robust kalman bucy filter development of a robust estimator for uncertain stochastic systems under persistent excitation is presented the given continuous time stochastic formulation assumes norm bounded parametric uncertainties and excitations when there are no system uncertainties the performance of the proposed robust estimator is similar to that of the kalman bucy filter and the proposed approach asymptotically recovers the desired optimal performance in the presence of uncertainties and or persistent excitation

algorithms for solving fuzzy relational equations in a probabilistic setting abstract we discuss methods suitable for finding approximate solutions to fuzzy relational equations defined in finite universe of discourse and taking the form of either a system of equations x k r y k k 1 2 k with r being unknown fuzzy relation or a single equation x r y with x being looked for the key idea of the proposed algorithms is to incorporate some statistics concerning the solution of a single equation and utilize it in the final process of approximation of the unknown fuzzy relation set numerical considerations support the established algorithms

a polynomial approach to robust estimation of uncertain discrete time systems the robust estimation problem for uncertain discrete time systems is treated in this paper considering parametric uncertainties in the polynomial framework the estimator is the minimiser of a cost function written in a epsilon contaminated form uncertainties are not formally modelled it is shown that in the present context the proposed approach can be connected to stochastic modelling of uncertainties the optimal robust estimator is obtained by computing a spectral factorisation and by solving a single diophantine equation an example shows the efficiency of the proposed method

the cutting of compositions this paper investigates the cutability of the fuzzy relational compositions the sup t composition the triangular compositions of bandler and kohout and their improved versions the theoretical and practical importance of fuzzy cuts is illustrated by means of a careful selection of results from the fuzzy literature some new potential properties of fuzzy implications operators and triangular norms that play an important role in this cutability study are introduced and discussed extensively the paper concludes with a study of the fuzzy cutability of the sup t composition

numerical and applicational aspects of fuzzy relational equations we discuss numerical methods leading to a resolution of fuzzy relational equations which create a formal description of ill defined systems an applicability of the numerical approach is shown in solving some problems in fuzzy systems such as identification and control an idea of fuzzy discretization fuzzy chopping as a meaningful tool for handling various problems is also investigated

convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing abstract this paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form x k 2 x k r y k k 1 2 k where x k and y k denote fuzzy sets r and 2 fuzzy relations the sup min compositional operator the inf max one and a fuzzy convex combinator whose complement is furthermore we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations focusing our attention on the modeling of fuzzy input output systems normality of fuzzy sets characterizing fuzzy input fuzzy logical aspects of systems and association between fuzzy information finally it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

conditional central algorithms for worst case set membership identification and filtering this paper deals with conditional central estimators in a set membership setting the role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering in contexts in which disturbances are described through norm bounds are reducible to the computation of conditional central algorithms the conditional chebyshev center problem is solved for the case when energy norm bounded disturbances are considered a closed form solution is obtained by finding the unique real root of a polynomial equation in a semi infinite interval

structure identification for gene regulatory networks via linearization and robust state estimation abstract inferring causal relationships among cellular components is one of the fundamental problems in understanding biological behaviours the well known extended kalman filter ekf has been proved to be a useful tool in simultaneously estimating both structure and actual gene expression levels of a gene regulatory network grn first order approximations however unavoidably result in modelling errors but the ekf based method does not take either unmodelled dynamics or parametric uncertainties into account which makes its estimation performances not very satisfactory to overcome these problems a sensitivity penalization based robust state estimator is adopted in this paper for revealing the structure of a grn based on the specific structure of the estimation problem it has been proved that under some weak conditions both the ekf based method and the method suggested in this paper provide a consistent estimate but the suggested method has a faster convergence speed compared with both the ekf and the unscented kalman filter ukf based methods simulation results and real data based estimations consistently show that both convergence speed and parametric estimation accuracy can be appreciably improved these lead to significant reductions in both false positive errors and false negative errors and may imply helpfulness of the suggested method in better understanding the structure and dynamics of actual grns

