a note on the set theoretical defuzzification the set theoretic defuzzification sd method has been claimed to be a rational defuzzification method which is exclusively based on the fuzzy set theory j valente de oliveira fuzzy sets and systems 76 1995 63 however this paper shows the examples that the method is not applicable with general t norms and t conorms for normal fuzzy sets we show that the sd values of a normalized fuzzy set are located outside the support of the given fuzzy set with the min type t norm operator for non normal fuzzy sets we show that the defuzzification values of certain kinds of non normal fuzzy sets are unit value regardless of the support of the fuzzy set finally we show that the sd method does not satisfy two of three basic constraints for rational defuzzification operator which is proposed by runkler and glesner proc 2nd ieee internat conf on fuzzy systems p 1161

fuzzy risk analysis based on similarity measures of generalized fuzzy numbers in this paper we present a new method for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers firstly we present a method called the simple center of gravity method scgm to calculate the center of gravity cog points of generalized fuzzy numbers then we use the scgm to propose a new method to measure the degree of similarity between generalized fuzzy numbers the proposed similarity measure uses the scgm to calculate the cog points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers we also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures the proposed similarity measure can overcome the drawbacks of the existing methods we also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems the proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers opinions

average optimal singular control and a related stopping problem we observe a 2 brownian motion xt we can increase or decrease the value of the process paying r times the size of increase and l times the size of decrease holding costs are incurred continuously at a rate h zt where zt is the resulting process we consider a convex holding cost function h which is either finite everywhere or finite inside a finite interval and equal to infinity outside this interval the objective is to minimize average per unit of time expected cost it is shown that the optimal behavior is characterized by two constants a and b a b such that the optimal policy is to keep the process inside the interval a b with minimal efforts it is shown that to find the optimal interval a b one must solve a free boundary problem for the second order differential equation we give a probabilistic solution of the free boundary problem in terms of the value of a special game this game is a generalization of the optimal stopping problem there are two players observing the 2

a solvable one dimensional model of a diffusion inventory system we analyse the optimal ordering policy for impulse control of a one product inventory system subject to a demand modelised by a diffusion process the purpose is to minimize the expected discounted cost that includes a fixed set up cost and linear costs of purchase storage and shortage the optimal cost is explicitly obtained as the smoothest solution of a quasi variational inequality derived from the optimal principle of dynamic programming the optimal s s policy is determined as the unique solution of a system of algebraic equations

a proposal for a defuzzification strategy by the concept of sensitivity analysis abstract a systematic procedure is proposed for defuzzifying fuzzy subsets and interval values employing the concept of sensitivity analysis with a kind of minmax principle such that the defuzzification minimizes the sensitivity rating the discrepancy between a would be most appropriate defuzzified value and the unknown ideal value of defuzzification in the possible worst case a criterion of defuzzification can be built into the sensitivity to give a rationale to the defuzzified value as examples defuzzification with respect to a criterion of distance and minimization problems of two types of functions with fuzzy parameters are discussed

characterization of fuzzy measures constructed by means of triangular norms abstract following the ideas presented by the author e p klement j math anal appl 85 1982 543 565 finite t fuzzy measures are introduced t being a measurable triangular norm we show that a t fuzzy measure is always a fuzzy measure as considered earlier e p klement j math anal appl 25 1980 330 339 then we study the relation to the integral with respect to some classical measure finally for some special triangular norms t we give precise characterizations of the corresponding classes of t fuzzy measures

a unifying approach to defuzzification and comparison of the outputs of fuzzy controllers this paper addresses the defuzzification of the fuzzy set outputs of fuzzy controllers from a comparison or ranking perspective this is done by emphasizing the fuzzy controller as a decision making system based on the extensive study and justification of the fuzzy set comparison criteria that were developed and published elsewhere by the author a ranking and thus a defuzzification index is introduced this index is shown to overcome the disadvantages of the commonly used defuzzification methods whose attempted justifications based on probabilistic arguments have not been successful in addition the proposed index is based on the generalization of the hurwicz criterion that is usually adopted in decision making under nonprobabilistic uncertainty and it encompasses the pessimistic maximin and the optimistic maximax criteria as special cases

on the concept of possibility probability consistency both probability and possibility may be seen as information about an experiment it is conceivable to have at some time these two forms of information about a same experiment and then the question of the relation between them arises at once in this paper some aspects of the concept of possibility probability consistency are studied the consistency is considered as a fuzzy property relative to the coherence between possibilistic and probabilistic information we analyse several measures of the degree of consistency and introduce an axiomatic to characterize them

