the riemann problem for reversible reactive flows with metastability a hyperbolic model for dynamic phase transitions is studied the model involves three phases liquid vapor and a mixture of them metastable regions are present both in the liquid and in the vapor phase results on the behavior of traveling wave profiles of the model involving viscosity species diffusion and relaxation are obtained these behaviors are consistent with physical intuitions admissibility criteria kinetic relations that mimic the behavior of traveling wave profiles are then proposed admissible basic waves of the model are liquefaction evaporation and isobaric waves in addition to lax shock and rarefaction waves based on these waves solutions of the riemann problem for the model are constructed for general riemann initial data most of the physical phenomena are embodied in the solver for some riemann initial data solutions are expected to be nonunique which solutions actually appear depends on whether nucleation already occurred or not the model admits both solutions as it sh

a vectorization optimization method based type 2 fuzzy neural network for noisy data classification this paper proposes a vectorization optimization method vom based type 2 fuzzy neural network vom2fnn for noisy data classification in handling problems with uncertainties such as noisy data type 2 fuzzy systems usually outperform their type 1 counterparts hence type 2 fuzzy sets are adopted in the antecedent parts to model the uncertainty to consider the classification problems the discriminative capability is crucial to determine the performance therefore a vom is proposed in the consequent parts to increase the discriminability and reduce the parameters compared with other existing fuzzy neural networks the novelty of the proposed vom2fnn is its consideration of both uncertainty and discriminability the effectiveness of the proposed vom2fnn is demonstrated by three classification problems experimental results and theoretical analysis indicate that the proposed vom2fnn performs better than the other fuzzy neural networks

sonic hyperbolic phase transitions and chapman jouguet detonations abstract we prove that the cauchy problem for an n n system of strictly hyperbolic conservation laws in one space dimension admits a weak global solution also in presence of sonic phase boundaries applications to chapman jouguet detonations liquid vapor transitions and elastodynamics are considered

radial basis function based adaptive fuzzy systems and their applications to system identification and prediction abstract in this paper we describe a neuro fuzzy system with adaptive capability to extract fuzzy if then rules from input and output sample data through learning the proposed system called radial basis function rbf based adaptive fuzzy system afs employs the gaussian functions to represent the membership functions of the premise part of fuzzy rules three architectural deviations of the rbf based afs are also presented according to different consequence types such as constant first order linear function and fuzzy variable these provide versatility of the network to handle arbitrary fuzzy inference schemes we present examples of system identification and time series prediction to illustrate how to solve these problems and to demonstrate its validity and effectiveness using the rbf based afs

a fuzzy model with online incremental svm and margin selective gradient descent learning for classification problems this paper proposes a new incremental learning approach to endow a takagi sugeno type fuzzy classification model with high generalization ability the proposed fuzzy model is learned through incremental support vector machine svm and margin selected gradient descent learning and is called fm3 in this learning approach training samples are fed incrementally one by one instead of all in one batch the fm3 evolves from an empty rule set a one pass clustering algorithm is used to determine the number of rules and initial fuzzy sets in the rule antecedent part an online incremental linear svm is proposed to tune the rule consequent parameters to endow the fm3 with high generalization ability the use of incremental instead of batch svm enables the fm3 to handle online training problems with only one new sample available at a time for antecedent parameter learning a margin selected gradient descent algorithm is proposed to prevent overtraining simulation results and comparisons with svms and fuzzy classifiers with different learning algorithms demonstrate the advantage of the fm3

fuzzy wavelet neural network models for prediction and identification of dynamical systems this paper presents fuzzy wavelet neural network fwnn models for prediction and identification of nonlinear dynamical systems the proposed fwnn models are obtained from the traditional takagi sugeno kang fuzzy system by replacing the then part of fuzzy rules with wavelet basis functions that have the ability to localize both in time and frequency domains the first and last model use summation and multiplication of dilated and translated versions of single dimensional wavelet basis functions respectively and in the second model then parts of the rules consist of radial function of wavelets gaussian type of activation functions are used in if part of the fuzzy rules a fast gradient based training algorithm i e the broyden fletcher goldfarb shanno method is used to find the optimal values for unknown parameters of the fwnn models simulation examples are also given to compare the effectiveness of the models with the other known methods in the literature according to simulation results we see that the proposed fwnn models have impressive generalization ability

