generalized multiple scale reproducing kernel particle methods abstract an approach to unify reproducing kernel methods under one large umbrella and an extension to include time and spatial shifting are proposed the study is divided into three major topics the groundwork is set by revisiting the fourier analysis of discrete systems the multiresolution concept and its significance in devising the reproducing kernel methods and its discrete counterpart reproducing kernel particle methods are explained an edge detection technique based on multiresolution analysis is developed this wavelet approach together with particle methods gives rise to a straightforward h adaptivity algorithm by using this framework a hermite reproducing kernel method is also proposed and its relation to wavelet methods is presented it is also shown that the new approach generalizes existing kernel methods and it can easily be degenerated into other widely used methods such as partition of unity moving least square interpolants smooth particle hydrodynamics scaling functions and wavelets and multiple scale analysis furthermore the hermite reproducing kernel particle method a particle based discrete version of the hermite reproducing kernel method is developed finally multiple scale methods based on frequency and wave number shifting techniques are presented a stability analysis is also presented for newmark time integration schemes for the low frequency equation numerical examples are presented throughout the paper to illustrate the flexibility and accuracy of this class of multiple scale methods

partial ordering in l underdeterminate sets abstract the purpose of this paper is to improve results on fuzzy partial orderings obtained by zadeh in 9 we overcome the difficulties connected with the axioms of antisymmetry and linearity moreover if the underlying lattice l is a complete residuated lattice we establish a szpilrajn theorem i e any l fuzzy partial ordering has a linear extension in opposition to zadeh s our point of view is that an axiom of antisymmetry without a reference to a concept of equality is meaningless therefore we first introduce the category lus cf 2 which can be considered as a mathematical model of fuzzy equality and subsequently we specify the axioms of l fuzzy partial orderings with respect to the frame given by lus the axioms we use clearly display the usefulness of having a zadeh like complementation and as a consequence the usefulness of a positivistic and nonintuitionistic frame of study an example concerning l rn which we give clearly shows that the lus version of the szpilrajn theorem cannot be reduced to a fuzzification of an already existing theorem but provides us with additional information

on some types of fuzzy covering based rough sets fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets recently an excellent introduction to the definition of a fuzzy covering is due to ma and two fuzzy covering based rough set models are presented in this paper by introducing some new definitions of fuzzy covering approximation spaces the properties of fuzzy covering approximation spaces and ma s fuzzy covering based rough set models are studied furthermore three new types of fuzzy covering based rough set models as generalizations of ma s models are first proposed in this paper first some properties of fuzzy covering and its fuzzy neighborhood family are proposed we present a necessary and sufficient condition for fuzzy neighborhood family induced by a fuzzy covering to be equal to the fuzzy covering itself then we study the characterizations of ma s fuzzy covering based rough set models and give a necessary and sufficient condition for two fuzzy coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation finally this paper proposes three new types of fuzzy covering based rough set models by introducing a new notion of a fuzzy complementary neighborhood

an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

a parallelized meshfree method with boundary enrichment for large scale cfd a parallel computational implementation of a meshfree method the reproducing kernel particle method rkpm is used for 3 d implicit cfd analysis a novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented using this enrichment along the essential boundaries produces results that more closely match experimental and analytical results for a flow past a cylinder problem than does either the finite element method or other meshfree methods that require matrix inversion for the application of essential boundary conditions this technique also allows the efficient parallelization of the algorithm and leads to higher parallel speedups than do other boundary condition implementations many of which involve inherently serial steps this is important because the expense of meshfree computations makes parallelization crucial for large size problems the performance of the parallelization technique and the accuracy of the implicit cfd algorithm are demonstrated in two example problems

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

l fuzzy covering relation we investigate lattice valued l fuzzy covering or fuzzy neighboring relation arising from a given lattice valued order we show that every l fuzzy covering is obtained by synthesis of crisp coverings arising from the corresponding cut orderings as a converse we introduce and investigate lattice valued relations which turn out to be fuzzy coverings of fuzzy orders