forecasting enrollments with fuzzy time series part ii abstract there have been a good many methods to forecast university enrollments in the literature however none of them could be applied when the historical data are linguistic values fuzzy time series is an effective tool to deal with such problems in this paper as an application of fuzzy time series in educational research the forecast of the enrollments of the university of alabama is carried out in so doing a fuzzy time series model is developed using historical data a complete procedure is proposed which includes fuzzifying the historical data developing a fuzzy time series model and calculating and interpreting the outputs to evaluate the forecasting model the robustness of the fuzzy time series model is tested advantages and problems of the forecasting method are also discussed

instantaneous control of brownian motion a controller continuously monitors a storage system such as an inventory or bank account whose content z zt t 0 fluctuates as a 2 brownian motion in the absence of control holding costs are incurred continuously at rate h zt at any time the controller may instantaneously increase the content of the system incurring a proportional cost of r times the size of the increase or decrease the content at a cost of l times the size of the decrease we consider the case where h is convex on a finite interval and h outside this interval the objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon it is shown that there exists an optimal control limit policy characterized by two parameters a and b a b roughly speaking this policy exerts the minimum amounts of control sufficient to keep zt a b for all t 0 put another way the optimal control limit policy imposes on z a lower reflecting barrier at a an

hybrid fuzzy least squares regression analysis and its relibabilty measures a method for hybrid fuzzy least squares regression is developed in this paper the method uses the new definition of weighted fuzzy arithmetic and the well accepted least squares fitting criterion first a bivariate regression model using asymmetrical triangular fuzzy variables is derived three sets of normal equations are formulated to solve the three parts of hybrid regression coefficients fuzzy center left fuzzy width and right fuzzy width then the method is extended to multiple regression analysis three numerical examples are used to demonstrate the proposed method two bivariate regression examples one for symmetrical triangular fuzzy numbers and the other for asymmetrical triangular fuzzy numbers and one multiple regression example for symmetrical triangular fuzzy numbers in each example hybrid regression equation and their reliability measures are calculated the results from hybrid regression are also compared with the corresponding results from ordinary regression and other fuzzy regression methods conclusions are drawn based on the reliability evaluations furthermore hybrid fuzzy least squares regression is extended to nonlinear models issues on the calibration of nonlinear equations and their reliability measures are also discussed in conclusions the merits and limitations of the proposed method are summarized

quantum control with piecewise constant control functions one of the long standing problems in the field of computational quantum control is to devise algorithms that converge to high yield controls with a desired structure particularly controls that can be reproduced by laboratory laser pulse shapers in this paper we propose an approach that is a considerable step forward toward the solution of this problem our treatment employs piecewise constant controls for these the concept of desired structure is addressed by including appropriate quadratic forms in the performance functionals thereafter correct extremal control equations are derived whereas the equations appearing in the literature are correct only to first or second order we illustrate numerically that our approach can give extremely high yield controls with a desired structure our results are valid not only in the context of quantum control but also for similiar bilinear systems arising in different areas in particular they are suitable for controlling linear flows with drift on unitary matrix groups

parametric representation of fuzzy numbers and application to fuzzy calculus we present several models to obtain simple parametric representations of the fuzzy numbers or intervals based on the use of piecewise monotonic functions of different forms the representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers we use the standard cuts setting but also the membership functions are obtained immediately and can be used directly to obtain error controlled approximations of the fuzzy calculus in terms of a finite set of parameters the general setting is the hermite type interpolation where the values and the slopes of the monotonic interpolators are given by appropriate parameters and the overall errors of the fuzzy computations can be controlled within a prefixed tolerance by eventually augmenting the total number of pieces and of the parameters by which the results are obtained the representations are designed to model the lower and the upper extremal values of each cut compact intervals of the fuzzy numbers and are able to produce almost any possible configuration differentiable continuous or with a finite number of discontinuity points by using parametric monotonic functions of different types we show applications in the standard fuzzy calculus and we stress the generality and the applicability of the proposed representation to a large class of problems including the numerical solution of fuzzy differential equations the fuzzy linear regression and the stochastic extensions of the fuzzy mathematics the proposed model is called the lower upper representation and we denote the associated fuzzy numbers or intervals as lu fuzzy

knowledge based defuzzification abstract we suggest a new approach to the problem of defuzzification this approach is a knowledge based approach in that it uses knowledge in terms of combinability function to help to more intelligently guide the defuzzification process this approach makes use of a view of the defuzzification process as a kind of clustering problem and uses the basic idea used in the mountain clustering method