evolving type 2 fuzzy classifier evolving fuzzy classifiers efcs have achieved immense success in dealing with nonstationary data streams because of their flexible characteristics nonetheless most real world data streams feature highly uncertain characteristics which cannot be handled by the type 1 efc a novel interval type 2 fuzzy classifier namely evolving type 2 classifier et2class is proposed in this paper which constructs an evolving working principle in the framework of interval type 2 fuzzy system the et2class commences its learning process from scratch with an empty or initially trained rule base and its fuzzy rules can be automatically grown pruned recalled and merged on the fly referring to summarization power and generalization power of data streams in addition the et2class is driven by a generalized interval type 2 fuzzy rule where the premise part is composed of the multivariate gaussian function with an uncertain nondiagonal covariance matrix while employing a subset of the nonlinear chebyshev polynomial as the rule consequents the efficacy of the et2class has been rigorously assessed by numerous real world and artificial study cases benchmarked against state of the art classifiers and validated through various statistical tests our numerical results demonstrate that the et2class produces more reliable classification rates while retaining more compact and parsimonious rule base than state of the art efcs recently published in the literature

recursive utility for stochastic trees stochastic trees are semi markov processes represented using tree diagrams such trees have been found useful for prescriptive modeling of temporal medical treatment choice we consider utility functions over stochastic trees which permit recursive evaluation in a graphically intuitive manner analogous to decision tree rollback such rollback is computationally intractable unless a low dimensional preference summary exists we present the most general classes of utility functions having specific tractable preference summaries we examine three preference summaries memoryless markovian and semi markovian which promise both computational feasibility and convenience in assessment their use is illustrated by application to a previous medical decision analysis of whether to perform carotid endarterectomy

discrete time credibilistic processes construction and convergences in this paper we discuss a method of constructing a credibilistic process which is a family of fuzzy variables on credibility space applying the extension theorem in credibility theory the finite or infinite horizon credibilistic process is made up from a family of credibilistic kernels also for the markov case convergence theorems are given and credibilistic risk models for reward processes are considered whose risk is completed by the recursive equation

stochastic shortest path problems with associative accumulative criteria we consider a stochastic shortest path problem with associative criteria in which for each node of a graph we choose a probability distribution over the set of successor nodes so as to reach a given target node optimally we formulate such a problem as an associative markov decision processes we show that an optimal value function is a unique solution to an optimality equation and find an optimal stationary policy also we give a value iteration method and a policy improvement method

computing derivatives in interval type 2 fuzzy logic systems this paper makes type 2 fuzzy logic systems much more accessible to fuzzy logic system designers because it provides mathematical formulas and computational flowcharts for computing the derivatives that are needed to implement steepest descent parameter tuning algorithms for such systems it explains why computing such derivatives is much more challenging than it is for a type 1 fuzzy logic system it provides derivative calculations that are applicable to any kind of type 2 membership functions since the calculations are performed without prespecifying the nature of those membership functions some calculations are then illustrated for specific type 2 membership functions

regularity and large time behaviour of solutions of a conservation law without convexity a l aide de la methode des caracteristiques generalisees on etudie la regularite et le comportement a grand des solutions faibles admissibles d une seule loi de conservation a 1 variable d espace avec un point d inflexion

fuzzy modeling of high dimensional systems complexity reduction and interpretability improvement fuzzy modeling of high dimensional systems is a challenging topic this paper proposes an effective approach to data based fuzzy modeling of high dimensional systems an initial fuzzy rule system is generated based on the conclusion that optimal fuzzy rules cover extrema redundant rules are removed based on a fuzzy similarity measure then the structure and parameters of the fuzzy system are optimized using a genetic algorithm and the gradient method during optimization rules that have a very low firing strength are deleted finally interpretability of the fuzzy system is improved by fine training the fuzzy rules with regularization the resulting fuzzy system generated by this method has the following distinct features 1 the fuzzy system is quite simplified 2 the fuzzy system is interpretable and 3 the dependencies between the inputs and the output are clearly shown this method has successfully been applied to a system that has 11 inputs and one output with 20 000 training data and 80 000 test data