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

building dynamical models from data and prior knowledge the case of the first period doubling bifurcation this paper reviews some aspects of nonlinear model building from data with gray box and without black box prior knowledge the model class is very important because it determines two aspects of the final model namely i the type of nonlinearity that can be accurately approximated and ii the type of prior knowledge that can be taken into account such features are usually in conflict when it comes to choosing the model class the problem of model structure selection is also reviewed it is argued that such a problem is philosophically different depending on the model class and it is suggested that the choice of model class should be performed based on the type of a priori available a procedure is proposed to build polynomial models from data on a poincare section and prior knowledge about the first period doubling bifurcation for which the normal form is also polynomial the final models approximate dynamical data in a least squares sense and by design present the first period doubling bifurcation at a specified value of parameters the procedure is illustrated by means of simulated examples

extended model set global data and threshold model identification of severely non linear systems abstract new parameter estimation algorithms based on an extended model set a global data model and a threshold model formulation are derived for identifying severely non linear systems it is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systems with complex structure simulation studies are included to illustrate the techniques discussed

moving least square reproducing kernel method part ii fourier analysis in part i of this work the moving least square reproducing kernel mlsrk method is formulated and implemented based on its generic construction an m consistency structure is discovered and the convergence theorems are established in this part of the work a systematic fourier analysis is employed to evaluate and further establish the method the preliminary fourier analysis reveals that the mlsrk method is stable for sufficiently dense non degenerated particle distribution in the sense that the kernel function family satisfies the riesz bound one of the novelties of the current approach is to treat the mlsrk method as a variant of the standard finite element method and depart from there to make a connection with the multiresolution approximation in the spirits of multiresolution analysis we propose the following mlsrk transformation fm k hu i 1npu k ik h x xi x w1 the highlight of this paper is to embrace the mlsrk formulation with the notion of the controlled fp approximation based on its characterization the strang fix condition for example a systematic procedure is proposed to design new window functions so they can enhance the computational performance of the mlsrk algorithm the main effort here is to obtain a constant correction function in the interior region of a general domain i e c h 1 this can create a leap in the approximation order of the mlsrk algorithm significantly if a highly smooth window function is embedded within the kernel one consequence of this development is the synchronized convergence phenomenon a unique convergence mechanism for the mlsrk method i e by properly tuning the dilation parameter the convergence rate of higher order error norms will approach the same order convergence rate of the l2 error norm they are synchronized

multiobjective parameter estimation for non linear systems affine information and least squares formulation this paper defines a class of system information affine information that includes both the dynamic residuals and some types of auxiliary information that can be used in system parameter estimation as special cases the types of information that can be cast under the affine information format give rise to quadratic functions that measure the extent to which a model fits such information and that can be aggregated in a single weighted quadratic cost functional this allows the definition of a multiobjective methodology for parameter estimation in non linear system identification which allows taking into account any type of affine information the results are presented in terms of a set of efficient solutions of the multiobjective estimation problem such a solution set is more meaningful than a single model since any affine information leads to a convex quadratic functional the whole set of efficient solutions is exactly accessible via the minimization of the quadratic functional with different weighti

a compendium of fuzzy weak orders representations and constructions the present paper gives a state of the art overview of representation and construction results for fuzzy weak orders we do not assume that the underlying domain is finite instead we concentrate on results that hold in the most general case that the underlying domain is possibly infinite this paper presents three fundamental representation results each of which also provides a construction method i score function based representations ii inclusion based representations iii representations by decomposition into crisp linear orders and fuzzy equivalence relations which also facilitates a pseudo metric based construction

model validity tests for non linear signal processing applications abstract time series model validity tests based on general correlations are presented in this paper it is shown that the tests xi xi xi xi 2 and xi xi xi 1 t2 can only detect a subset of any possible unmodelled terms in the residuals whereas xi 2 xi 2 detects all possible terms these basic results are then extended to include functions of process or residual terms as entries in the correlation simulation studies are included to demonstrate the effectiveness of the tests when applied to estimated models of both simulated and real data sequences

a top down algorithm for generating the hasse tree of a fuzzy preorder closure this paper describes a new top down algorithm for the stepwise generation of the different levels or hasse diagrams of the hasse tree associated to the fuzzy preorder closure min transitive closure of a given reflexive binary fuzzy relation the algorithm is based upon a recently established weight driven method for computing the min transitive closure of a reflexive binary fuzzy relation the way in which this method gradually establishes the fuzzy preorder closure implies that for the generation of a specific level of the hasse tree the newly proposed algorithm does not require the complete computation of this closure

representing ordered structures by fuzzy sets an overview we present a survey on representations of ordered structures by fuzzy sets any poset satisfying some finiteness condition semilattice lattice belonging to a special class e g distributive noetherian complete and others can be represented by a single function i e by a fuzzy set its domain and co domain are particular subsets of the same structure and consist of irreducible elements the representation is minimal in the sense that another representation could not be obtained by replacing the domain of the former by its proper subset by this approach the structure itself is uniquely represented by the collection of cuts ordered dually to inclusion

