approximation schemes for infinite linear programs this paper presents approximation schemes for an infinite linear program in particular it is shown that under suitable assumptions the program s optimum value can be approximated by the values of finite dimensional linear programs and that in addition every accumulation point of a sequence of optimal solutions for the approximating programs is an optimal solution for the original problem

multifactorial functions in fuzzy sets theory abstract the multifactorial function is a very important new concept which can be used to many aspects in fuzzy sets theory it appeared firstly in 5 where it was used to define fuzzy perturbation function and where the stability for the solutions of fuzzy relation equations by using fuzzy perturbation was studied in 6 by means of multifactorial functions multifactorial fuzzy sets and the multifactorial degree of nearness which are two new concepts too were given and they were used to multifactorial pattern recognition and clustering analysis with fuzzy characteristics in fact generally speaking most of the mathematical models dependent on several factors should use multifactorial functions especially fuzzy decision making fuzzy games fuzzy programming and fuzzy linear programming with several objective functions should here we study properties of multifactorial functions how to generate a new multifactorial function and we introduce in detail its applications in fuzzy pattern recognition fuzzy decision making fuzzy clustering fuzzy games and fuzzy programming etc

a class of hamiltonian systems with increasing periods on considere un systeme hamiltonien de la forme x g y y f x ou h f et h g satisfont certaines hypotheses on montre qu il y a un intervalle maximal 0 a a 0 tel que chaque solution x t y t avec x 0 a 0 a y 0 0 est periodique avec son orbite enfermant 0 0 soit p a la plus petite periode de cette solution alors p 0 a r est differentiable avec p a 0

fuzzy perturbation analysis part 2 undirectional perturbation abstract in this paper the stability of the solutions of fuzzy relation equations is discussed by the method of undirectional fuzzy perturbation first a general definition of fuzzy perturbation is given from this the concept of fuzzy perturbation equation is introduced and thus stability of the solutions is defined next the degree of stability of the solutions a kind of metric of the stability is advanced three ordered quotient sets are induced by use of the degree of stability these quotient sets have a well chained characteristic

a dual to lyapunov s stability theorem lyapunov s second theorem is a standard tool for stability analysis of ordinary differential equations here we introduce a theorem which can be viewed as a dual to lyapunov s result from existence of a scalar function satisfying certain inequalities it follows that almost all trajectories of the system tend to zero the scalar function has a physical interpretation as the stationary density of a substance that is generated in all points of the state space and flows along the system trajectories if the stationary density is bounded everywhere except at a singularity in the origin then almost all trajectories tend towards the origin the weaker notion of stability allows for applications also in situations where lyapunov s theorem cannot be used moreover the new criterion has a striking convexity property related to control synthesis

almost global stochastic stability we develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point with respect to the lebesgue measure is asymptotically attracted to the origin with unit probability the method can be viewed as a dual to lyapunov s second method for stochastic differential equations and extends the deterministic result of a rantzer syst control lett 42 2001 pp 161 168 the result can also be used in certain cases to find stabilizing controllers for stochastic nonlinear systems using convex optimization the main technical tool is the theory of stochastic flows of diffeomorphisms

a new kind of fuzzy relation equations based on inner transformation this paper mainly deals with a new kind of fuzzy relation equations based on inner transformation first the inner projection of a fuzzy relation and the inner transformation by a fuzzy relation are introduced and also what is a fuzzy relation equation based on inner transformation is described second the discriminative matrix and the discriminative vector are defined on the basis of them an approach of discriminating whether such a fuzzy relation equation has nonzero solution is obtained at last a procedure of solving such fuzzy relation equations is presented the solution set of a fuzzy relation equation based on inner transformation is not closed with respect to join and meet operations in general this shows that the traditional methods being used for solving email protected composite fuzzy relation equations cannot be applied into the study of this kind of fuzzy relation equations based on inner transformation

on pseudo transitive approximations of fuzzy relations abstract in the present paper we consider a generalization of the well known notion of transitive fuzzy relations this may be useful for preference relations or similarity relations describing butterfly like configurations where the widely used transitive closure is rather different from the original relation moreover the proposed concept enables us to determine relations which are transitive only for a part of the elements under consideration some examples demonstrate the usefulness of our approach

