inverse possibility analysis method for possibility based design optimization doi 10 2514 1 16546 structural analysis and design optimization have recently been extended to the stochastic approach to consider variousuncertainties however inareaswhereitisnotpossibletoproduceaccurate statistical information forinput data the probabilistic method is not appropriate for stochastic structural analysis and design optimization because improper modeling of uncertainty could cause a greater degree of statistical uncertainty than those of physical uncertainty for systems with insufficient information for input data possibility based or fuzzy set methods have recently been introduced in structural analysis and design optimization using possibility methods the extended fuzzy operations are much simpler than of random variables possibility based design optimization will provide more conservative designs than those from probability methods andwill provide a system level of failure possibility automatically this paper proposes a new formulation of possibility based design optimization using the performance measure approach for the inverse possibility analysis the maximal possibility search method is proposed to improve numerical efficiency and accuracy comparing with the vertex method and the multilevel cut method two mathematical examples including a nonmonotonic response and a physical example of vehicle side impact are used to demonstrate the proposed maximal possibility search method and possibility based design optimization

complex dynamics in a singular leslie gower predator prey bioeconomic model with time delay and stochastic fluctuations in this paper a class of singular leslie gower predator prey bioeconomic models with environment fluctuations and time delays is investigated local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting by choosing the delay as a bifurcation parameter it is shown that the hopf bifurcations can occur as the delay crosses some critical values then the effect of a fluctuating environment on the singular stochastic delayed predator prey bioeconomic model is discussed finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment

stability analysis in a delayed prey predator resource model with harvest effort and stage structure abstract in this paper a prey predator resource model with harvest effort on resource biomass is proposed where maturation delay and stage structure for prey population are considered positivity and boundedness of solutions are studied by performing local stability around all equilibria dynamic effects of maturation delay and harvest effort on model system are discussed and region of local stability around interior equilibrium is found by analyzing the associated characteristic transcendental equation furthermore global stability of the interior equilibrium is investigated due to variation of maturation delay and harvest effort numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper

mixed finite element approximations based on 3d hp adaptive curved meshes with two types of h div conforming spaces summary two stable approximation space configurations are treated for the mixed finite element method for elliptic problems based on curved meshes their choices are guided by the property that in the master element the image of the flux space by the divergence operator coincides with the potential space by using static condensation the sizes of global condensed matrices which are proportional to the dimension of border fluxes are the same in both configurations the meshes are composed of different topologies tetrahedra hexahedra or prisms simulations using asymptotically affine uniform meshes exactly fitting a spherical like region and constant polynomial degree distribution k show l2 errors of order k 1 or k 2 for the potential variable while keeping order k 1 for the flux in both configurations the first case corresponds to rt k and bdfm k 1 spaces for hexahedral and tetrahedral meshes respectively but holding for prismatic elements as well the second case further incrementing the order of approximation of the potential variable holds for the three element topologies the case of hp adaptive meshes is considered for a problem modelling a porous media flow around a cylindrical horizontal well with elliptical drainage area the effect of parallelism and static condensation in cpu time reduction is illustrated this article is protected by copyright all rights reserved

inferring a possibility distribution from empirical data several transformations from probabilities to possibilities have been proposed in particular dubois and prade s procedure produces the most specific possibility distribution among the ones dominating a given probability distribution in this paper this method is generalized to the case where the probabilities are unknown the only information being a data sample represented by a histogram it is proposed to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level email protected from this imprecise specification a procedure for constructing a possibility distribution is described insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100 email protected of the cases finally a simple efficient algorithm is given which makes the computations tractable even if the number of classes is high

an interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators part i case of type 1 fuzzy sets abstract the grade of membership is assumed to be determined as the relative size of evidence grounds supporting a given element s membership compared to all the necessary reference grounds relevant to the judgement of membership grade and is interpreted as conditional probability conditioned by the given element by assigning the dependence relations of the evidence grounds to those of the fuzzy subsets the set operators are defined as probabilistic operators with dependence relations the properties of the operators are studied and it is found that with type 1 fuzzy subsets they satisfy all the basic properties satisfied by the crisp set operators illustrative examples are given describing the construction of membership functions and the selection of set operators in relation to the situations to be modelled the proposed operators a kind of parametrized operators with an index value of the dependence relations as a parameter cover the entire operators ranging from the so called max min operators to the bold union intersection operators an extension of the above operator range is also discussed

fuzzy sets modeling and optimization for disaster control systems planning abstract various forms of disasters natural and man made abound although to some extent some of these have been exacerbated by modern civilization various technologies have been invoked to control or mitigate their adverse effects modeling and optimization based techniques have also been employed we outline some efforts based on fuzzy sets theory which are utilized in conjunction with classical methods to enhance the reliability and utility of these efforts in particular disasters caused by floods and storm water pollution are used as vehicles for the exemplification of our models

stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and levy jumps abstract in this paper a hybrid stochastic prey predator system with double time delays and commercial exploitation is established where combined dynamic effects of telephone noise and levy jumps on stochastic population dynamics are taken into accounts existence and uniqueness of globally positive solution to the proposed system are investigated by constructing appropriate stochastic lyapunov functions existence of an ergodic and unique stationary distribution of the positive solution is discussed sufficient conditions for permanence in mean and extinction of corresponding population are derived furthermore sufficient and necessary criteria for optimal exploitation strategy are studied numerical simulations are carried out to show consistency with theoretical analysis