improved structure selection for nonlinear models based on term clustering in this paper the concepts of term clusters and cluster coefficients are defined and used in the context of system identification it is argued that if a certain type of term in a nonlinear model is spurious the respective cluster coefficient is small compared with the coefficients of the other clusters represented in the model once the spurious clusters have been detected the corresponding terms can be deleted from the set of candidate terms the consequences of doing this are i a drastic reduction in the size of the set of candidate terms and consequently a substantial gain in computation time is achieved ii the final estimated model is more likely to reproduce the dynamics of the original system and iii the final model is more robust to overparametrization numerical examples are included to illustrate the new procedure

a theory of vague lattices based on many valued equivalence relations ii complete lattices as a continuation of part i two sorts of vague lattices called complete vague lattices and ordinarily complete vague lattices both of which correspond to the generalization of complete lattices based on many valued equivalence relations are introduced and some of their elementary properties are presented in this paper furthermore the representations and the constructions of ordinarily complete vague lattices are studied in details

discretization errors associated with reproducing kernel methods one dimensional domains abstract the reproducing kernel particle method rkpm is a discretization technique for partial differential equations that uses the method of weighted residuals classical reproducing kernel theory and modified kernels to produce either mesh free or mesh full methods although rkpm has many appealing attributes the method is new and its numerical performance is just beginning to be quantified in order to address the numerical performance of rkpm von neumann analysis is performed for semi discretizations of three model one dimensional pdes the von neumann analyses results are used to examine the global and asymptotic behavior of the semi discretizations the model pdes considered for this analysis include the parabolic and hyperbolic first and second order wave equations numerical diffusivity for the former and phase speed for the latter are presented over the range of discrete wavenumbers and in an asymptotic sense as the particle spacing tends to zero group speed is also presented for the hyperbolic problems excellent diffusive and dispersive characteristics are observed when a consistent mass matrix formulation is used with the proper choice of refinement parameter in contrast the row sum lumped mass matrix formulation severely degraded performance the asymptotic analysis indicates that very good rates of convergence o x 6 o x 8 are possible when the consistent mass matrix formulation is used with an appropriate choice of refinement parameter and quadrature rule

on lattice valued up sets and down sets isotone and anti isotone mappings from a poset into a complete lattice are investigated as lattice valued up sets and down sets respectively cuts of these are shown to be analogue crisp sub posets of the domain up set or semi filters and down sets or semi ideals the collection of all lattice valued up sets down sets of a poset is a complete lattice under the order inherited from the lattice among other results for a collection of crisp up sets down sets of a poset necessary and sufficient conditions are given under which this collection consists of cuts of a lattice valued up set down sets a generalization in the sense of closed fuzzy sets with respect to fuzzy relations is also carried out

mapping non linear integro differential equations into the frequency domain a recursive algorithm is derived to compute the generalized frequency response functions for a large class of non linear integro differential equations applications to duffing s equation and a modified van der pol model are discussed

recovering map static nonlinearities from chaotic data using dynamical models abstract this paper is concerned with the estimation from chaotic data of maps with static nonlinearities a number of issues concerning model construction such as structure selection over parametrization and model validation are discussed in the light of the shape of the static non linearities reproduced by the estimated maps a new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach the paper discusses model limitations and some useful principles to select the structure of nonlinear maps some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit

recursive algorithm for computing the frequency response of a class of non linear difference equation models abstract a recursive algorithm is developed which is both computationally compact and enables the nth order frequency response functions of a large class of non linear difference equation models to be found without restriction on the order n

detecting periodicity in experimental data using linear modeling techniques fourier spectral estimates and to a lesser extent the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences we propose a new method which is more reliable than traditional techniques and is able to make clear identification of periodic behavior when traditional techniques do not this technique is based on an information theoretic reduction of linear autoregressive models so that only the essential features of an autoregressive model are retained these models we call reduced autoregressive models rarm the essential features of reduced autoregressive models include any periodicity present in the data we provide theoretical and numerical evidence from both experimental and artificial data to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data there are strong information theoretic arguments to support the statement that rarm detects periodicities if they are present surrogate data techniques are used to ensure the converse furthermore our calculations demonstrate that rarm is more robust more accurate and more sensitive than traditional spectral techniques

analysis of the effects of time delay in nonlinear systems using generalised frequency response functions abstract a recursive algorithm for computing the generalised frequency response functions gfrfs of nonlinear time delay systems described by nonlinear differential difference equation models is derived using the operator e n and used to analyse the effects of time delay in nonlinear systems the algorithm shows an explicit relationship between the model parameters and the gfrfs such a relationship provides important insight into the behaviour of nonlinear systems the effect of delay on several properties of nonlinear systems such as harmonic generation gain compression expansion and desensitisation is studied by considering the example of a duffing oscillator with retarded damping results of the studies convincingly demonstrate that the system delay has a significant effect on several important properties of nonlinear systems