dulac time of a resonant saddle in the loud family abstract we study the critical periods of the loud family of quadratic centers we give the first terms of the asymptotic expansion of the period function and we conclude that no bifurcation occurs for certain values of the parameters this result contributes to complete the bifurcation diagram of critical periods in the loud family

optimal motion planning using navigation measure abstractwe introduce navigation measure as a new tool to solve the motion planning problem in the presence of static obstacles existence of navigation measure guarantees collision free convergence at the final destination set beginning with almost every initial condition with respect to the lebesgue measure navigation measure can be viewed as a dual to the navigation function while the navigation function has its minimum at the final destination set and peaks at the obstacle set navigation measure takes the maximum value at the destination set and is zero at the obstacle set a linear programming formalism is proposed for the construction of navigation measure set oriented numerical methods are utilised to obtain finite dimensional approximation of this navigation measure application of the proposed navigation measure based theoretical and computational framework is demonstrated for a motion planning problem in a complex fluid flow

asymptotic expansion of the period function abstract let p be a not necessarily bounded polycycle of an analytic vector field on an open set of the plane suppose that the singularities which appear after desingularization of the vertices of p are formally linearizable consider the function t defined by the return time near p it is shown that the function t and its derivative t have asymptotic expansions in x r and x log x r it is also shown that under some other conditions imposed on the polycycle vertices the asymptotic expansions of t and t converge absolutely and uniformly to these functions respectively these results are applied to the polycycles of the analytic vector fields which have a darboux first integral in particular it is obtained that if p is a polycycle of a hamiltonian vector field with an analytic polynomial if p is unbounded hamiltonian function t is a nonoscillating function another application concerns the nilpotent centers or focus since the singularities which appear after desingularization of such a singularity have analytic first integrals

factor space theory in fuzzy information processing composition of states of factors and multifactorial decision making abstract the concept of factor space used in fuzzy information processing is investigated the composition of the states of factors which is a basic tool in multifactorial decision making is first considered then a general model of multifactorial decision making is formulated finally multi factorial decision making with multiple objectives is introduced numerical examples are given to illustrate the approaches

optimal stabilization using lyapunov measures numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this technical note set theoretic notion of almost everywhere stability introduced by the lyapunov measure weaker than conventional lyapunov function based stabilization methods is used for optimal stabilization the linear perron frobenius transfer operator is used to pose the optimal stabilization problem as an infinite dimensional linear program set oriented numerical methods are used to obtain the finite dimensional approximation of the linear program we provide conditions for the existence of stabilizing feedback controls and show the optimal stabilizing feedback control can be obtained as a solution of a finite dimensional linear program the approach is demonstrated on stabilization of period two orbit in a controlled standard map

fuzzy clustering method based on perturbation abstract based on the results obtained in the earlier paper 1 the fuzzy clustering method based on perturbation fcmbp is further studied and several important results are obtained first since the fuzzy similarity matrix equation x2 x is one of the most important basic components of the fcmbp approach the structure of the solutions of this matrix equation is investigated to express the solutions the concept of fuzzy equivalent standard form is proposed second the existence of the globally and locally optimal fuzzy equivalent matrices which are nearest to the given fuzzy similarity matrix is proved third an effective fuzzy clustering method based on the above results is proposed finally two examples which show that the result obtained by the fcmbp method is more accurate than that obtained by the transitive closure method are solved

linear programming approach to deterministic long run average problems of optimal control we establish that deterministic long run average problems of optimal control are asymptotically equivalent to infinite dimensional linear programming problems lpps and we establish that these lpps can be approximated by finite dimensional lpps the solutions of which can be used for construction of the optimal controls general results are illustrated with numerical examples