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

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data the paper deals with implementation of a general scheme for fuzzy logic inference with the aid of fuzzy relational equations it is shown that antecedents and consequents are related in terms of a fuzzy relation various implementation methods of generalized modus ponens and modus tollens are put into extensive study it is pointed out that fuzzy relational equations form an effective and plausible tool for implementations of reasoning methods with fuzzy premises two examples of fuzzy controllers being a direct application of schemes of approximate reasoning are also discussed

direct and inverse problem in comparison of fuzzy data abstract discussed is the direct and inverse problem of comparison of two linguistic quantities specified as fuzzy sets relations in the same universe of discourse the proposed way of comparison makes use of some logical properties of connectives and implication operators stemming from the foundations of fuzzy sets a list of plausible equality indices is provided the inverse problem is formulated a set of its solutions is provided direct impacts of the discussed approach on development of fuzzy modelling are clearly indicated also it is pointed out how fuzzy sets of higher type or interval valued sets can be generated as a result of analysis of performance of any fuzzy model

fuzzy relation equations theory as a basis of fuzzy modelling an overview abstract we give a wide overview on the applications of fuzzy relation equations theory to decision making processes to the construction of preference relations and to knowledge engineering mainly fuzzy control and fuzzy pattern recognition general theoretical results and methodological aspects are pointed out

optimal robust linear quadratic regulator for systems subject to uncertainties in this technical note a robust recursive regulator for linear discrete time systems which are subject to parametric uncertainties is proposed the main feature of the optimal regulator developed is the absence of tuning parameters in online applications to achieve this purpose a quadratic cost function based on the combination of penalty function and robust weighted least squares methods is formulated the convergence and stability proofs for the stationary system and a numerical comparative study among the standard linear quadratic regulator guaranteed cost and h controllers are provided

diagnosis problem solving using fuzzy relations this paper deals with the restoration and the identification of the causes diagnoses through the observed effects symptoms on the basis of fuzzy relations and zadeh s compositional rule of inference we propose an approach for building fuzzy systems of diagnosis which enables solving fuzzy relational equations together with design and tuning of fuzzy relations on the basis of expert and experimental information the essence of tuning consists of the selection such membership functions for fuzzy causes and effects and also fuzzy relations which minimize the difference between model and experimental results of diagnosis the genetic algorithm is used for solving the optimization problem the proposed approach is illustrated by the computer experiment and the real example of diagnosis

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

convex combinations of generalized fuzzy relational equations abstract convex combinations of two fuzzy relational equations are studied these equations are built with compositions of the type conorm norm and norm conorm this study is a generalization of the works of ohsato and sekigushi previous results concerning usual fuzzy relational equations lead to the development of convexly combined equations first conditions for the existence of solutions are studied then the resolution of equations is discussed finally the concept of pseudo solutions of a system of several equations is introduced

optimal robust filtering for systems subject to uncertainties in this paper we deal with an optimal filtering problem for uncertain discrete time systems parametric uncertainties of the underlying model are assumed to be norm bounded we propose an approach based on regularization and penalty function to solve this problem the optimal robust filter with the respective recursive riccati equation is written through unified frameworks defined in terms of matrix blocks these frameworks do not depend on any auxiliary parameters to be tuned simulation results show the effectiveness of the robust filter proposed

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

ranking multiple aspect alternatives fuzzy relational equations approach abstract the paper discusses a general approach to the algorithms of ranking multiple aspect alternatives constructed with the aid of fuzzy relational equations it is pointed out that the algorithms can be constructed by considering data sets provided by prototypical situations discriminating properties of the proposed method are also taken into consideration

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

relevancy of fuzzy model abstract a problem of relevancy of fuzzy models viz models with ability to cope with fuzziness is stated its importance in any identification scheme is underlined and discussed in light of some shortcomings existing in procedures of fuzzy model building two novel concepts viz equality index and confidence interval are introduced and utilized for fuzzy model evaluation a flexible way of interpreting results with the aid of fuzzy models is formulated by means of interval valued fuzzy sets fuzzy sets the clear importance of studies on the relevancy of fuzzy models for problem formulation and solution is pointed out