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

a fitting model for attribute reduction with fuzzy β covering abstract as an intuitive extension of covering based rough set models fuzzy covering provides an effective means to deal with uncertain information however classical fuzzy covering can not fit a given data set well which limits its popularization and application on the one hand this model can not guarantee that the lower approximation is contained in the upper approximation it does not ideally describe the differences in sample classification on the other hand fuzzy covering is sensitive to noise hidden in data which leads to unstable classification performance to address these issues we set forth a new fitting model for attribute reduction based on fuzzy covering to this end parameterized fuzzy neighborhoods in terms of a family of fuzzy coverings are introduced to characterize the similarity between samples using which the granular structures of fuzzy lower and upper approximations of a decision are presented fuzzy covering decision tables are then formalized to deal with knowledge reduction from the viewpoint of maintaining the discriminative ability of a fuzzy covering family furthermore a heuristic attribute reduction algorithm is developed to reduce redundant fuzzy coverings extensive numerical experiments are further conducted to examine the effectiveness and feasibility of the proposed model

additive decomposition of fuzzy pre orders fuzzy pre orders reflexive and min transitive fuzzy relations constitute an important class of fuzzy relations by means of an indifference generator a fuzzy pre order can be decomposed additively into two parts an indifference relation and a strict preference relation when using a frank t norm as indifference generator we fully characterize the transitivity of these parts only in case the minimum operator is used as generator both parts are min transitive the transitivity of the indifference relation is determined by the frank t norms while the transitivity of the strict preference relation is determined by transforms of the nilpotent minimum t norm

identification of smooth nonlinear dynamical systems with non smooth steady state features abstract this work discusses the identification of single block smooth nonlinear discrete time polynomial models with non smooth steady state features based on bifurcation theory conditions are developed and used to determine some general aspects of the model structure and also to determine some constraints on the parameters required to guarantee the aforementioned features the procedure uses only smooth functions of the regressors a single possibly smooth input and some prior knowledge about the steady state behavior the non smooth static function is here obtained by interchanging the stability of two sets of equilibria at the break point which corresponds to guaranteeing a transcritical bifurcation this work discusses how to determine the domain over which the results are valid the procedure is illustrated with simulated and experimental data

fuzzy neighborhood operators and derived fuzzy coverings abstract fuzzy coverings are natural extensions of the coverings by replacing crisp sets with fuzzy sets recently some fuzzy neighborhood operators based on a fuzzy covering were defined and their properties were investigated by d eer et al in this paper we propose four types of fuzzy neighborhood operators by introducing the notions such as neighborhood system fuzzy minimal description and fuzzy maximal description first we propose these notions and investigate their properties then we construct four types of fuzzy neighborhood operators based on the fuzzy coverings properties and relationship among these four types of fuzzy neighborhood operators are studied finally six types of fuzzy coverings were derived by using these four types of fuzzy neighborhood operators and their properties are considered

the influence of the mass matrix on the dispersive nature of the semi discrete second order wave equation abstract the application of discrete solution methods to the second order wave equation can yield a dispersive representation of the non dispersive wave propagation problem resulting in a phase speed that depends not only upon the wavelength of the signal being propagated but also upon the direction of propagation in this work the dependence of the dispersive errors on the wave propagation direction mesh aspect ratio and wave number is investigated with the goal of understanding and hopefully reducing the phase and group errors associated with the two dimensional bilinear finite element an analysis of the dispersive effects associated with the consistent row sum lumped and higher order mass matrices has led to a reduced coupling penta diagonal mass matrix that yields improved phase and group errors with respect to wavelength and propagation direction the influence of row sum lumping the finite element mass matrix is demonstrated to always introduce lagging phase and group error while a linear combination of the lumped and consistent mass matrices i e a higher order mass matrix is shown to improve the dispersion characteristics of both the reduced and full integration element using a 2 5 phase error metric the higher order mass matrix can reduce the mesh resolution requirements relative to the lumped mass matrix by nearly a factor of two in one dimension a factor of 4 in two dimensions similarly the reduced coupling mass matrix can reduce the grid requirements by a factor of approximately four relative to the lumped mass matrix a factor of 16 in two dimensions although the reduced coupling mass matrix requires additional storage relative to the lumped mass the factor of 16 reduction in grid requirements promises tremendous overall savings for computing a fixed wavelength spectrum or alternatively for resolving shorter wavelengths with a fixed grid resolution