on the return time function around monodromic polycycles abstract in this paper we study the period function of centers of planar polynomial differential systems with a convenient compactification of the phase portrait the boundary of the period annulus of the center has two connected components the center itself and a polycycle we are interested in the behaviour of the period function near the polycycle the desingularization of its critical points gives rise to a new polycycle monodromic as well with hyperbolic saddles or saddle nodes at the vertices in this paper we compute the first terms in the asymptotic development of the time function around any orbitally linearizable saddle that may come from this desingularization process in addition we use these developments to study the bifurcation diagram of the period function of the dehomogenized loud s centers more generally the tools developed here can be used to study the return time function around a monodromic polycycle this work is a continuation of the results in p mardesic d marin j villadelprat on the time function of the dulac map for families of meromorphic vector fields nonlinearity 16 2003 855 881 p mardesic d marin j villadelprat the period function of reversible quadratic centers j differential equations 224 2006 120 171

stability in the almost everywhere sense a linear transfer operator approach abstract the problem of almost everywhere stability of a nonlinear autonomous ordinary differential equation is studied using a linear transfer operator framework the infinitesimal generator of a linear transfer operator perron frobenius is used to provide stability conditions of an autonomous ordinary differential equation it is shown that almost everywhere uniform stability of a nonlinear differential equation is equivalent to the existence of a non negative solution for a steady state advection type linear partial differential equation we refer to this non negative solution verifying almost everywhere global stability as lyapunov density a numerical method using finite element techniques is used for the computation of lyapunov density

the structural clustering and analysis of metric based on granular space in this paper the research on granular space theory and structural clusters of metric based on granular space is introduced and a comprehensive of theoretical and analyzing methodologies is developed the granular space theory is established based on normalized equicrural metric and the consistent cluster characteristics of ordered granular spaces are derived details are shared for some related subject such as the granular representation of structural cluster from normalized metric the optimal cluster determination the fusion of structural cluster and the structural clustering analysis of metric space based on granular space etc theories and methodologies are established for structural clustering based on metric space and developed a series of mathematical models and formal description tools for the research on its potential applications direct and geometric interpretations for structural clustering analysis are provided to assist deeper understanding the essence of clustering or classifying procedure

convex dynamic programming for hybrid systems a classical linear programming approach to optimization of flow or transportation in a discrete graph is extended to hybrid systems the problem is finite dimensional if the state space is discrete and finite but becomes infinite dimensional for a continuous or hybrid state space it is shown how strict lower bounds on the optimal loss function can be computed by gridding the continuous state space and restricting the linear program to a finite dimensional subspace upper bounds can be obtained by evaluation of the corresponding control laws

error estimation and adaptive discretization for the discrete stochastic hamilton jacobi bellman equation generalizing an idea from deterministic optimal control we construct a posteriori error estimates for the spatial discretization error of the stochastic dynamic programming method based on a discrete hamilton jacobi bellman equation these error estimates are shown to be efficient and reliable furthermore a priori bounds on the estimates depending on the regularity of the approximate solution are derived based on these error estimates we propose an adaptive space discretization scheme whose performance is illustrated by two numerical examples

darboux linearization and isochronous centers with a rational first integral abstract in this paper we study isochronous centers of polynomial systems it is known that a center is isochronous if and only if it is linearizable we introduce the notion of darboux linearizability of a center and give an effective criterion for verifying darboux linearizability if a center is darboux linearizable the method produces a linearizing change of coordinates most of the known polynomial isochronous centers are darboux linearizable moreover using this criterion we find a new two parameter family of cubic isochronous centers and give the linearizing changes of coordinates for centers belonging to that family we also determine all hamiltonian cubic systems which are darboux linearizable in the second part of this work we restrict to the study of isochronous centers having a rational first integral we prove that under certain conditions the cycle vanishing at the isochronous center is either zero homologous in the closure of a generic fiber or the function obtained from the first integral by eliminating the indeterminacy points has several critical points in the singular fiber passing through the isochronous center