narmax time series model prediction feedforward and recurrent fuzzy neural network approaches the nonlinear autoregressive moving average with exogenous inputs narmax model provides a powerful representation for time series analysis modeling and prediction due to its capability of accommodating the dynamic complex and nonlinear nature of real world time series prediction problems this paper focuses on the modeling and prediction of narmax model based time series using the fuzzy neural network fnn methodology both feedforward and recurrent fnns approaches are proposed furthermore an efficient algorithm for model structure determination and parameter identification with the aim of producing improved predictive performance for narmax time series models is developed experiments and comparative studies demonstrate that the proposed fnn approaches can effectively learn complex temporal sequences in an adaptive way and they outperform some well known existing methods

markov decision problems where means bound variances we identify a rich class of finite horizon markov decision problems mdps for which the variance of the optimal total reward can be bounded by a simple linear function of its expected value the class is characterized by three natural properties reward nonnegativity and boundedness existence of a do nothing action and optimal action monotonicity these properties are commonly present and typically easy to check implications of the class properties and of the variance bound are illustrated by examples of mdps from operations research operations management financial engineering and combinatorial optimization

smooth and discontinuous junctions in the p system abstract consider the p system describing the subsonic flow of a fluid in a pipe with section a a x we prove that the resulting cauchy problem generates a lipschitz semigroup provided the total variation of the initial datum and the oscillation of a are small an explicit estimate on the bound of the total variation of a is provided showing that at lower fluid speeds higher total variations of a are acceptable an example shows that the bound on tv a is mandatory for otherwise the total variation of the solution may grow arbitrarily

mean variance tradeoffs in an undiscounted mdp the unichain case the problem analyzed here is the computation of pareto optima in the sense of high mean and low variance of the stationary distribution in the unichain undiscounted markov decision process mdp for short

introducing validity into self organizing fuzzy neural network applied to impedance force control abstract in this paper a novel self organizing fuzzy neural network is proposed that constructed by an input output mapping and monitored by a hierarchy of validity degrees we define new operators called validification and devalidification to propagate validity into the six layers of proposed architecture self organizing in structure learning is accomplished through a new measure that depends on error the number of rules and validity degrees additionally a parameter learning condition is derived through studying the stability of proposed approach to evaluate the proposed approach an impedance controller is designed facing three challenges different kinds of uncertainty partial truth and real time realization in the proposed controller considering the challenge of partial truth we assume that the manipulator s inertia is known according to first principle knowledge while other parts are uncertain simulation results show the effectiveness of the proposed approach in the presence of disturbance the proposed approach emerges as a promising approach by involving self organizing property and possibility fuzzy and validity aspects of information

automatic construction of feedforward recurrent fuzzy systems by clustering aided simplex particle swarm optimization this paper proposes a new approach for automating the structure and parameter learning of fuzzy systems by clustering aided simplex particle swarm optimization called cspso unlike most evolutionary fuzzy systems where the structure of the fuzzy system is assigned in advance an on line fuzzy clustering approach is proposed for system structure learning this structure learning not only helps determine the number of rules automatically but also avoids the generation of highly similar fuzzy sets on each input variable in addition it improves subsequent parameter learning performance by assigning suitable initial locations of the fuzzy sets on each input variable once a new rule is generated the corresponding parameters are further tuned by the hybrid of the simplex method and particle swarm optimization pso in cspso each fuzzy system corresponds to a particle in pso and the idea of the simplex method is incorporated to improve pso searching performance to verify the performance of cspso two simulations on feedforward fuzzy systems design are performed in addition design of a recurrent fuzzy controller for a practical experiment on water bath temperature control is performed comparisons with other design approaches are also made in these examples