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

dynamic analysis of a hybrid bioeconomic plankton system with double time delays and stochastic fluctuations abstract in this paper we establish a double delayed hybrid bioeconomic plankton system with stochastic fluctuations and commercial harvesting on zooplankton where maturation delay for toxin producing phytoplankton and gestation delay for zooplankton are considered stochastic fluctuations are incorporated into the proposed system in form of gaussian white noises to depict stochastic environmental factors in plankton system for deterministic system without double time delays existence of singularity induced bifurcation is studied due to variation of economic interest of commercial harvesting and state feedback controllers are designed to eliminate singularity induced bifurcation for deterministic system with double time delays positivity and uniform persistence of solutions are studied and some sufficient conditions associated with asymptotic stability of interior equilibrium are investigated for stochastic system without double time delays stochastic stability and existence of stochastic hopf bifurcation are discussed based on singular boundary theory of diffusion process and invariant measure theory for stochastic system with double time delays existence and uniqueness of global positive solution are investigated and asymptotic behaviors of the interior equilibrium are studied by constructing appropriate lyapunov functions numerical simulations are carried out to validate theoretical analysis

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained

designing fuzzy sets with the use of the parametric principle of justifiable granularity this study is concerned with a design of membership functions of fuzzy sets the membership functions are formed in such a way that they are experimentally justifiable and exhibit a sound semantics these two requirements are articulated through the principle of justifiable granularity the parametric version of the principle is discussed in detail we show linkages with type 2 fuzzy sets which are constructed on a basis of type 1 fuzzy sets several experimental studies are reported which illustrate a behavior of the introduced method

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

modeling and analysis in a prey predator system with commercial harvesting and double time delays both maturation delay for prey and gestation delay for predator are considered positivity of solutions and uniform persistence of system are investigated combined dynamic effects of double time delays and economic interest are studied existence and control for singularity induced bifurcation are investigated local stability analysis and properties of hopf bifurcation are studied a differential algebraic prey predator system with commercial harvesting on predator is proposed where maturation delay for prey and gestation delay for predator are considered since commercial harvesting is dynamically influenced by variation of economic interest we will investigate combined dynamic effects of double time delays and economic interest on population dynamics positivity of solutions and uniform persistence of system are studied in the absence of time delay by taking economic interest as bifurcation parameter existence of singularity induced bifurcation is investigated based on differential algebraic system theory state feedback controllers are designed to eliminate singularity induced bifurcation and stabilize the proposed system around corresponding interior equilibrium in the presence of double time delays by analyzing associated characteristic transcendental equation it is found that interior equilibrium loses local stability when double time delays cross corresponding critical values according to hopf bifurcation theorem for functional differential equation existence of hopf bifurcation is investigated as local stability switches based on normal form theory and center manifold theorem directions of hopf bifurcation and stability of the bifurcating periodic solutions are studied numerical simulations are carried out to show consistency with theoretical analysis

analysis of stochastic two prey one predator model with levy jumps abstract taking white noises and levy noises into account a two prey one predator model in random environments is proposed and investigated under some simple assumptions the critical value between persistence in the mean and extinction for each population is obtained then sufficient conditions for stability in distribution of the model are established finally some numerical examples are introduced to validate the analytical findings

fuzzy rule based models for infiltration modeling water movement in the unsaturated zone requires a great number of parameters such as the initial water content the saturated moisture content and the saturated hydraulic conductivity which can relatively easily be assessed other functions such as the suction head and the relative hydraulic conductivity which are highly nonlinear functions of the actual water content are more difficult to find furthermore infiltration experiments carried out at a few locations can only define these parameters at selected locations and a reasonable interpolation of these parameters is extremely difficult in this paper two fuzzy logic based models are presented for the infiltration process basic definitions of fuzzy sets are given and basic operations are explained principles of the rule based infiltration models are presented the rules for the first model are based on the moisture content of the adjacent layers and the depth of the wetting front using these rules the flows can be calculated as exact quantities the rules are derived from a training set which was obtained from several test runs of a green and ampt ga infiltration model separate rules are derived for the flow dynamics in the upper layer runoff and infiltration and for water flow between the layers examples of the application of the model are given the model performs with similar accuracy as the ga model using only 40 of its parameters and running 2 orders of magnitude faster a training set obtained by numerical solution of the richards equation was used to create a second fuzzy rule based model here the rules are based on the moisture content of the adjacent layers results obtained by the use of the models are compared with measured values showing a very accurate reproduction of the values

fuzzy sets and membership functions abstract in this paper we try to provide an analytical basis for the theory of fuzzy sets the main idea is to introduce the the notions of consensus sets and subjective variables which strongly resemble respectively the events and random variables in the probability theory the resemblance is a natural consequence from the fact that one of the most important roles of the fuzzy set theory is to present a method for the analysis of the uncertainty originated in human subjectivity while the probability theory for that of randomness