the period function of the generalized lotka volterra centers abstract the present paper deals with the period function of the quadratic centers in the literature different terminologies are used to classify these centers but essentially there are four families hamiltonian reversible q 3 r codimension four q 4 and generalized lotka volterra systems q 3 lv chicone c chicone review in mathscinet ref 94h 58072 conjectured that the reversible centers have at most two critical periods and that the centers of the three other families have a monotonic period function with regard to the second part of this conjecture only the monotonicity of the hamiltonian and q 4 families w a coppel l gavrilov the period function of a hamiltonian quadratic system differential integral equations 6 1993 1357 1365 y zhao the monotonicity of period function for codimension four quadratic system q 4 j differential equations 185 2002 370 387 has been proved concerning the q 3 lv family no substantial progress has been made since the middle 80s when several authors showed independently the monotonicity of the classical lotka volterra centers f rothe the periods of the volterra lokta system j reine angew math 355 1985 129 138 r schaaf global behaviour of solution branches for some neumann problems depending on one or several parameters j reine angew math 346 1984 1 31 j waldvogel the period in the lotka volterra system is monotonic j math anal appl 114 1986 178 184 by means of the first period constant one can easily conclude that the period function of the centers in the q 3 lv family is monotone increasing near the inner boundary of its period annulus i e the center itself thus according to chicone s conjecture it should be also monotone increasing near the outer boundary which in the poincare disc is a polycycle in this paper we show that this is true in addition we prove that except for a zero measure subset of the parameter plane there is no bifurcation of critical periods from the outer boundary finally we show that the period function is globally i e in the whole period annulus monotone increasing in two other cases different from the classical one

a relaxation approach to the fuzzy clustering problem abstract in this paper a new algorithm for fuzzy clustering is presented the proposed algorithm utilizes the idea of relaxation convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived stopping criteria and resulting convergence behaviour of the algorithms are discussed the performance of the new algorithm is compared to the fuzzy c means algorithm by testing both on three published data sets theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings

computing a t transitive lower approximation or opening of a proximity relation since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation assuming that such a violation is mainly due to decision maker estimation errors in some way the more number of elicitations the more probable inconsistency is this is mostly the case within a fuzzy framework even when the number of alternatives or object to be classified is relatively small in this paper we propose a fast method to compute a t indistinguishability from a reflexive and symmetric fuzzy relation being t any left continuous t norm the computed approximation we propose will take o n 3 time complexity where n is the number of elements under consideration and is expected to produce a t transitive opening to the authors knowledge there are no other proposed algorithm that computes t transitive lower approximations or openings while preserving the reflexivity and symmetry properties

bifurcation of critical periods for plane vector fields on etudie un probleme de bifurcation dans des familles de champs de vecteurs analytiques plans qui ont un centre non degenere a l origine pour toutes les valeurs d un parametre r n on definit la fonction periode p on determine les points critiques de cette fonction pres du centre avec comme parametre de bifurcation

a set oriented approach to optimal feedback stabilization we present a numerical construction of an optimal control based feedback law for the stabilization of discrete time nonlinear control systems the feedback is based on a recently developed numerical solution method for optimal control problems using set oriented and graph theoretic algorithms we show how this method can be used to construct approximately optimal and stabilizing feedback laws and present an a posteriori error estimation technique for the adaptive generation of the underlying set oriented space discretization

on transitive solutions of fuzzy equations inequalities and lower approximations of fuzzy relations abstract in the present paper we determine the greatest resp maximal transitive solution of a fuzzy equation resp inequality such problem arises among others when we approximate arbitrary fuzzy relations by transitive ones from below a sketch of extension of these results to interval valued fuzzy sets is given as well

finiteness for critical periods of planar analytic vector fields limburgs univ centrum dept math b 3610 diepenbeek belgium chicone c univ missouri dept math columbia mo 65211

multifactorial fuzzy sets and multifactorial degree of nearness abstract two new concepts multifactorial fuzzy sets and multifactorial degree of nearness are advanced first an axiomatic definition for multifactorial functions is given and multifactorial fuzzy sets and multifactorial degree of nearness are defined by using the multifactorial function second three direct methods of multifactorial pattern recognition and two methods for fuzzy clustering with fuzzy characteristics are given last we advance an interesting open problem