reduced interval type 2 neural fuzzy system using weighted bound set boundary operation for computation speedup and chip implementation this paper proposes a reduced interval type 2 neural fuzzy system using weighted bound set boundaries rit2nfs wb for the simplification of type reduction operations the objective of this simplification is to reduce the system training time in software implementation and chip size in hardware implementation especially when the number of rules is large the antecedent part in the rit2nfs wb uses interval type 2 fuzzy sets it2fss and the consequent part can be of the takagi sugeno kang tsk or mamdani type the rit2nfs wb is built through an online structure and parameter learning to improve model accuracy in addition the interpretability of the rit2nfs wb is improved by considering distributions of the it2fss in input variables a distinguishability oriented cost function is used in parameter learning to generate distinguishable it2fss and improve semantics based interpretability for highly overlapped it2fss they are merged to reduce the number of it2fss and improve complexity based interpretability the software implemented tsk type rit2nfs wb is hardware implemented on a field programmable gate array chip to accelerate the chip execution speed the chip utilizes not only the parallel execution properties of fuzzy rules and bound set boundaries but the pipeline technique as well in particular the flexibility of the chip is considered so that no redesign of the circuits is required when the rit2nfs wb is applied to different problems the characteristics of the software and hardware implemented rit2nfs wb are verified through various examples and comparisons with various type 1 and interval type 2 fuzzy models

risk sensitive optimal control of hidden markov models structural results the authors consider a risk sensitive optimal control problem for finite state and action spaces hidden markov models hmm they present results of an investigation on the nature and structure of risk sensitive controllers for hmm several general structural results are presented as well as a particular case study of a popular benchmark problem for the latter they obtain structural results for the optimal risk sensitive controller and compare it to that of the risk neutral controller furthermore they show that indeed the risk sensitive controller and its corresponding information state converge to the known solutions for the risk neutral situation as the risk factor goes to zero they also study the infinite and general risk aversion cases

global well posedness of traffic flow models with phase transitions abstract this note is devoted to the study of traffic flow models that develop phase transitions from the analytical point of view this is a first example of a well posedness result for conservation laws developing phase transitions which is independent from the number of phase boundaries in the initial data or in the solutions we consider below the cauchy problem as well as the problem with boundaries

a mutually recurrent interval type 2 neural fuzzy system mrit2nfs with self evolving structure and parameters in this paper a mutually recurrent interval type 2 neural fuzzy system mrit2nfs is proposed for the identification of nonlinear and time varying systems the mrit2nfs uses type 2 fuzzy sets in order to enhance noise tolerance of the system in the mrit2nfs the antecedent part of each recurrent fuzzy rule is defined using interval type 2 fuzzy sets and the consequent part is of the takagi sugeno kang type with interval weights the antecedent part of mrit2nfs forms a local internal feedback and interaction loop by feeding the rule firing strength of each rule to others including itself the consequent is a linear combination of exogenous input variables the learning of mrit2nfs starts with an empty rule base and all rules are learned online via structure and parameter learning the structure learning of mrit2nfs uses online type 2 fuzzy clustering for parameter learning the consequent part parameters are tuned by rule ordered kalman filter algorithm to reinforce parameter learning ability the type 2 fuzzy sets in the antecedent and weights representing the mutual feedback are learned by the gradient descent algorithm after the training a weight elimination scheme eliminates feedback connections that do not have much effect on the network behavior this method can efficiently remove redundant recurrence and interaction weights finally the mrit2nfs is used for system identification under both noise free and noisy environments for this we consider both time series prediction and nonlinear plant modeling compared with type 1 recurrent fuzzy neural networks simulation results show that our approach produces smaller root mean squared errors using the same number of iterations

risk averse control of undiscounted transient markov models we use markov risk measures to formulate a risk averse version of the undiscounted total cost problem for a transient controlled markov process using the new concept of a multikernel we derive conditions for a system to be risk transient that is to have finite risk over an infinite time horizon we derive risk averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations we illustrate the results on an optimal stopping problem and an organ transplantation problem

kinetic stabilization of a nonlinear sonic phase boundary we consider a system arising in the study of phase transitions in elastodynamics a system of two conservation laws in a single space dimension the system has two hyperbolic regions with an elliptic zone in between a phase boundary is a strong discontinuity in a solution with left and right states belonging to different hyperbolic regions we call such a solution a phase wave

admissible riemann solvers for genuinely nonlinear p systems of mixed type abstract we consider in this paper the riemann problem for p systems of mixed type that define two hyperbolic phases with a stress function satisfying general genuinely nonlinear hypotheses we describe here all the global riemann solvers that are continuous for the l 1 distance with respect to initial data while conserving the natural symmetry properties of the p system and coinciding with the lax solution when defined these riemann solvers can be described entirely by a kinetic function used to select a manifold of subsonic phase transitions and a corresponding set of supersonic phase transitions