defuzzification filters and applications to power system stabilization problems defuzzification is a very important step in fuzzy systems applications there are a number of different defuzzification methods reported in the literature in this paper the concept of defuzzification filters in a control system setting is first discussed and a methodology for designing such filters considered as will be seen the design of such filters requires the knowledge of the plant model and its inverse a reference control signal is computed and then is used to generate the actual defuzzified control signal which will be applied to control the plant the application of the defuzzification filter is made by introducing the filter into a power system in which a neuro fuzzy self learning controller was applied to stabilize the system but success could not always be guaranteed with the defuzzification filter however the system is always stabilized simulation results are presented

some properties of defuzzification neural networks abstract fuzzy systems have gained more and more attention from researchers and practitioners of various fields in such systems the output represented by a fuzzy set sometimes needs to be transformed into a scalar value and this task is known as the defuzzification process several analytic methods have been proposed for this problem but lately the neural network approach has been used for this purpose when employed as defuzzifiers a neural network is called a defuzzification neural network in this paper some preliminary results on properties of such defuzzification networks will be reported

applicability of the fuzzy operators in the design of fuzzy logic controllers a study of the different roles played by the fuzzy operators in fuzzy control is developed in this paper the behavior of a very large amount of fuzzy operators is analyzed and a comparison of the accuracy of many fuzzy logic controllers designed by means of these operators is carried out in order to do that a comparison methodology is defined and two fuzzy control applications are selected the inverted pendulum problem and the fuzzy modeling of the real curve y x

handling forecasting problems using fuzzy time series abstract in 6 9 song et al proposed fuzzy time series models to deal with forecasting problems in 10 sullivan and woodall reviewed the first order time invariant fuzzy time series model and the first order time variant model proposed by song and chissom 6 8 where the models are compared with each other and with a time invariant markov model using linguistic labels with probability distributions in this paper we propose a new method to forecast university enrollments where the historical enrollments of the university of alabama shown in 7 8 are used to illustrate the forecasting process the average forecasting errors and the time complexity of these methods are compared the proposed method is more efficient than the ones presented in 7 8 10 due to the fact that the proposed method simplifies the arithmetic operation process furthermore the average forecasting error of the proposed method is smaller than the ones presented in 2 7 8

monotonic parareal control for quantum systems following encouraging experimental results in quantum control numerical simulations have known significant improvements through the introduction of efficient optimization algorithms yet the computational cost still prevents using these procedures for high dimensional systems often present in quantum chemistry using parareal framework we present here a time parallelization of these schemes which allows us to reduce significantly their computational cost while still finding convenient controls

a simple method of forecasting based on fuzzy time series in fuzzy time series forecasting various methods have been developed to establish the fuzzy relations on time series data having linguistic values for forecasting the future values however the major problem in fuzzy time series forecasting is the accuracy in the forecasted values the present paper proposes a new method of fuzzy time series forecasting based on difference parameters the proposed method is a simplified computational approach for the forecasting the method has been implemented on the historical enrollment data of university of alabama adapted by song and chissom and the forecasted values have been compared with the results of the existing methods to show is superiority further the proposed method has also been implemented on a real life problem of crop production forecast of wheat crop and the results have been compared with other methods

a fuzzy linguistic approach to a multi criteria sequencing problem abstract in this paper a fuzzy approach to a single machine scheduling problem is considered in this approach the system s variables are defined using linguistic terms each of these variables may take values described via fuzzy triangular numbers the scheduling criteria are the common due date the total earliness and tardiness and the controllable duration of the jobs processing times the aim is to determine the length of the processing times to sequence the jobs in the machine and finally to determine the common due date in a near optimal way the problem is solved using an algorithmic procedure which is illustrated by means of an example

a set theoretical defuzzification method a defuzzification method coinciding with the result of the subsethood theorem and including a family of averaging methods like mean of maxima and center of gravity as special cases is presented the defuzzification method named subsethood defuzzification sd method has the advantage of being exclusively based on set theoretical operations giving thus an insight on the nature of the computations involved in one of the most controversial stages of the fuzzy controller architecture in addition the sd method allows its customization also in the aim of set theory customization is believed as a necessary feature as the defuzzification problem seems ill defined and application dependent

a robust method of forecasting based on fuzzy time series present study proposes an improved and versatile method of forecasting based on the concept fuzzy time series forecasting the developed model has been presented in a form of simple computational algorithms it utilizes various difference parameters being implemented on current state for forecasting the next state values to accommodate the possible vagueness in the data in a better way and making it a robust method the developed model has been implemented on the historical student enrollments data of university of alabama adapted by song and chissom and the obtained forecasted values have been compared with the existing methods to show its superiority the robustness of the model has also been tested in comparison the suitability of the developed model has also been examined in the crop production forecasting by implementing it on historical time series data of rice production of pantnagar farm india