results of von neumann analyses for reproducing kernel semi discretizations the reproducing kernel particle method rkpm has many attractive properties that make it ideal for treating a broad class of physical problems rkpm may be implemented in a mesh full or a mesh free manner and provides the ability to tune the method via the selection of a window function and its associated dilation parameter in order to achieve the requisite numerical performance rkpm also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multi scale problems although the method has many appealing attributes it is quite new and its numerical performance is still being quantified with respect to more traditional discretization techniques in order to assess the numerical performance of rkpm detailed studies of the method on a series of model partial differential equations has been undertaken the results of von neumann analyses for rkpm semi discretizations of one and two dimensional first and second order wave equations are presented in the form of phase and group errors excellent dispersion characteristics are found for the consistent mass matrix with the proper choice of dilation parameter in contrast row sum lumping the mass matrix is demonstrated to introduce severe lagging phase errors a higher order mass matrix improves the dispersion characteristics relative to the lumped mass matrix but also yields significant lagging phase errors relative to the fully integrated consistent mass matrix published in 2000 by john wiley sons ltd

a fuzzy covering based rough set model and its generalization over fuzzy lattice in this paper we study a new type of fuzzy covering based rough set model by introducing the notion of fuzzy minimal description we mainly address the following issues in this paper first we present the definition of fuzzy minimal description and study its properties then we define a novel type of fuzzy covering based rough set model and investigate the properties of this model furthermore the axiomizations and matrix representations of the fuzzy covering lower and fuzzy covering upper approximations are the vital problems we investigate in this paper moreover we explore the conditions under which two fuzzy coverings generate the same fuzzy covering lower or fuzzy covering upper approximations finally we generalize the model to l fuzzy covering based rough set which is defined over fuzzy lattices similar to the fuzzy covering based rough set model we also address the issues mentioned above to the l fuzzy covering based rough set

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

moving least square reproducing kernel methods i methodology and convergence this paper formulates the moving least square interpolation scheme in a framework of the so called moving least square reproducing kernel mlsrk representation in this study the procedure of constructing moving least square interpolation function is facilitated by using the notion of reproducing kernel formulation which as a generalization of the early discrete approach establishes a continuous basis for a partition of unity this new formulation possesses the quality of simplicity and it is easy to implement moreover the reproducing kernel formula proposed is not only able to reproduce any mth order polynomial exactly on an irregular particle distribution but also serves as a projection operator that can approximate any smooth function globally with an optimal accuracy in this contribution a generic m consistency relation has been found which is the essential property of the mlsrk approximation an interpolation error estimate is given to assess the convergence rate of the approximation it is shown that for sufficiently smooth function the interpolant expansion in terms of sampled values will converge to the original function in the sobolev norms as a meshless method the convergence rate is measured by a new control variable dilation parameter of the window function instead of the mesh size h as usually done in the finite element analysis to illustrate the procedure convergence has been shown for the numerical solution of the second order elliptic differential equations in a galerkin procedure invoked with this interpolant in the numerical example a two point boundary problem is solved by using the method and an optimal convergence rate is observed with respect to various norms

an introduction to vague complemented ordered sets abstract the purpose of this paper is to introduce a theory of fuzzily defined complement operations on nonempty sets equipped with fuzzily defined ordering relations many valued equivalence relation based fuzzy ordering relations also called vague ordering relations provide a powerful and a comprehensive mathematical modelling of fuzzily defined partial ordering relations for this reason starting with a nonempty set x equipped with a many valued equivalence relation and a vague ordering relation a fuzzily defined complement operation called a vague complement operation on x will be formulated by means of the underling many valued equivalence relation and vague ordering relation because of the fact that the practical implementations of vague complement operations basically depend on their representation properties a considerable part of this paper is devoted to the representations of vague complement operations in addition to this the present paper provides various nontrivial examples for vague complements and introduces a many valued logical interpretation of quantum logic as a real application of vague complements

completion of ordered structures by cuts of fuzzy sets an overview the aim of the paper is to present a role of fuzzy sets in the theory of ordered structures main algebraic properties of cuts of fuzzy sets are given and a completion of partially ordered sets to complete lattices is described it turns out that this completion is equivalent with the famous dedekind macneille completion but the algorithm presented here is much simpler

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

a theory of vague lattices based on many valued equivalence relations i general representation results the present work introduces a new and general theory of ordering relations and lattices based on many valued equivalence relations under the name vague ordering relations and vague lattices respectively representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper and various desirable results in this direction are established furthermore algebraic characterizations of vague lattices are studied