivity analyzes for the second model are also presented

the numerical solution of forward backward differential equations decomposition and related issues this paper focuses on the decomposition by numerical methods of solutions to mixed type functional differential equations mfdes into sums of forward solutions and backward solutions we consider equations of the form x t ax t bx t 1 cx t 1 and develop a numerical approach using a central difference approximation which leads to the desired decomposition and propagation of the solution we include illustrative examples to demonstrate the success of our method along with an indication of its current limitations

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

fuzzy quadratic minimum spanning tree problem in this paper a fuzzy quadratic minimum spanning tree problem is formulated as expected value model chance constrained programming and dependent chance programming according to different decision criteria then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers furthermore a simulation based genetic algorithm using prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents finally a numerical example is provided for illustrating the effectiveness of the genetic algorithm

patterns of chaos synchronization small networks of chaotic units which are coupled by their time delayed variables are investigated in spite of the time delay the units can synchronize isochronally i e without time shift moreover networks cannot only synchronize completely but can also split into different synchronized sublattices these synchronization patterns are stable attractors of the network dynamics different networks with their associated behaviors and synchronization patterns are presented in particular we investigate sublattice synchronization symmetry breaking spreading chaotic motifs synchronization by restoring symmetry and cooperative pairwise synchronization of a bipartite tree

impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations abstract the global dynamics of coupled systems of differential equations defined on an interaction network are investigated local dynamics at each vertex when interactions are absent are assumed to be simple solutions to each vertex system are assumed to converge to an equilibrium either on the boundary or in the interior of the feasible region the interest is to investigate the collective behaviours of the coupled system when interactions among vertex systems are present it was shown in li and shuai 2010 that if the interaction network is strongly connected then solutions to the coupled system synchronize at a single equilibrium we focus on the case when the underlying network is not strongly connected and the coupled system may have mixed equilibria whose coordinates are in the interior at some vertices while on the boundary at others we show that solutions on a strongly connected component of the network will synchronize considering a condensed digraph by collapsing each strongly connected component we are able to introduce a partial order on the set p of all equilibria and show that all solutions of the coupled system converge to a unique equilibrium p that is the maximizer in p we further establish that behaviours of the coupled system at minimal elements of the condensed digraph determine whether the global limit p is a mixed equilibrium the theory are applied to mathematical models from epidemiology and spatial ecology

mixed type functional differential equations a numerical approach the equations considered in this paper are mixed type functional equations sometimes known as forward backward differential equations that take the form u t au t bu t 1 cu t 1 t i r we consider basic existence and uniqueness properties when i t 1 t 2 and we seek solutions u c t 1 1 t 2 1 that satisfy u t w 1 t t t 1 1 t 1 u t w 2 t t t 2 t 2 1 for prescribed functions w 1 w 2 absolutely continuous respectively on t 1 1 t 1 t 2 t 2 1 with arbitrary boundary conditions specified in this way the problem turns out to be ill posed and so existence and uniqueness questions have an important role to play in developing numerical schemes we consider with t 1 t 2 n numerical approximations of a solution when it exists the numerical methods that we consider are linear q methods and we investigate computationally their effectiveness through some illustrative examples

mean variance skewness model for portfolio selection with fuzzy returns numerous empirical studies show that portfolio returns are generally asymmetric and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same in order to measure the asymmetry of fuzzy portfolio return a concept of skewness is defined as the third central moment in this paper and its mathematical properties are studied as an extension of the fuzzy mean variance model a mean variance skewness model is presented and the corresponding variations are also considered in order to solve the proposed models a genetic algorithm integrating fuzzy simulation is designed finally several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

symmetry types and phase shift synchrony in networks abstract in this paper we discuss what is known about the classification of symmetry groups and patterns of phase shift synchrony for periodic solutions of coupled cell networks specifically we compare the lists of spatial and spatiotemporal symmetries of periodic solutions of admissible vector fields to those of equivariant vector fields in the three cases of r n coupled equations t n coupled oscillators and r k n where k 2 coupled systems to do this we use the h k theorem of buono and golubitsky 2001 applied to coupled equations and coupled systems and prove the h k theorem in the case of coupled oscillators josic and torok 2006 prove that the h k lists for equivariant vector fields and admissible vector fields are the same for transitive coupled systems we show that the corresponding theorem is false for coupled equations we also prove that the pairs of subgroups h k for coupled equations are contained in the pairs for coupled oscillators which are contained in the pairs for coupled systems finally we prove that patterns of rigid phase shift synchrony for coupled equations are contained in those of coupled oscillators and those of coupled systems