non uniform order mixed fem approximation implementation post processing computable error bound and adaptivity the present work provides a straightforward and focused set of tools and corresponding theoretical support for the implementation of an adaptive high order finite element code with guaranteed error control for the approximation of elliptic problems in mixed form the work contains details of the discretisation using non uniform order mixed finite elements of arbitrarily high order a new local post processing scheme for the primary variable the use of the post processing scheme in the derivation of new fully computable bounds for the error in the flux variable and an hp adaptive refinement strategy based on the a posteriori error estimator numerical examples are presented illustrating the results obtained when the procedure is applied to a challenging problem involving a ten pole electric motor with singularities arising from both geometric features and discontinuities in material properties the procedure is shown to be capable of producing high accuracy numerical approximations with relatively modest numbers of unknowns

approximate solutions of fuzzy relational equations and a characterization of t norms that define metrics for fuzzy sets abstract if one considers the membership degrees of fuzzy sets as truth values of a many valued logic there is a canonical way to define a fuzzified equality for fuzzy sets this generalized equality relation can be used to define a degree to which some value of the unknown variable is a solution of the fuzzy equation as well as a degree of solvability of the whole equation furthermore there is an intimate relationship between such a degree to which some fuzzy set is a solution and the quality to which it is an approximate solution the background is that the negation of the fuzzified equality measures a kind of distinctness of fuzzy sets formally the definition of this fuzzified equality contains as parameter some t norm which acts as truth functions of a conjunction connective for some such t norms this negation of the fuzzified equality really has the properties of a metric in the mathematical sense of the word the paper gives a necessary and sufficient condition which characterizes all those t norms which in that way yield a metric for fuzzy sets

fuzzy finite element method for frequency response function analysis of uncertain structures a concept is presented for incorporating fuzzy uncertainties in dynamic e nite element analyses of uncertain structures the objective is twofold the e rst goal is to clarify and extend the classical fuzzy e nite element ffe method as it was introduced for static analyses the shortcomings of the classical approach are described and an extension to a generalized approach is proposed this generalized approach is proven to be a more realistic and therefore more reliable concept for taking uncertainty into account the second goal is to illustrate the applicability of the method for dynamic analyses the classical and the generalized approach are compared using an eigenvalue analysis of a simple numerical example the ffe method is also applied to the calculation of the total envelope frequency response function frf using the modal superposition principle this method requires safe approximations of the individual mode envelope frequency response functions for this purpose a number of safe approximate optimization strategies are introduced the numerical example shows that useful results are obtained using this ffe approach for frf calculations

bayesian estimation in forest surveys when samples or prior information are fuzzy abstract fuzzy phenomena are frequently encountered in forestry due to the complexity of the systems under investigation in this paper existing inference methods are presented to accommodate situations in which random events take place in fuzzy circumstances fuzzy concepts are incorporated into these commonly accepted approaches to account for uncertainties used by factors other than randomness which traditional statistical approaches deal primarily with based on two extensions of likelihood functions for fuzzy samples bayesian estimates are generalized for use when sample information and prior distribution of parameters are fuzzy the estimators are developed for some typical membership functions for fuzzy samples and fuzzy priors applications are illustrated using examples for forestry

quadrilateral h div finite elements we consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the piola transform extending results previously obtained for scalar approximation the finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element which is then transformed to a space of vector fields on each convex quadrilateral element via the piola transform associated to a bilinear isomorphism of the square onto the element for affine isomorphisms a necessary and sufficient condition for approximation of order r 1 in l2 is that each component of the given space of functions on the reference element contain all polynomial functions of total degree at most r in the case of bilinear isomorphisms the situation is more complicated and we give a precise characterization of what is needed for optimal order l2 approximation of the function and of its divergence as applications we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for some standard finite element approximations of h div we also derive new estimates for approximation by quadrilateral raviart thomas elements requiring less regularity and propose a new quadrilateral finite element space which provides optimal order approximation in h div finally we demonstrate the theory with numerical computations of mixed and least squares finite element approximations of the solution of poisson s equation

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

hierarchical high order finite element bases for h div spaces based on curved meshes for two dimensional regions or manifolds the mixed finite element formulation for elliptic problems is characterized by simultaneous calculations of the potential primal variable and of the flux field dual variable this work focuses on new h div conforming finite element spaces which are suitable for flux approximations based on curved meshes of a planar region or a manifold domain embedded in r 3 the adopted methodology for the construction of h div bases consists in using hierarchical h 1 conforming scalar bases multiplied by vector fields that are properly constructed on the master element and mapped to the geometrical elements by the piola transformation followed by a normalization procedure they are classified as being of edge or internal type the normal component of an edge function coincides on the corresponding edge with the associated scalar shape function and vanishes over the other edges and the normal components of an internal shape function vanishes on all element edges these properties are fundamental for the global assembly of h div conforming functions locally defined by these vectorial shape functions for applications to the mixed formulation the configuration of the approximation spaces is such that the divergence of the dual space and the primal approximation space coincides results of verification numerical tests are presented for curved triangular and quadrilateral partitions on circular cylindrical and spherical regions demonstrating stable convergence with optimal convergence rates coinciding for primal and dual variables innovative two dimensional hdiv approximation spaces for curved quadrilateral and triangular elements hdiv bases properly constructed on the master element and mapped to the geometrical elements by the piola transformation followed by a normalization procedure stable convergence with optimal convergence rates coinciding for primal and dual variables study of number of condensed equations as a function of the polynomial order of the shape functions