optimality of an s s policy with compound poisson and diffusion demands a quasi variational inequalities approach we prove that an s s policy is optimal in a continuous review stochastic inventory model with a fixed ordering cost when the demand is a mixture of i a diffusion process and a compound poisson process with exponentially distributed jump sizes and ii a constant demand and a compound poisson process the proof uses the theory of impulse control the bellman equation of dynamic programming for such a problem reduces to a set of quasi variational inequalities qvi an analytical study of the qvi leads to showing the existence of an optimal policy as well as the optimality of an s s policy finally the combination of a diffusion and a general compound poisson demand is not completely solved we explain the difficulties and what remains open we also provide a numerical example for the general case

impulse control of brownian motion consider a storage system such as an inventory or cash fund whose content fluctuates as a 2 brownian motion in the absence of control holding costs are continuously incurred at a rate proportional to the storage level and we may cause the storage level to jump by any desired amount at any time except that the content must be kept nonnegative both positive and negative jumps entail fixed plus proportional costs and our objective is to minimize expected discounted costs over an infinite planning horizon a control band policy is one that enforces an upward jump to q whenever level zero is hit and enforces a downward jump to q whenever level s is hit 0 q q s we prove the existence of an optimal control band policy and calculate explicitly the optimal values of the critical numbers q q s

constructive solution of a bilinear optimal control problem for a schrodinger equation abstract often considered in numerical simulations related to the control of quantum systems the so called monotonic schemes have not been so far much studied from the functional analysis point of view yet these procedures provide an efficient constructive method for solving a certain class of optimal control problems this paper aims both at extending the results already available about these algorithms in the finite dimensional case i e the time discretized case and at completing those of the continuous case this paper starts with some results about the regularity of a functional related to a wide class of models in quantum chemistry these enable us to extend an inequality due to ojasiewicz to the infinite dimensional case finally some inequalities proving the cauchy character of the monotonic sequence are obtained followed by an estimation of the rate of convergence

a globalized newton method for the accurate solution of a dipole quantum control problem a theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nanoelectronic devices and quantum computing this method is based on a reduced hessian krylov newton scheme applied to a norm preserving discrete model of a dipole quantum control problem the use of second order numerical methods for solving the control problem is justified proving the existence of optimal solutions and analyzing first and second order optimality conditions criteria for the discretization of the nonconvex optimization problem and for the formulation of the hessian are given to ensure accurate gradients and a symmetric hessian robustness of the newton approach is obtained using a globalization strategy with a robust linesearch procedure results of numerical experiments demonstrate that the newton approach presented in this paper is able to provide fast and accurate controls for high energy state transitions

formulation and numerical solution of finite level quantum optimal control problems optimal control of finite level quantum systems is investigated and iterative solution schemes for the optimization of a control representing laser pulses are developed the purpose of this external field is to channel the system s wavefunction between given states in its most efficient way physically motivated constraints such as limited laser resources or population suppression of certain states are accounted for through an appropriately chosen cost functional first order necessary optimality conditions and second order sufficient optimality conditions are investigated for solving the optimal control problems a cascadic non linear conjugate gradient scheme and a monotonic scheme are discussed results of numerical experiments with a representative finite level quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches

fast and accurate center of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions in this article three methods are presented to perform the center of gravity cog defuzzification method in the context of linguistic fuzzy models with t norm based inference one well known method the discretisation method and two new methods the slope based method and the modified transformation function method the methods are worked out for trapezoidal membership functions forming a fuzzy partition in the sense of ruspini experimental results show that the newly introduced methods exhibit excellent accuracy at an extremely low computational cost compared to the widely applied discretisation method

optimal policies for brownian inventory systems with a piecewise linear ordering cost we consider a stochastic inventory system with general piecewise linear ordering cost the cumulative demand is modeled as a brownian motion process the ordering cost function is neither convex nor concave it may not be monotone and it is not even necessarily continuous and it includes most ordering cost functions studied in the literature e g economies of scale or dis economies of scale all unit discount or incremental discount and multiple setup costs as special cases in addition to ordering cost the system incurs the usual holding shortage cost and the objective is to minimize the average system cost per unit of time despite the complexity in the ordering cost function we show that an optimal control policy is very simple it is either an s s policy or a one sided singular control policy