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

on some finite fuzzy relation equations abstract we give a necessary and sufficient condition for the resolution of a new type of finite fuzzy relation equation whose set of solutions is entirely characterized an example of application to approximate reasoning is also given

a semi analytical approach to solve integro differential equations in this work we present a semi analytical method for solving integro differential equations under multi point or mixed boundary conditions the proposed method solves linear and nonlinear fredholmvolterra integro differential equations a convergence analysis of the proposed method is directly examined numerical examples are worked out to demonstrate the main results moreover proper graphs are provided to confirm the efficiency and the accuracy of the proposed scheme we show that with a few number of obtained approximating terms we achieve a high accuracy level of the obtained results however increasing the number of approximating terms yields a significant decrease of the error of the approximation the proposed method is very useful reliable and flexible for solving different kinds of integro differential equations

a new look at solving a system of fuzzy relational equations abstract solving a system of fuzzy relational equations exactly has been studied for many years a usual understanding on the solvable conditions is that the input fuzzy sets must be normal and pairwise disjoint such understanding is reexamined in this paper we show that the usual pairwise disjoint condition is too conservative and a system of max t fuzzy relational equations can be solved exactly when the input fuzzy sets are semi overlapped a condition commonly found in most rule based system applications in addition the boundary condition of solvability with respect to the compactness of the input fuzzy sets is derived if it cannot be satisfied we show that the system of equations could still be solved almost exactly by specifying the t norm as drastic product the results have been applied to study the capacity of fuzzy relations

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

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

periodically time varying cal h _ infty memory filter design for discrete time lti systems with polytopic uncertainty this technical note focuses on the development of a general periodically time varying memory filter ptvmf to improve the robust h filtering performance for discrete time linear time invariant lti systems with polytopic parameter uncertainties a sufficient condition to design the h ptvmf is given in terms of convex optimizations expressed as linear matrix inequalities lmis finally examples demonstrate its potential less conservatism

interval valued fuzzy backward reasoning the importance and efficiency of backward reasoning in nonfuzzy reasoning has been stressed for a long time especially in the case of expert systems and decision support systems the extension of this reasoning method to fuzzy theory however has never been considered in this paper the authors propose a definition of fuzzy backward reasoning based on the generalized modus ponens and show the necessity of considering interval valued fuzzy backward reasoning then the authors propose solving methods for fuzzy backward reasoning in the case of a rule with one or several conditions as well as in the case of several rules

inverse problem in fuzzy relational equations abstract the paper deals with the problem of handling fuzzy relational equations of the form x r y in the case of an empty solution set with respect to x x r y discussing the essence of the structure of the fuzzy relation r with respect to provided y algorithms have been proposed which enable us to modify the original equation i e the fuzzy set y in a way leading to its genuine solution or at least an approximate one it is explained how these modifications relax a set of constraints needed to be satisfied for any solvable equation a grade of the modification of the original problem is expressed in terms of distortion of the fuzzy set y which forms a cornerstone of the proposed procedures numerical examples are provided some aspects related to the area of diagnostic models in which these equations are studied are also treated

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

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

a new collocation method for solution of mixed linear integro differential difference equations numerical solution of mixed linear integro differential difference equation is presented using chebyshev collocation method the aim of this article is to present an efficient numerical procedure for solving mixed linear integro differential difference equations our method depends mainly on a chebyshev expansion approach this method transforms mixed linear integro differential difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system maple10

a new mechanical algorithm for solving the second kind of fredholm integral equation integral equation has been one of principal tool of various areas of applied mathematics physics and engineering in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of fredholm integral equation is established and a mechanical maple algorithm fredholmproc is established too the algorithm can provide the continuous solution of the second kind of fredholm integral equation ten examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for solving the integral equation