optimal policy for minimizing risk models in markov decision processes we consider the minimizing risk problems in discounted markov decisions processes with countable state space and bounded general rewards we characterize optimal values for finite and infinite horizon cases and give two sufficient conditions for the existence of an optimal policy in an infinite horizon case these conditions are closely connected with lemma 3 in white 1993 which is not correct as wu and lin 1999 point out we obtain a condition for the lemma to be true under which we show that there is an optimal policy under another condition we show that an optimal value is a unique solution to some optimality equation and there is an optimal policy on a transient set

equalization of nonlinear time varying channels using type 2 fuzzy adaptive filters presents a kind of adaptive filter type 2 fuzzy adaptive filter faf one that is realized using an unnormalized type 2 takagi sugeno kang tsk fuzzy logic system fls we apply this filter to equalization of a nonlinear time varying channel and demonstrate that it can implement the bayesian equalizer for such a channel has a simple structure and provides fast inference a clustering method is used to adaptively design the parameters of the faf two structures are used for the equalizer transversal equalizer te and decision feedback equalizer dfe a decision tree structure is used to implement the decision feedback equalizer in which each leaf of the tree is a type 2 faf this dfe vastly reduces computational complexity as compared to a te simulation results show that equalizers based on type 2 fafs perform much better than nearest neighbor classifiers nnc or equalizers based on type 1 fafs

multi objective hierarchical genetic algorithm for interpretable fuzzy rule based knowledge extraction a new scheme based on multi objective hierarchical genetic algorithm mohga is proposed to extract interpretable rule based knowledge from data the approach is derived from the use of multiple objective genetic algorithm moga where the genes of the chromosome are arranged into control genes and parameter genes these genes are in a hierarchical form so that the control genes can manipulate the parameter genes in a more effective manner the effectiveness of this chromosome formulation enables the fuzzy sets and rules to be optimally reduced some important concepts about the interpretability are introduced and the fitness function in the moga will consider both the accuracy and interpretability of the fuzzy model in order to remove the redundancy of the rule base proactively we further apply an interpretability driven simplification method to newborn individuals in our approach we first apply the fuzzy clustering to generate an initial rule based model then the multi objective hierarchical genetic algorithm and the recursive least square method are used to obtain the optimized fuzzy models the accuracy and the interpretability of fuzzy models derived by this approach are studied and presented in this paper we compare our work with other methods reported in the literature on four examples a synthetic nonlinear dynamic system a nonlinear static system the lorenz system and the mackey glass system simulation results show that the proposed approach is effective and practical in knowledge extraction

optimal threshold probability and expectation in semi markov decision processes we consider undiscounted semi markov decision process with a target set and our main concern is a problem minimizing threshold probability we formulate the problem as an infinite horizon case with a recurrent class we show that an optimal value function is a unique solution to an optimality equation and there exists a stationary optimal policy also several value iteration methods and a policy improvement method are given in our model furthermore we investigate a relationship between threshold probabilities and expectations for total rewards

multiobjective programming for type 2 hierarchical fuzzy inference trees this paper proposes a design of hierarchical fuzzy inference tree hfit an hfit produces an optimum tree like structure i e a natural hierarchical structure that accommodates simplicity by combining several low dimensional fuzzy inference systems fiss such a natural hierarchical structure provides a high degree of approximation accuracy the construction of the hfit takes place in two phases first a nondominated sorting based multiobjective genetic programming mogp is applied to obtain a simple tree structure a low complexity model with a high accuracy second the differential evolution algorithm is applied to optimize the obtained tree s parameters in the derived tree each node acquires a different input s combination where the evolutionary process governs the input s combination hence hfit nodes are heterogeneous in nature which leads to a high diversity among the rules generated by the hfit additionally the hfit provides an automatic feature selection because it uses mogp for the tree s structural optimization that accepts inputs only relevant to the knowledge contained in data the hfit was studied in the context of both type 1 and type 2 fiss and its performance was evaluated through six application problems moreover the proposed multiobjective hfit was compared both theoretically and empirically with recently proposed fiss methods from the literature such as mcit2fis tscit2fnn sit2fnn rit2fns wb et2fis mrit2nfs it2fnn svr etc from the obtained results it was found that the hfit provided less complex and highly accurate models compared to the models produced by the most of other methods hence the proposed hfit is an efficient and competitive alternative to the other fiss for function approximation and feature selection