a fourier method solution for the time dependent schrodinger equation as a tool in molecular dynamics a new method is presented for the solution of the time dependent schrbdinger equation in its application to physical and chemical molecular phenomena the method is based on discretizing space and time on a grid and using the fourier method to produce both spatial derivatives and second order differencing for time derivatives the method conserves norm and energy and preserves quantum mechanical commutation relations one and twodimensional examples where a comparison to analytic results is possible are investigated many phenomena of physics and chemistry have a common dynamical evolution pattern this pattern begins with an initial state which under the influence of the potentials evolves through time to produce a final asymptotic state among such phenomena are chemical reactions photodissociation unimolecular breakdown surface scattering and desorption the present study presents a numerical solution based on quantum mechanics for the common pattern or for the time dependent evolution of the state of the system the importance of exact numerical solutions is twofold first these solutions give a quantitative description of physical problems and also are of use as a bench mark to check approximation methods and to define their range of validity

a generalized α cut for a fixed value 0 1 we introduce the relation sharpness and a measure of fuzziness of fuzzy sets then we propose an approximation of a fuzzy set a by its generalized cut g a a generalized cut of a is a special type of fuzzy set that is sharper than a and less sharp than the crisp approximation of a by its ordinary cut a attention will be given to the generalized cuts of fuzzy numbers

aggregation operators and fuzzy systems modeling abstract a general class of aggregation operators called mica having the properties of monotonicity symmetry and an identity element are introduced we stress the significance of the choice of identity in characterizing the operator we show that the t norm and t conorm are special cases of these operators other classees of these operators are introduced notably an additive class which is very much in the spirit of the kind of aggregation used in neural networks it is shown how a general description of the fuzzy system modeling technique can be obtained using these operators

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

central values of fuzzy numbers defuzzification abstract axioms for defining a central value of a fuzzy set are developed various proposed central values are examined implications for defuzzification are discussed

impulse control of brownian motion the constrained average cost case when a manufacturer places repeated orders with a supplier to meet changing production requirements he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes we consider an inventory whose content fluctuates as a brownian motion in the absence of control at any moment a controller can adjust the inventory level by any positive or negative quantity but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment the inventory level must be nonnegative at all times and continuously incurs a linear holding cost the objective is to minimize long run average cost we show that control band policies are optimal for the average cost brownian control problem and explicitly calculate the parameters of the optimal control band policy this form of policy is described by three parameters q q s 0 q q s when the inventory falls to zero rises to s the controller expedites curtails shipments to return it to q q employing apparently new techniques based on methods of lagrangian relaxation we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level we also extend these results to the discounted cost problem

alpha cut representation used for defuzzification in rule based systems abstract alpha cut representation of fuzzy sets has been used as a basis for fuzzy numbers ranking in some applications but rarely used for defuzzification of rule based systems or fuzzy controllers moreover such alpha cut defuzzification called acd here is not yet formally linked to the membership function mf or to the common mf based defuzzification methods namely the centroid the acd can be considered as a generalisation of the similar algorithms in fuzzy numbers to any fuzzy set a close form formula for acd is developed that involves both mf and its derivative which shows that acd reflects both static and dynamic aspects of a fuzzy set moreover formal links between acd and some mf based defuzzification methods are shown through two groups of experiments the utility of the new method is compared with centroid defuzzification particularly we examined how the acd significantly outperforms the centroid for noisy time series prediction finally the computation complexity of acd is shown to be about the same as the centroid method for convex fuzzy sets our tests suggest that acd can be considered as a viable alternative defuzzification method for fuzzy system designers

fuzzy sets and statistical data abstract specific features of probability and possibility theories are discussed with emphasis on semantical aspects instead of putting forward the acknowledged usefulness of possibility theory for the non statistical modelling of subjective categories we try to figure out how statistical data and possibility theory could be matched as a result procedures for constructing weak possibilistic substitutes of probability measures and for processing imprecise statistical data are outlined they provide new insights on relationship between fuzzy sets and probability theories

a defuzzification method respecting the fuzzification abstract when designing a fuzzy controller the first thing to do is to choose input and output fuzzifications the next step consists of building the fuzzy rules table describing the behaviour of the controller finally in order to convert the fuzzy output in a usable form we need to select a defuzzification strategy this selection can be realized by testing one by one the defuzzification methods available in the literature and taking the best one in terms of output error however this approach is not theoretically convincing this selection can also be realized by considering the following logical criterion fuzzification and defuzzification are by nature two complementary processes in other words the choice of a defuzzification strategy must be made with respect to the output fuzzification in this paper we present a defuzzification method which takes into account the parameters of the fuzzification in order to respect it