event based state estimation with time synchronous updates to reduce the amount of data transfer in networked systems measurements are usually taken only when an event occurs rather than at each synchronous sample instant however this complicates estimation problems considerably especially in the situation when no measurement is received anymore the goal of this paper is therefore to develop a state estimator that can successfully cope with event based measurements and attains an asymptotically bounded error covariance matrix to that extent a general mathematical description of event sampling is proposed this description is used to set up a state estimator with a hybrid update i e when an event occurs the estimated state is updated using the measurement while at synchronous instants the update is based on knowledge that the sensor value lies within a bounded subset of the measurement space furthermore to minimize computational complexity of the estimator the algorithm is implemented using a sum of gaussians approach the benefits of this implementation are demonstrated by an illustrative example of state estimation with event sampling

approximate solutions of fuzzy relational equations in the previous chs we have discussed various problems concerning solutions of fuzzy relation equations obviously an underlying assumption is that there exists a nonempty set of solutions a situation may occurr and indeed it is quite common in which no solution exists nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution this stream of investigations is particularly interesting for applicational purposes contrary to the topics already discussed in the previous chs this is a field of research which has not been developed enough so far it concerns studies on solvability properties of fuzzy relation equations in this ch we shall try to answer by using several techniques the following basic question how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

on the controllability and observability of networked dynamic systems some necessary and sufficient conditions are obtained for the controllability and observability of a networked system with linear time invariant lti dynamics the topology of this system is fixed but arbitrary and every subsystem is permitted to have different dynamics these conditions essentially depend only on transmission zeros of every subsystem and the subsystem connection matrix which makes them attractive in the analysis and synthesis of a large scale networked system as an application these conditions are utilized to characterize systems whose steady estimation accuracy with the distributed predictor of zhou 2013 is equal to that of the lumped kalman filter it has been made clear that to guarantee this equivalence the steady update gain matrix of the kalman filter must be block diagonal

regularized robust filters for time varying uncertain discrete time systems this note develops robust filters for time varying uncertain discrete time systems the developed filters are based on a data regularization solution and they enforce a minimum state error variance property simulation results confirm their superior performance over other robust filter designs

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

fuzzy modelling fundamentals construction and evaluation abstract the paper is devoted to fundamental aspects of fuzzy modelling namely modelling articulated with the use of methodology of fuzzy sets open issues are addressed which summarize advantages of fuzzy models and point out some methodological deficiencies blurring existing approaches the problem of relevancy of fuzzy models and its direct impact on a suitable interpretation of derived results is studied in detail finally we analyze some particular fuzzy models developed in terms of relational equations

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

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

a new algorithm for integral of trigonometric functions with mechanization in this paper by using the theories of mathematical analysis the authors systematically studied the problem of integrating of trigonometric functions utilizing omnipotence expressions tan x2 t a new integral algorithm for the integral of trigonometric functions was established and a new maple program trigint for the calculation mechanizing for the integral of trigonometric functions was established trigint could evaluate not only the integral of trigonometric functions utilizing omnipotence expresssions correctly but also all the other kinds of functions the results indicated that the algorithm established in this paper had advantages of simple idea excellent property for operation and powerful competence this would be useful for some calculating problems of engineering mathematics

comparison of fuzzy reasoning methods l a zadeh e h mamdani and m mizumoto et al have proposed methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition if x is a then y is b with a and b being fuzzy concepts mizumoto et al have investigated the properties of their methods in the case of generalized modus ponens this paper deals with the properties of their methods in the case of generalized modus tollens and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems finally the properties of syllogism and contrapositive are investigated under each fuzzy reasoning method

solvability of fuzzy relational equations and manipulation of fuzzy data abstract the problem of characterization of fuzzy relational equations with respect to their solvability property is studied some aspects of manipulation of fuzzy data with the aid of fuzzy relational equations are considered two stages of manipulation process are indicated combining pieces of evidence and inferring their mutual correspondence both of them are formulated and solved by the use of fuzzy relational equations the role of a solvability index is extensively studied numerical considerations give an illustration of the approach we propose and deal with some real data used for fuzzy controllers