fuzzy dynamic programming fuzzy adaptive neuro control and the general medical diagnosis problem abstract the fuzzy medical diagnosis decision models of esogbue and elder employed fuzzy sets theory to directly and more correctly model all the information nets useful in reaching a scientific understanding of a patient s health status this knowledge was utilized in constructing a sensible medical hypothesis decision problem in this paper we show how fuzzy dynamic programming and neural networks can be used to extend the process to other phases by linking the four stages of medical hypothesis physician s observation preliminary diagnosis and final diagnosis in an adroit manner

effects of membership function parameters on the performance of a fuzzy signal detector this paper describes a signal detection algorithm based on fuzzy logic the detector combines evidence provided by two waveform features and explicitly considers uncertainty in the detection decision the detector classifies waveforms including a signal not including a signal or being uncertain in which case no conclusion regarding presence or absence of a signal is drawn piecewise linear membership functions are used and a method to describe the membership functions in terms of two parameters is developed the performance of the detector is compared to a bayesian maximum likelihood detector using brainstem auditory evoked potential signals in simulated noise and the effects of the steepness slope and overlap of the membership functions on detector performance are evaluated by varying the membership function steepness and overlap the fuzzy detector can almost completely eliminate classification errors at the cost of a large number of uncertain classifications or it can be made to perform similarly to the bayesian detector

a fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution in a regression analysis it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model y f x email protected however a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters when faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions this regression model has been termed the switching regression model and it is expressed with y l f l x email protected l email protected i 1 pl i here l i indicates the class number of each independent variable and p is indicative of the number of independent variables j r jang anfis adaptive network based fuzzy inference system ieee transaction on systems man and cybernetics 23 3 1993 665 685 m michel fuzzy clustering and switching regression models using ambiguity and distance rejects fuzzy sets and systems 122 2001 363 399 e q richard a new approach to estimating switching regressions journal of the american statistical association 67 338 1972 306 310 in this study adaptive networks have been used to construct a model that has been formed by gathering obtained models there are methods that suggest the class numbers of independent variables heuristically alternatively in defining the optimal class number of independent variables the use of suggested validity criterion for fuzzy clustering has been aimed in the case that independent variables have an exponential distribution an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function which is suitable for exponential distribution

the approximation of piecewise linear membership functions and łukasiewicz operators in this paper we propose an approximation of piecewise linear membership functions with the help of sigmoid functions and certain arithmetic operations the gradient based tuning of piecewise linear membership functions can be achieved with the proposed efficient approximation because it has simple continuous derivatives with this construction we can even approximate the lukasiewicz operator family which plays an important role in fuzzy logic first of all from the theoretical point of view although in practice in optimization and learning it is rarely used because the lack of good analytical properties e g a continuous gradient the proposed approximation enlarges the applicability of fuzzy methods to the operators and membership functions where the differentiability is desirable

after the fuzzy wave reached europe abstract we briefly describe the situation of the fuzzy community in europe before the fuzzy wave we show that there was a lot of expertise in almost all subareas of fuzzy logic then we describe some aspects of the fuzzy wave itself in particular fuzzy control and first generation fuzzy systems that played a role during the time the fuzzy wave reached europe we also make some remarks about european companies and their activities during this time then we discuss the situation after the fuzzy wave some aspects of second generation fuzzy systems the combination of fuzzy logic with other theories and techniques and some new application areas finally we will discuss the chances of fuzzy systems in europe in the future

fuzzy sets probability and measurement abstract in recent years the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory various formal settings including but not restricted to fuzzy sets and possibility measures have been proposed based on different intuitions and dealing with various kinds of uncertain data the two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures and distorted probabilities for the descriptive assessment of partial belief possibility measures and thereby fuzzy sets stand at the crossroads of these new approaches traditional views interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches betting theories comparative uncertainty relations are currently extended to the generalized uncertainty measures these works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory conversely zadeh s logical point of view on fuzzy sets suggests a set theoretic perspective on uncertainty measures that brings together numerical quantification and logic

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

global dynamics and bifurcation in a stage structured prey predator fishery model with harvesting abstract this paper describes a prey predator model with stage structure for predator and selective harvesting effort on predator population the holling type ii functional response function is taken into consideration all the equilibria of the proposed system are determined and the behavior of the system is investigated near them local stability of the system is analyzed geometric approach is used to derive the sufficient conditions for global stability of the system the occurrence of hopf bifurcation of the model system in the neighborhood of the co existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource sustainability properties of the stock and the resource rent earned from the resource pontryagin s maximum principle is used to characterize the optimal control the optimal system is derived and then solved numerically using an iterative method with runge kutta fourth order scheme simulation results show that the optimal control scheme can achieve sustainable ecosystem

fuzzy boundary element method for the analysis of imprecisely defined systems many engineering systems contain uncertainties that cannot be described by either deterministic or probabilistic approaches the uncertainties present may be associated with parameters that are vague imprecise or linguistic for example the geometry material properties external actions loads and boundary conditions may be imprecise in a practical system a fuzzy boundary element method for the analysis of imprecisely defined systems is developed starting from the basic concepts of fuzzy sets and fuzzy arithmetic the various steps of the boundary element method are redefined using fuzzy concepts the resulting fuzzy equations are solved using a fuzzified version of gaussian elimination procedure coupled with truncation the truncation method limits the growth of interval ranges of response parameters to obtain realistic and accurate solutions the procedure is illustrated by considering the analysis of a potential flow problem the methodology is applicable to uncertain systems that are described in linguistic terms as well as those that are described by incomplete information the approach represents a unique methodology that enables the analysis and design of many engineering systems more realistically