optimal control of a brownian production inventory system with average cost criterion in this paper we study a stochastic production inventory system with finite production capacity and random demand the cumulative production and demand are modeled by a two dimensional brownian motion process there is a setup cost for switching on the production and a convex holding and shortage cost and our objective is to find the optimal production inventory control that minimizes the average cost both lost sales and backlog cases are studied for the lost sales model we show that within a large class of policies the optimal production strategy is either to produce according to an s s policy or never turn on the machine at all thus it is optimal for the firm to not enter the business whereas for the backlog model we prove that the optimal production policy is always of the s s type our approach first develops a lower bound for the average cost among a large class of nonanticipating policies and then shows that the value function of the desired policy reaches the lower bound the results offer insights on the structure of the optimal control policies as well as the interplays between system parameters

on a stochastic inventory model with a generalized holding costs this paper is concerned with finding the optimal replenishment policy for an inventory model that minimizes the total expected discounted costs over an infinite planning horizon the demand is assumed to be driven by a brownian motion with drift and the holding costs inventory and shortages are assumed to take some general form this generalizes the earlier work where holding costs were assumed linear it turns out that problem of finding the optimal replenishment schedule reduces to the problem of solving a quasi variational inequality problem qvi this qvi is then shown to lead to an s s policy where s and s are determined uniquely as a solution of some algebraic equations

fuzzy drive control of an autonomous mobile robot abstract this paper deals with the fuzzy drive control of an autonomous mobile robot first a fuzzy model fuzzy expert system for the human thought process is designed by using the idea of fuzziness and secondly it is applied to the autonomous mobile robot the autonomous mobile robot is being investigated very actively in many research laboratories of companies and universities around the world for example there are the unmanned automated carrier in a factory the working robot in extreme situations and the house service robot 1 3 a human makes a proper decision and puts the decision into a proper action instantly under fuzzy and insufficient information the fuzzy drive control system architecture is a hierarchy that is constructed by a visual sensor subsystem a motor drive unit and a fuzzy drive expert system which manages these subsystems the visual sensor subsystem which perceives the outer environment such as the road the obstacles etc is comprised of a tv camera and an image processing unit the motor drive unit motor controller has the function of controlling the speed and the steering of the mobile robot by changing the revolution rate of motors mounted on the robot the fuzzy drive expert system which is the core of the fuzzy drive control system recognizes the environment with the image data and sends control commands to the subsystems by these commands from the drive expert system each subsystem motivates the self subsisting control function to achieve that purpose this expert system has an inference unit and rules such as recognition rules and control rules which were obtained experimentally as an application of the fuzzy drive control experiments of driving an autonomous mobile robot on a straight road and one with corners are performed from the experimental results it was found that the robot control system has the faculty of flexible circumstantial decision about equal to what a human is able to realize

analytic properties of maximum entropy owa operators we discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging owa aggregation operator the resulting weights are called the meowa weights using the method of lagrange multipliers we obtain an analytic form for these weights and describe some of their properties the concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker s degree of optimism this transformation which is affected by an owa operator is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the meowa weights

some numerical aspects of center of area defuzzification method this paper deals with center of area or gravity defuzzification method via a computationally attractive method called transformation function method it is shown that the proposed method enormously reduces number of mathematical operations and amount of memory space required to compute defuzzified value moreover the computational superiority of transformation function method over the conventional numerical technique is also shown

a characterization of a general class of ranking functions on triangular fuzzy numbers this paper aims to the discussion of properties for ranking fuzzy numbers an approach of axiomatic type is followed providing the definition of two groups of requirements which characterize a ranking function through its behaviour on triangular fuzzy numbers particularly the problem of making the evaluations on triangular fuzzy numbers sensitive to their spread has been deeply analyzed

combustion control of refuse incineration plant by fuzzy logic abstract refuse incineration plant operations involve many kinds of uncertain factors such as the variable physical properties of refuse as fuel and the complexity of the burning phenomenon that makes it very difficult to apply conventional control methods to the combustion control of the refuse this paper describes a fuzzy control system for the refuse combustion process which applies sensing and controlling rules of skilled operators from a simulation analysis and some test runs on an actual incineration plant it is concluded that the fuzzy control system is effective and practical toward plant automation

on the controllability of quantum mechanical systems the systems theoretic concept of controllability is elaborated for quantum mechanical systems sufficient conditions being sought under which the state vector can be guided in time to a chosen point in the hilbert space h of the system the schrodinger equation for a quantum object influenced by adjustable external fields provides a state evolution equation which is linear in and linear in the external controls thus a bilinear control system for such systems the existence of a dense analytic domain d in the sense of nelson together with the assumption that the lie algebra associated with the system dynamics gives rise to a tangent space of constant finite dimension permits the adaptation of the geometric approach developed for finite dimensional bilinear and nonlinear control systems conditions are derived for global controllability on the intersection of d with a suitably defined finite dimensional submanifold of the unit sphere sh in h several soluble examples are presented to illuminate th