controller design and value function approximation for nonlinear dynamical systems this work considers the infinite time discounted optimal control problem for continuous time input affine polynomial dynamical systems subject to polynomial state and box input constraints we propose a sequence of sum of squares sos approximations of this problem obtained by first lifting the original problem into the space of measures with continuous densities and then restricting these densities to polynomials these approximations are tightenings rather than relaxations of the original problem and provide a sequence of rational controllers with value functions associated to these controllers converging under some technical assumptions to the value function of the original problem in addition we describe a method to obtain polynomial approximations from above and from below to the value function of the extracted rational controllers and a method to obtain approximations from below to the optimal value function of the original problem thereby obtaining a sequence of asymptotically optimal rational controllers with explicit estimates of suboptimality numerical examples demonstrate the approach

algebraic particular integrals integrability and the problem of the center in this work we clarify the global geometrical phenomena corresponding to the notion of center for plane quadratic vector fields we first show the key role played by the algebraic particular integrals of degrees less than or equal to three in the theory of the center these curves control the changes in the systems as parameters vary the bifurcation diagram used to prove this result is realized in the natural topological space for the situation considered namely the real four dimensional projective space next we consider the known four algebraic conditions for the center for quadratic vector fields one of them says that the system is hamiltonian a condition which has a clear geometric meaning we determine the geometric meaning of the remaining other three algebraic conditions i ii iii

lyapunov measure for almost everywhere stability this paper is concerned with the analysis and computational methods for verifying global stability of an attractor set of a nonlinear dynamical system based upon a stochastic representation of deterministic dynamics a lyapunov measure is proposed for these purposes this measure is shown to be a stochastic counterpart of stability transience just as an invariant measure is a counterpart of the attractor recurrence it is a dual of the lyapunov function and is useful for the study of more general weaker and set wise notions of stability in addition to the theoretical framework constructive methods for computing approximations to the lyapunov measures are presented these methods are based upon set oriented numerical approaches several equivalent descriptions including a series formula and a system of linear inequalities are provided for computational purposes these descriptions allow one to carry over the intuition from the linear case with stable equilibrium to nonlinear systems with globally stable attractor sets finally in certain cases the exact relationship between lyapunov functions and lyapunov measures is also given

fuzzy clustering in cell formation with multiple attributes an approach based on fuzzy clustering and aggregation operators is proposed to design cell formation involving multiple criteria or multiple attributes the three most basic attributes in cell formation namely number of machines required processing time and common tools required on machines are considered the results are compared with the single attribute results of chu and hayya 1991 27

fuzzy clustering methods based on perturbation the fuzzy clustering method as it is known to us transforms a fuzzy similarity matrix r into a fuzzy equivalent matrix r t r which is the transmission closure of r in this paper we put forward a new fuzzy clustering method using the idea to find a fuzzy equivalent matrix r which is closest to r by a certain distance in general the distance between r and r is much less than the distance between r and r which means that the lack of fidelity that is brought about by clustering according to r is much less than the lack of fidelity by r

convex duality and nonlinear optimal control problems in nonlinear optimal control can be reformulated as convex optimization problems over a vector space of linear functionals in this way methods of convex analysis can be brought to bear on the task of characterizing solutions to such problems the result is a necessary and sufficient condition of optimality that generalizes well known sufficient conditions referred to as verification theorems in dynamic programming as a byproduct we obtain a representation of the minimum cost in terms of the upper envelope of subsolutions to the hamilton jacobi equation it is a striking illustration of the wide range of problems to which convex analysis and in particular convex duality is applicable the approach applied to parametric problems in the calculus of variations was pioneered by l c young lectures on the calculus of variations and optimal control theory w b saunders philadelphia pa 1969 as recent work has shown however it is equally fruitful when applied in optimal control thi

approximation of infinite dimensional linear programming problems which arise in stochastic control we study a general approximation scheme for infinite dimensional linear programming lp problems which arise naturally in stochastic control we prove that the optimal value of the approximating problems converges to the value of the original lp problem for the controls we show that if the approximating optimal controls converge the limiting control is an optimal control for the original lp problem as an application of this theory we present numerical approximations to the lp formulation of stochastic control problems in continuous time we study long term average and discounted control problems for the example for which the theoretical solution is known our approximation results are very accurate