digital signal restoration using fuzzy sets a new signal restoration method with considerable flexibility in incorporating a priori information is developed the method defines a fuzzy set for each piece of information to restrict the set of acceptable solutions using fuzzy sets makes it possible to model partially defined information as well as exact knowledge the intersection of all the fuzzy sets is the feasibility set the original signal is a member of this set with a high membership value and any high membership valued element of this set is a nonrejectable solution such solutions can be computed by using optimization techniques ideally the feasibility set contains only the original signal the chance of recovering the original signal decreases as the feasibility set gets larger thus the size of the feasibility set gives a quality measure for the solution the method generated successful results in many restorations for which the conventional techniques have failed and may be applied in image coding and tomography

period doubling cascades in a predator prey model with a scavenger the dynamics of the classic planar two species lotka volterra predator prey model are well understood we introduce a scavenger species that scavenges the predator and is also a predator of the common prey for this model we analytically prove that all trajectories are bounded in forward time and numerically demonstrate persistent bounded paired cascades of period doubling orbits over a wide range of parameter values standard analytical and numerical techniques are used in the analysis of this model making it an ideal pedagogical tool we include exercises and an open ended project to promote mastery of these techniques

three dimensional hierarchical mixed finite element approximations with enhanced primal variable accuracy abstract there are different possibilities of choosing balanced pairs of approximation spaces for dual flux and primal pressure variables to be used in discrete versions of the mixed finite element method for elliptic problems arising in fluid simulations three cases shall be studied and compared for discretized three dimensional formulations based on tetrahedral hexahedral and prismatic meshes the principle guiding the constructions is the property that the divergence of the dual space and the primal approximation space should coincide while keeping the same order of accuracy for the flux variable and varying the accuracy order of the primal variable there is the classic case of b d m k spaces based on tetrahedral meshes and polynomials of total degree k for the dual variable and k 1 for the primal variable showing stable simulations with optimal convergence rates of orders k 1 and k respectively another case is related to r t k and b d f m k 1 spaces for hexahedral and tetrahedral meshes respectively but holding for prismatic elements as well it gives identical approximation order k 1 for both primal and dual variables an improvement in accuracy obtained by increasing the degree of primal functions to k and by enriching the dual space with some properly chosen internal shape functions of degree k 1 while keeping degree k for the border fluxes a new type of approximation is proposed by further incrementing the order of some internal flux functions to k 2 and matching primal functions to k 1 higher than the border fluxes of degree k thus higher convergence rate of order k 2 is obtained for the primal variable using static condensation the global condensed system to be solved in all the cases has same dimension and structure which is proportional to the space dimension of the border fluxes for each element geometry illustrating results comparing the three different space configurations are presented for simulations based on hierarchical high order shape functions for h div conforming spaces which are specially constructed for affine tetrahedral hexahedral and prismatic meshes expected convergence rates are obtained for the flux pressure and divergence variables

contribution to application of energy measure of fuzzy sets abstract the works of de luca termini continued by for example knopfmacher loo and gottwald are the most important on the topic of determination of measures of fuzzy sets the matter is to evaluate how fuzzy a fuzzy set is there are two general concepts of measures of fuzzy set i e entropy and energy measures we show that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations applications of the use of energy measure discussed in detail include decision making fuzzy process control and prediction in fuzzy systems

a survey of non probabilistic uncertainty treatment in finite element analysis the objective of this paper is to critically review the emerging non probabilistic approaches for uncertainty treatment in finite element analysis the paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis first the applicability of the non probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint the necessary conditions for a useful application of the non probabilistic concepts are determined and are proven to be complementary rather than competitive to the classical probabilistic approach the second part of the paper focuses on numerical aspects of the interval finite element method it describes two principal strategies for the implementation i e the anti optimisation and the interval arithmetic approach and gives a state of the art of the interval finite element algorithms available from literature it is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output and the main sources of this conservatism are identified a numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built up benchmark structure

finite element differential forms on curvilinear cubic meshes and their approximation properties we study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n n dimensions specifically we consider meshes in which each element is the image of a cubical reference element under a diffeomorphism and finite element spaces in which the shape functions and degrees of freedom are obtained from the reference element by pullback of differential forms in the case where the diffeomorphisms from the reference element are all affine i e mesh consists of parallelotopes it is standard that the rate of convergence in l 2 l 2 exceeds by one the degree of the largest full polynomial space contained in the reference space of shape functions when the diffeomorphism is multilinear the rate of convergence for the same space of reference shape function may degrade severely the more so when the form degree is larger the main result of the paper gives a sufficient condition on the reference shape functions to obtain a given rate of convergence