partial synchronization in linearly and symmetrically coupled ordinary differential systems in this paper we discuss partial synchronization of linearly and symmetrically coupled ordinary differential equations lscodes the synchronization phenomena are investigated via invariant synchronization manifolds on the basis of geometrical analysis of the synchronization manifold several criteria for the global attractivity of the invariant synchronization manifold are obtained combining these criteria with some numerical examples we investigate how topological structure affects partial synchronization and give a valuable discussion about the possibility of partial synchronization with increasing coupling strength

an interactive fuzzy satisficing method for multiobjective stochastic linear programming problems through an expectation model abstract for decision making problems involving uncertainty both stochastic programming as an optimization method based on the theory of probability and fuzzy programming representing the ambiguity by fuzzy concept have been developing in various ways in this paper we focus on multiobjective linear programming problems with random variable coefficients in objective functions and or constraints for such problems as a fusion of these two approaches after incorporating fuzzy goals of the decision maker for the objective functions we propose an interactive fuzzy satisficing method for the expectation model to derive a satisficing solution for the decision maker an illustrative numerical example is provided to demonstrate the feasibility of the proposed method

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production optimizing the charge in secondary steel production is challenging because the chemical composition of the scrap is highly uncertain the uncertainty can cause a considerable risk of the scrap mix failing to satisfy the composition requirements for the final product in this paper we represent the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure consequently the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem since the constraints of the model mainly address the specification of the product the crisp equivalent of the fuzzy constraints should be less relaxed than that purely based on the concept of soft constraints based on the application context we adopt a strengthened version of soft constraints to interpret fuzzy constraints and form a crisp model with consistent and compact constraints for solution simulation results based on realistic data show that the failure risk can be managed by proper combination of aspiration levels and confidence factors for defining fuzzy numbers there is a tradeoff between failure risk and material cost the presented approach applies also for other scrap based production processes

numerical solution of stiff and singularly perturbed boundary value problems with a segmented adaptive formulation of the tau method this paper concerns the application of ortiz recursive formulation of the tau method to the construction of piecewise polynomial approximations to the solution of linear and nonlinear boundary value problems for ordinary differential equations a practical error estimation technique related to the concept of correction in zadunaisky s sense is considered and used in the design of an adaptive approach to the tau method it proves efficient in the numerical treatment of problems with rapid functional variations stiff and singularly per turbed problems a technique of increased accuracy at matching points of segmented tau approximants is also discussed and successfully applied to several problems numerical examples show that for a given degree of approximation our segmented tau approximant gives an accuracy comparable to that of the best segmented approximation of the exact solution by means of algebraic polynomials 1 introduction we discuss the use of ortiz recursive formulation of the tau method 23 25 in the numerical solution of boundary value problems for linear and nonlinear differential equations defined over an interval a x b we con sider global approximations over a b with a single polynomial expression and segmented forms based on a step by step formulation of the tau method considered by ortiz in 26 the tau approximate solution of a differential problem defined by a differential operator d is represented in terms of the elements of a sequence q of canonical polynomials such a sequence is uniquely determined by d it is independent of the specific boundary conditions of the problem and of the particular interval a b in which the solution is required these properties make possible the use of segmenta tion within the framework and with the software 32 designed for the recursive formulation of the tau method the concept of correction in zadunaisky s sense 37 see also stetter 36 is discussed in the context of the tau method and related to a practical error estimation technique this technique based on tau estimators introduced here is systematically applied to all examples linear or nonlinear it is

enumerating periodic patterns of synchrony via finite bidirectional networks periodic patterns of synchrony are lattice networks whose cells are coloured according to a local rule or balanced colouring and such that the overall system has spatial periodicity these patter