robust filtering for linear time invariant continuous systems the problem of robust filtering for linear time invariant lti continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations and then in the state space domain the basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv contaminated model the general solution to the problem is given in the transfer function representation while in the polynomial framework the causal estimator is obtained by means of a spectral factorization and a diophantine equation the state space realization of the causal estimator is discussed examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty

mechanical algorithm for solving the second kind of volterra integral equation in this paper by using the theories and methods of mathematical analysis and computer algebra a reliable algorithm for solving the second kind of volterra integral equation is established and a new maple procedure voltproc is established too in particular the algorithm can provide the exact solution of the second kind of volterra integral equation by the methods of neumann series and mathematical induction i e the algorithm also can computing the nth term by finite terms of the iterative kernel some examples are presented to illustrate the efficiency and accuracy of the algorithm this will be useful for the integral equation solving and mathematical theorems automatic proving

computations of multi resultant with mechanization abstract resultant is a classical algebraic tool for determining whether or not a polynomial systems have a common root without explicitly solving for the roots but the complexity of resultants can be very high in practice in this paper by using the theories and methods of computer algebra two reliable algorithms for computing multi resultant problems dixon resultant and macaulay resultant were established two new maple procedures dixonres and macaulayres were established too some examples are presented to illustrate the implementations of the programs this would be useful for solving a system of polynomial equations

approximate optimal periodic scheduling of multiple sensors with constraints a constrained periodic multiple sensor scheduling problem is considered in this paper for each sensor constraints on dwell time and activation times are imposed at each time instant only one sensor can update its measurement with the estimator and the objective is to minimize the average state estimation error an approximation framework is proposed to calculate the objective function which transforms the original scheduling problem into an approximate optimal scheduling problem aosp an upper bound on the approximation error is presented to evaluate the performance of the framework to solve the aosp a necessary condition is first proposed on the optimal schedules when no constraints on activation times exist a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity when activation time constraints exist we show that the aosps can be solved by solving traveling salesman problems examples are provided to illustrate the proposed results

a new algorithm for the solution of nonlinear two dimensional volterra integro differential equations of high order abstract in this manuscript a new numerical approach is developed for approximating the solution of the one dimensional and two dimensional volterra integro differential equations 2d vides of high order new operational matrices of integration based on shifted jacobi polynomials are presented and used in combination with the collocation method to convert the 2d vide into a system of algebraic equations in addition the convergence analysis of the suggested approach is investigated the efficiency of the algorithm is demonstrated by means of several examples and the results are compared with those given using other numerical schemes

further relation equations with equality and difference composition operators in this ch we will introduce other composition operators which have a plausible logical interpretation they will be called equality and difference operator respectively we first define a notion of equality and difference of any two grades of membership of a fuzzy set and of a fuzzy relation in the sequel this concept will be utilized to form the respective composition operators and the related fuzzy equations afterwards we provide a method of resolution of these equations characterizing completely the set of the solutions all the fuzzy sets involved are defined on finite sets and with membership values in 0 1

computer aided solving the high order transition probability matrix of the finite markov chain in this paper by using theories of stochastic process and computer algebra a reliable algorithm for computing the high order transition probability matrix of finite markov chain is established a new mechanical procedure markovproc is established too the procedure markovproc give not only the exact expression of the markov chains but also the limiting probability some examples are presented to illustrate the implementation of the algorithm

a rule based method to calculate exactly the widest solution sets of a max min fuzzy relational inequality abstract in this paper we propose a rule based method to calculate exactly all the widest solution sets of a fuzzy relational inequality viewed as an extension of fuzzy relational equations fuzzy relational inequalities can be applied to many fields of fuzzy logic yet they provide with more flexibility as they enable to get rid of the sensitivity of fuzzy relational equations to numerical values up to now however fuzzy relational inequalities have received few attention from researchers and few methods have been proposed to solve these inequalities the proposed analytical methods furthermore do not calculate exactly all the widest solutions sets of a fuzzy relational inequality and often lead to redundant solution sets the rule based method we propose in this paper determines easily exactly all the widest solution sets of a fuzzy relational inequality