a bioeconomic modeling of two prey and one predator fishery model with optimal harvesting policy through hybridization approach abstract this paper introduces an imprecise prey predator model by using interval and fuzzy number in modeling of prey and predator interaction in a prey predator system values of the biological parameter are based on the collection of data by the experts from nature therefore we consider them as interval numbers the proposed prey predator model is consisting of two species which are not only affected by the harvesting of the species but also by the present of predator species all possible existence of the biological and bionomic equilibrium points of the model are discussed under impreciseness we derive the conditions for local and global stability the optimal harvesting policy is studied by considering instantaneous annual rate of discount under fuzziness by logically hybridizing the interval and fuzzy number methodologies we find the optimal equilibrium points and harvesting efforts in the form of interval finally numerical examples are illustrated to support the proposed approach

hopf bifurcation and spatial patterns of a delayed biological economic system with diffusion in this paper a delayed biological economic system which considers a plankton system with harvest effort on phytoplankton is proposed by using the theory of partial functional differential equations hopf bifurcation of the proposed system with delay as the bifurcation parameter is investigated it reveals that the discrete time delay has a destabilizing effect in the plankton dynamics and a phenomenon of hopf bifurcation occurs as the delay increases through a certain threshold then by numerical simulations the impact of delay diffusion and economic interest on plankton system are explored it is found that delay can cause system into chaos and can trigger the emergence of irregular spatial patterns via a hopf bifurcation moreover diffusion and economic profit can also affect the dynamic behavior of the system

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

optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps abstract this paper systematically investigates the optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps under some simple assumptions the sufficient conditions for extinction and stable in the time average of each species are established the stability in distribution of this model is proved under our assumptions finally the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained and some numerical simulations are introduced to demonstrate the theoretical results

naive possibilistic classifiers for imprecise or uncertain numerical data in real world problems input data may be pervaded with uncertainty in this paper we investigate the behavior of naive possibilistic classifiers as a counterpart to naive bayesian ones for dealing with classification tasks in the presence of uncertainty for this purpose we extend possibilistic classifiers which have been recently adapted to numerical data in order to cope with uncertainty in data representation here the possibility distributions that are used are supposed to encode the family of gaussian probabilistic distributions that are compatible with the considered dataset we consider two types of uncertainty i the uncertainty associated with the class in the training set which is modeled by a possibility distribution over class labels and ii the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data moreover the approach takes into account the uncertainty about the estimation of the gaussian distribution parameters due to the limited amount of data available we first adapt the possibilistic classification model previously proposed for the certain case in order to accommodate the uncertainty about class labels then we propose an algorithm based on the extension principle to deal with imprecise attribute values the experiments reported show the interest of possibilistic classifiers for handling uncertainty in data in particular the probability to possibility transform based classifier shows a robust behavior when dealing with imperfect data

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

stationary distribution and ergodicity of a stochastic food chain model with levy jumps abstract in this paper a three species stochastic food chain model with levy jumps is proposed and analyzed sharp sufficient criteria for the existence and uniqueness of an ergodic stationary distribution are established the effects of levy jumps on the existence of the stationary distribution are revealed in some cases the levy jumps could make the stationary distribution appear while in some cases the levy jumps could make the stationary distribution disappear some numerical simulations are introduced to illustrate the theoretical results

sparsity optimized high order finite element functions for h div on simplices this paper deals with conforming high order finite element discretizations of the vector valued function space h div in 2 and 3 dimensions a new set of hierarchic basis functions on simplices with the following two main properties is introduced when working with an affine simplicial triangulation first the divergence of the basis functions is l 2 orthogonal and secondly the l 2 inner product of the interior basis functions is sparse with respect to the polynomial degree p the construction relies on a tensor product based construction with properly weighted jacobi polynomials as well as an explicit splitting of the higher order basis functions into solenoidal and non solenoidal ones the basis is suited for fast assembling strategies the general proof of the sparsity result is done by the assistance of computer algebra software tools several numerical experiments document the proved sparsity patterns and practically achieved condition numbers for the parameter dependent div div problem even on curved elements a tremendous improvement in condition numbers is observed the precomputed mass and stiffness matrix entries in general form are available online

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

a new procedure for the construction of hierarchical high order hdiv and hcurl finite element spaces this paper considers a systematic procedure for the construction of a hierarchy of high order finite element approximation for hdiv and hcurl spaces based on triangular and quadrilateral partitions of bidimensional domains the principle is to choose an appropriate set of vectors based on the geometry of each element which are multiplied by an available set of h 1 hierarchical scalar basic functions this strategy produces vector basis functions with continuous normal or tangent components on the elements interfaces properties that characterise functions in hdiv or hcurl respectively we also present a numerical study to evaluate the correct balancedness of the resulting hdiv spaces of degree k and l 2 spaces of degree k 1 on the resolution of the mixed formulation for a steklov eigenvalue problem

fuzzy control with fuzzy inputs this paper is concerned with the use of fuzzy inputs in fuzzy logic controllers a precise representation of fuzzy logic controllers by means of mappings is used to introduce different ways for dealing with fuzzy inputs two types of fuzzy inputs are presented and their potential use in fuzzy control is discussed the proposed concepts are applied to control a first order process with a pi controller this simple process is chosen to clearly illustrate the behavior of the closed loop system using fuzzy inputs for fuzzy reference and fuzzy measurement finally a nonlinear process is used to illustrate the effects of fuzzy inputs on a more complex system although it is sometimes speculated that fuzzy inputs may improve the behavior of fuzzy controllers experiments developed in this paper show this point is not straightforward and that the relevance of fuzzy inputs should be questioned in closed loop fuzzy control