modified fuzzy c means algorithm for cellular manufacturing several studies have used the fuzzy c means fcm algorithm for part machine grouping in cellular manufacturing however the application of the standard fcm algorithm to this problem has a number of drawbacks this paper proposes a modified fcm mfcm algorithm that groups components and machines in parallel and through an annealing process with the weighting exponent arrives at a crisp solution and an objective function value which can be interpreted in terms of the number of voids and intercellular movements of the part machine grouping obtained computational experiences show that although mfcm may sometimes require slightly more computing time than other methods not only is it able to find better solutions but also it has higher discriminating power for determining the number of cells

controllability for a class of area preserving twist maps abstract in this paper we study controllability of two dimensional integrable twist maps with bounded area preserving time dependent control perturbations in contrast to the time independent perturbation case of the kolmogorov arnold moser theorem there are no invariant sets other than the whole phase space if the perturbation is made a function of time we give necessary and sufficient conditions for global controllability of these maps

an improved fcmbp fuzzy clustering method based on evolutionary programming in current pc computing environment the fuzzy clustering method based on perturbation fcmbp is failed when dealing with similar matrices whose orders are higher than tens the reason is that the traversal process adopted in fcmbp is exponential complexity this paper treated the process of finding fuzzy equivalent matrices with smallest error from an optimization point of view and proposed an improved fcmbp fuzzy clustering method based on evolutionary programming the method seeks the optimal fuzzy equivalent matrix which is nearest to the given fuzzy similar matrix by evolving a population of candidate solutions over a number of generations a new population is formed from an existing population through the use of a mutation operator better solutions survive into next generation and finally the globally optimal fuzzy equivalent matrix could be obtained or approximately obtained compared with fcmbp the improved method has the following advantages 1 traversal searching is avoided by introducing an evolutionary programming based optimization technique 2 for low order matrices the method has much better efficiency in finding the globally optimal fuzzy equivalent matrix 3 matrices with hundreds of orders could be managed the method could quickly get a more accurate solution than that obtained by the transitive closure method and higher precision requirement could be achieved by further iterations and the method is adaptable for matrices of higher order 4 the method is robust and not sensitive to parameters

averaging method for discontinuous mayer s problem of singularly perturbed control systems abstract in the present paper we prove that the optimal cost of a mayer s problem for a control system with singular perturbation does converge to the optimal cost of a mayer s problem associated with control system obtained by averaging the main novelty of our result lies on the fact that we did not require any continuity assumption on the final cost

l 1 norm based fuzzy clustering abstract the paper presents the l1 version of the well known fuzzy clustering method namely fuzzy isodata proposed by bezdek and dunn due to their robustness l1 norm based methods gained much attention in statistics the presented fuzzy clustering problem uses the distance between observations and location parameter vectors which is based on the l1 norm instead of the inner product induced norm used in classical fuzzy isodata two alternative methods to solve the l1 fuzzy clustering problem are derived in practice both membership grades and location parameter vectors are unknown the paper presents two iterative algorithms each the implementation of the derived method finally numerical examples are presented one of them refers to famous iris data

convex programs for temporal verification of nonlinear dynamical systems a methodology for safety verification of continuous and hybrid systems using barrier certificates has been proposed recently conditions that must be satisfied by a barrier certificate can be formulated as a convex program and the feasibility of the program implies system safety in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region the dual of this problem i e the reachability problem concerns proving the existence of a trajectory starting from the initial set that reaches another given set using insights from the linear programming duality appearing in the discrete shortest path problem we show in this paper that reachability of continuous systems can also be verified through convex programming several convex programs for verifying safety and reachability as well as other temporal properties such as eventuality avoidance and their combinations are formulated some examples are provided to illustrate the application of the proposed methods finally we exploit the convexity of our methods to derive a converse theorem for safety verification using barrier certificates