adaptive learning defuzzification techniques and applications abstract in this paper adaptive learning defuzzification techniques are studied under the consideration of system performance indices by treating defuzzification processes as continuous mappings from space 0 1 n to the real line the concept of the optimal defuzzification mapping can be developed since all the continuous defuzzification mappings considered in this paper form a banach space approximation to the optimal mapping with some known functions can be expressed as the parametric optimization problem to find the optimal parameters adaptive learning of the optimal defuzzification mapping is investigated learning laws for the parameters in the defuzzification mapping are derived in one case numerical results indicate that the adaptive learning defuzzification method can give superior defuzzification results to some popular defuzzification methods

median alpha levels of a fuzzy number three median alpha levels of a fuzzy number a are introduced two of them are based on the vertical and horizontal dimensions of a one on the cardinality of a approximation of fuzzy numbers by alpha cuts associated with the median alpha levels is discussed percentile characterizations of alpha cuts with respect to the selected properties of fuzzy numbers are proposed

monotonic time discretized schemes in quantum control most of the numerical simulations in quantum bilinear control have used monotonically convergent algorithms of krotov introduced by tannor et al 15 of zhu rabitz 16 or their unified formulation in 17 however the properties of the discrete version of these procedures have not been yet tackled with we present in this paper a stable time and space discretization which preserves the monotonic properties of the monotonic algorithms numerical results show that the newly derived algorithms are stable and enable various experimentations

optimal bilinear control of an abstract schro dinger equation well posedness of abstract quantum mechanical systems is considered and the existence of optimal control of such systems is proved first order optimality systems are derived convergence of the monotone scheme for the solution of the optimality system is proved

optimal quantum control by an adapted coordinate ascent algorithm this paper explores an adaption of the coordinate ascent approach to quantum control problems it was motivated by the observation that several of the existing monotone converging schemes for quantum control may be viewed as approximations of the well known coordinate ascent method our implementation employs line searches in coordinate directions in control space using only evaluations of the performance functional without invoking its derivatives it is based on recasting the performance functional as a local tracking function which gives the future quality of a control at each moment in time back propagation of a basis of the target space enables these performance functional i e tracking function evaluations to be done efficiently the performance functional may include or not include regularization terms as needed convergence of the resulting algorithm and its relation to previous schemes are discussed and numerical examples are provided in our tests the coordinate ascent algorithm exhib

simultaneous solution of fuzzy models an application to economic equilibrium analysis abstract the fuzzy modeling technology which uses a rule based description of the relationship between variables is discussed we then turn to the problem of the simultaneous solution of relationships involving fuzzy models we illustrate this problem by considering the equilibrium problem in economics in this case we have two relationships one between price and supply and the other between price and demand and we desire to find the price for which the supply equals the demand it is shown that if the fuzzy models have antecedent fuzzy sets which are of the trapezoidal triangular type then a solution technique can be found

on the issue of defuzzification and selection based on a fuzzy set abstract we are concerned with the problem of selecting a crisp element based on information provided by a fuzzy set a problem which manifests itself in the defuzzification step in fuzzy logic controllers we provide a unifying approach to this selection process among other characteristics this unification puts the defuzzification methods of mean of maxima and center of gravity in the same framework we show that this selection can be viewed as a three step operation transformation of the decision fuzzy set normalization to probability distribution selection based on the probability distribution a number of different procedures for selection are discussed

generalizing the modeling of fuzzy logic controllers by parameterized aggregation operators abstract we describe the type of reasoning used in the typical fuzzy logic controller the mamdani reasoning method we point out the basic assumptions in this model we discuss the s owa operators which provide families of parameterized andlike and orlike operators we generalize the mamdani model by introducing these operators we introduce a method which we call direct fuzzy reasoning dfr which results from one choice of the parameters we develop some learning algorithms for the new method we show how the takagi sugeno kang tsk method of reasoning is an example of this dfr method

a trainable transparent universal approximator for defuzzification in mamdani type neuro fuzzy controllers a novel technique of designing application specific defuzzification strategies with neural learning is presented the proposed neural architecture considered as a universal defuzzification approximator is validated by showing the convergence when approximating several existing defuzzification strategies the method is successfully tested with fuzzy controlled reverse driving of a model truck the transparent structure of the universal defuzzification approximator allows us to analyze the generated customized defuzzification method using the existing theories of defuzzification the integration of universal defuzzification approximator instead of traditional methods in mamdani type fuzzy controllers can also be considered as an addition of trainable nonlinear noise to the output of the fuzzy rule inference before calculating the defuzzified crisp output therefore nonlinear noise trained specifically for a given application shows a grade of confidence on the rule base providing an additional opportunity to measure the quality of the fuzzy rule base the possibility of modeling a mamdani type fuzzy controller as a feedforward neural network with the ability of gradient descent training of the universal defuzzification approximator and antecedent membership functions fulfil the requirement known from multilayer preceptrons in finding solutions to nonlinear separable problems