systematic and generic construction of shape functions for p adaptive meshes of multidimensional finite elements this paper presents a methodology for generating high order shape functions for the complete family of finite elements the geometric entities presented are the point line triangle quadrilateral tetrahedron pyramid prism and hexahedron the shape functions constructed are hierarchical and generate continuous approximation spaces the order of interpolation of the shape function can be determined independently for each edge face and volume the space of interpolation of order p for each element is complete this definition allows for the construction of hybrid meshes with any combination of these elements including elements of distinct dimension and or interpolation order the reader will observe that our systematic way of constructing shape functions can be extended to elements of higher dimension

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

specificity shift in solving fuzzy relational equations abstract studied is a system of n fuzzy relational equations with a max t composition x k r y k where the input output fuzzy sets x k and y k are available while the fuzzy relation r needs to be determined the solution to these equations is derived through a new paradigm of specificity shift the main objective is to modify a level of specificity of the fuzzy sets relational constraint so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable in more detail the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets the optimization of the specificity levels is discussed in detail numerical studies are also included finally the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient based techniques

dynamical analysis of a differential algebraic bio economic model with stage structured and stochastic fluctuations abstract this study considers a class of differential algebraic stage structured bio economic models with stochastic fluctuations the stochastic bio economic model is simplified to an ito equation using the stochastic averaging method the stochastic stability hopf bifurcation and p bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems numerical simulations are presented to illustrate our main results

dynamic behaviour of a delayed predator prey model with harvesting abstract in this paper we analyze the dynamics of a delayed predator prey system in the presence of harvesting this is a modified version of the leslie gower and holling type ii scheme the main result is given in terms of local stability global stability influence of harvesting and bifurcation direction of hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

fuzzy control from the logical point of view abstract this paper is a discussion of the logical aspect in fuzzy control which is an application of the theory of approximate reasoning first we analyze approximate reasoning and show that it is a concise logical theory based on many valued logic integrated with some parts of linguistics then we demonstrate that fuzzy control based on equality relations can transparently be formulated as a result of the logical theory finally we demonstrate that fuzzy control can be seen as a repeated derivation in a continuously modified logical theory and propose a hypothesis on the role of linguistics in the controllability problem

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

asymptotic behavior of a stochastic delayed seir epidemic model with nonlinear incidence abstract this paper is concerned with a stochastic delayed seir epidemic model with nonlinear incidence firstly we verify that there exists a unique global positive solution of the system then by constructing some suitable lyapunov functions we study the asymptotic behaviors of the disease free equilibrium and the endemic equilibrium respectively

implementation of continuous h p adaptive finite element spaces without limitations on hanging sides and distribution of approximation orders adaptive techniques using h p refinement are known to be one of the most efficient methodologies to accelerate the convergence of finite element algorithms however the implementation of computational tools for the development of h p adaptive algorithms is intricate and depends strongly on the data structure there exist few computational environments available to the scientific finite element community capable to implement h p adaptive approximation spaces for the complete family of finite element topologies and which implement hanging sides this article describes a methodology for the development of continuous h p adaptive finite element approximation spaces without constraints on the refinement strategy concerning the difference of levels and approximation orders between neighboring elements the shape functions are hierarchical and the coefficient constraints associated with hanging sides that can occur in non conformal geometric meshes are defined using l 2 projections the topological and functional aspects of the construction are described in one two and three dimensions for a variety of geometric entities line triangle quadrilateral tetrahedron pyramid prism and hexahedron the implementation is demonstrated in the object oriented scientific computational environment neopz http github com labmec neopz neopz is a general finite element approximation software which incorporates a variety of variational formulations validation of the refinement methodology is demonstrated by two and three dimensional numerical experiments

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

modeling and dynamical analysis of a triple delayed prey predator scavenger system with levy jumps abstract in this paper a hybrid triple delayed prey predator scavenger system with commercial harvesting and levy jumps is established where both maturation delay for prey population and gestation delays for predator and scavenger population are considered for deterministic system positivity and uniform permanence of solution are discussed local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays for stochastic system without time delay sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed for stochastic system with triple time delays existence and uniqueness of global positive solution are studied by constructing appropriate lyapunov functions asymptotic behavior of the hybrid stochastic system with triple time delays and levy jumps is discussed numerical simulations are supported to illustrate theoretical results

geometric decompositions and local bases for spaces of finite element differential forms abstract we study the two primary families of spaces of finite element differential forms with respect to a simplicial mesh in any number of space dimensions these spaces are generalizations of the classical finite element spaces for vector fields frequently referred to as raviart thomas brezzi douglas marini and nedelec spaces in the present paper we derive geometric decompositions of these spaces which lead directly to explicit local bases for them generalizing the bernstein basis for ordinary lagrange finite elements the approach applies to both families of finite element spaces for arbitrary polynomial degree arbitrary order of the differential forms and an arbitrary simplicial triangulation in any number of space dimensions a prominent role in the construction is played by the notion of a consistent family of extension operators which expresses in an abstract framework a sufficient condition for deriving a geometric decomposition of a finite element space leading to a local basis

positive periodic solutions in a non selective harvesting predator prey model with multiple delays abstract this paper is concerned with a predator prey model with hassell varley type functional response non selective harvesting and multiple delays some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem in addition the results are delay dependent which is different from the previous work finally simulations illustrate the effectiveness of our results