slide a simple adaptive defuzzification method we introduce a parameterized family of defuznfica tion operators called the semi linear defuzzification slide method this method is based upon a simple transformation of the fuzzy output set of the controller we suggest an algorithm for the learning of the parameter from a data set in an attempt to simplify the parameter learning we suggest a modified version of the slide method which results in a simple learning algorithm the development of the learning algorithm is based upon the use of the kalman filter n fuzzy logic control systems l 2 the defuzzification i step involves the selection of one value as the output of the controller more specifically starting with a fuzzy subset possibility distribution f over the output space x of the controller the defuzzification step uses this fuzzy subset to select a representative element x the two most often used methods of defuzzification found in the literature are the center of area coa and mean of maxima mom 3 6 methods we recall that the mom method takes as its defuzzified value the mean of the elements that attain the maximum membership grade in f the coa method takes as its defuzzified value d ci ui xi where ui f xi cj f xj in 7 and 8 we formulated a general defuzzification method via basic defuzzification distribution badd transformations the main idea of this badd approach is to transform the possibility distribution f into a probability distribution p and then the defuzzified value is the expected value of the probability distribution the process of transforming f into p was seen as a two step process the first step was to transform f into a new possibility distribution e and then to normalize e to obtain p the step of obtaining e from f involved the use of a badd transformation in which e xi f z where 6 e o co it was shown in 7 that the generalized badd method implies the coa and mom methods as special cases in particular the coa method is obtained for a 1 and the mom is obtained for 6 00 when s 0 we get a defuzzified value that is the unweighted mean of the output space d xi xi the badd transformation has the advantage of being based on a single parameter which allows us the potential of adaptively learning the best method of defuzzification for a given controller while the family of all defuzzified values that can be obtained by the generalized badd defuzzification method was parameterized an undesirable property of the method was the nonlinear

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach

application of fuzzy naive bayes and a real valued genetic algorithm in identification of fuzzy model we present a method to identify a fuzzy model from data by using the fuzzy naive bayes and a real valued genetic algorithm the identification of a fuzzy model is comprised of the extraction of if then rules that is followed by the estimation of their parameters the involved parameters include those which determine the membership function of fuzzy sets and the certainty factors of fuzzy if then rules in our method as long as the fuzzy partition in the input output space is given the certainty factor of each rule is computed with the fuzzy conditional probability of the consequent conditioned on the antecedent by using the fuzzy naive bayes which is a generalization of naive bayes the fuzzy model involves the rules characterized by the highest values of certainty factors the certainty factor of each rule is the fuzzy conditional probability and it reflects the inner relationship between the antecedent and the consequent in order to improve the accuracy of the fuzzy model the real valued genetic algorithm is incorporated into our identification process this process concerns the optimization of the membership functions occurring in the rules we just involve the parameters of membership function of the fuzzy sets into the real valued genetic algorithm since the certainty factor of each rule can be computed automatically the performance of the model is shown for the backing truck problem and the prediction of mackey glass time series

an adaptive approach to defuzzification based on level sets abstract we look at the process of defuzzification used in fuzzy logic controllers we provide a parametrized formulation for this procedure based upon the use of level sets which we call generalized level set defuzzification we show that the commonly used defuzzification procedures mean of maxima and center of area are special cases of this general procedure and are simply distinguished by the choice of the parameter we provide a simple algorithm for adaptive choice of the best defuzzification procedure

handling the nonlinearity of a fuzzy logic controller at the transition between rules abstract a fuzzy logic controller approximates a desired control surface by using the outputs of its fuzzy control rules the shape of this control surface is mainly influenced by the linguistic variables of the rule base the basic operators of the fuzzy sets the implication the inference and the defuzzification method the linearity nonlinearity of this control surface is discussed in many studies however none of those studies has explicitly considered the linearity nonlinearity at the transition between fuzzy logic rules in this paper a simple approach to control the linearity nonlinearity at this transition by a modified center of gravity defuzzification method is proposed namely by introducing the so called defuzzification weights to the overlapping areas of the consequent those defuzzification weights can be determined heuristically or automatically both cases will be demonstrated for the latter a feedforward neural network is employed