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

bernstein bezier finite elements of arbitrary order and optimal assembly procedures algorithms are presented that enable the element matrices for the standard finite element space consisting of continuous piecewise polynomials of degree n on simplicial elements in mathbb r d to be computed in optimal complexity mathcal o n 2d the algorithms i take into account numerical quadrature ii are applicable to nonlinear problems and iii do not rely on precomputed arrays containing values of one dimensional basis functions at quadrature points although these can be used if desired the elements are based on bernstein polynomials and are the first to achieve optimal complexity for the standard finite element spaces on simplicial elements

hierarchical high order finite element spaces in h div ω h1 ω for a stabilized mixed formulation of darcy problem abstract the classical dual mixed finite element method for flow simulations is based on h div conforming approximation spaces for the flux which guarantees continuous normal components on element interfaces and discontinuous approximations in l 2 for the pressure however stability and convergence can only be obtained for compatible approximation spaces stabilized finite element methods may provide an alternative stable procedure to avoid this kind of delicate balance the main purpose of this paper is to present a high order finite element methodology to solve the darcy problem based on the combination of an unconditionally stable mixed finite element method with a hierarchical methodology for the construction of finite dimensional subspaces of h div and h 1 the chosen stabilized method is free of mesh dependent stabilization parameters and allows for the use of different high order finite element approximations for the flux and the pressure variables without requiring any compatibility constraint as required in mixed methods for these problems convergence studies are presented comparing the numerical solutions obtained for different approximation orders on quadrilateral elements with the ones given by classical mixed formulation with raviart thomas elements

fuzzy finite element approach for the analysis of imprecisely defined systems many engineering systems are too complex to be defined in precise mathematical terms they often contain information and features that are vague imprecise qualitative linguistic or incomplete the traditional deterministic and probabilistic techniques are not adequate to analyze such systems this paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems the development of the methodology starts from the basic concepts of fuzzy numbers of fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation manipulation and solution of the finite element equations simple stress analysis problems involving vaguely defined geometry material properties external loads and boundary conditions are solved to establish and to illustrate the new procedure the approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information if complete data are known the method handles the information similar to that of a probabilistic approach the present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

orientation embedded high order shape functions for the exact sequence elements of all shapes a unified construction of high order shape functions is given for all four classical energy spaces h1 h curl h div and l2 and for elements of all shapes segment quadrilateral triangle hexahedron tetrahedron triangular prism and pyramid the discrete spaces spanned by the shape functions satisfy the commuting exact sequence property for each element the shape functions are conforming hierarchical and compatible with other neighboring elements across shared boundaries so they may be used in hybrid meshes expressions for the shape functions are given in coordinate free format in terms of the relevant affine coordinates of each element shape the polynomial order is allowed to differ for each separate topological entity vertex edge face or interior in the mesh so the shape functions can be used to implement local p adaptive finite element methods each topological entity may have its own orientation and the shape functions can have that orientation embedded by a simple permutation of arguments

fuzzy particle filtering for uncertain systems in this paper we propose a novel fuzzy particle filtering method for online estimation of nonlinear dynamic systems with fuzzy uncertainties this approach uses a sequential fuzzy simulation to approximate the possibilities of the state intervals in the state space and estimates the state by fuzzy expected value operator to solve the degeneracy problem of the fuzzy particle filter one corresponding resampling technique is introduced in addition we compare the fuzzy particle filter with ordinary particle filter in both aspects of the theoretical basis and algorithm design and demonstrate that the proposed filter outperforms standard particle filters especially when the number of the particles is small the numerical simulations of two continuous state nonlinear systems and a jump markov system are employed to show the effectiveness and robustness of the proposed fuzzy particle filter

evaluation of design alternatives in mechanical engineering abstract the paper gives a description of a structure dedicated to evaluation of design alternatives in mechanical engineering a list of particular features of the system such as its ability to cope with fuzziness and a uniform way of treating various criteria involved in design processes is given and discussed in length special attention is focused on empirical engineering oriented aspects of membership functions estimation with a particular emphasis on expressing achieved precision the paper re analyzes some existing methods of multiobjective decision making some original contributions of the study to this area are focussed on developing new indices significantly facilitating interpretation of results of ranking such as e g specificity of different alternatives as well as strength of dominance observed among them an illustration of the performance of the system is completed with the aid of an evaluation of different types of joints found in hydraulic cylinders

the fuzzy delphi method via fuzzy statistics and membership function fitting and an application to the human resources a new fuzzy delphi method is proposed the method employs the fuzzy statistics and technique of the conjugate gradient search to fit membership functions membership functions besides triangles may be derived for the fuzzy forecasts a procedure termed as stabilization rather than convergence of the iterative interval valued surveys is utilized in which the a level set of the fuzzy forecasts is used the testing of stability of the process is conducted on the fuzzy forecasts between two consecutive iterations instead of within each iteration an application of this method to the problem of managerial talent assessment for a company located in taiwan and the obtained results are provided