noninteracting adaptive control of pmsm using interval type 2 fuzzy logic systems based on the type 2 fuzzy logic systems and adaptive control theory this paper develops a decentralized adaptive fuzzy controller for a permanent magnet synchronous motor pmsm the adaptive law is designed to compensate for the interconnection effects and the reconstruction errors using a sliding mode term the type 2 fuzzy logic systems are used to model the unknown functions based on lyapunov s stability theorem the stability of closed loop systems can be verified moreover the proposed overall control schemes guarantee that all the signals that are involved are bounded to demonstrate the effectiveness of the proposed methods simulation results are illustrated in this paper

a self evolving interval type 2 fuzzy neural network with online structure and parameter learning this paper proposes a self evolving interval type 2 fuzzy neural network seit2fnn with online structure and parameter learning the antecedent parts in each fuzzy rule of the seit2fnn are interval type 2 fuzzy sets and the fuzzy rules are of the takagi sugeno kang tsk type the initial rule base in the seit2fnn is empty and the online clustering method is proposed to generate fuzzy rules that flexibly partition the input space to avoid generating highly overlapping fuzzy sets in each input variable an efficient fuzzy set reduction method is also proposed this method independently determines whether a corresponding fuzzy set should be generated in each input variable when a new fuzzy rule is generated for parameter learning the consequent part parameters are tuned by the rule ordered kalman filter algorithm for high accuracy learning performance detailed learning equations on applying the rule ordered kalman filter algorithm to the seit2fnn consequent part learning with rules being generated online are derived the antecedent part parameters are learned by gradient descent algorithms the seit2fnn is applied to simulations on nonlinear plant modeling adaptive noise cancellation and chaotic signal prediction comparisons with other type 1 and type 2 fuzzy systems in these examples verify the performance of the seit2fnn

mean variance tradeoffs in an undiscounted mdp a stationary policy and an initial state in an mdp markov decision process induce a stationary probability distribution of the reward the problem analyzed here is generating the pareto optima in the sense of high mean and low variance of the stationary distribution in the unichain case pareto optima can be computed either with policy improvement or with a linear program having the same number of variables and one more constraint than the formulation for gain rate optimization the same linear program suffices in the multichain case if the ergodic class is an element of choice

estimating time varying parameters by the kalman filter based algorithm stability and convergence convergence and stability properties of the kalman filter based parameter estimator are established for linear stochastic time varying regression models the main features are both the variances and sample path averages of the parameter tracking error are shown to be bounded the regression vector includes both stochastic and deterministic signals and no assumptions of stationarity or independence are requires and the unknown parameters are only assumed to have bounded variations in an average sense

an interval type 2 neural fuzzy classifier learned through soft margin minimization and its human posture classification application this paper proposes an interval type 2 neural fuzzy classifier learned through soft margin minimization it2nfc smm and applies it to human body posture classification the it2nfc smm consists of interval type 2 zero order takagi sugeno t s fuzzy rules established through online structure learning the antecedent part of the it2nfc smm uses interval type 2 fuzzy sets to decrease the number of rules and manage noisy data for parameter learning the consequent parameters are learned through a linear support vector machine svm for soft margin minimization to improve the generalization ability the proposed svm based learning addresses the problem that the orders of the fuzzy rules in computing the outputs of an interval type 2 fuzzy system depend on the consequent values that are unknown in advance to address this problem the it2nfc smm uses weighted bound set boundaries to simplify the type reduction operation and a novel crisp to interval linear svm learning algorithm based on the soft margin minimization the antecedent parameters are tuned using the gradient descent algorithm the it2nfc smm is applied to a vision based human body posture classification system the system uses two cameras and novel classification features extracted from a silhouette of the human body to classify the four postures of standing bending sitting and lying the classification performance of the it2nfc smm is verified through results in clean and noisy classification examples and through the posture classification problem as well as through comparisons with various type 1 and type 2 fuzzy classifiers the overall result shows that the it2nfc smm achieves higher classification rates with a smaller or similar model size than the classifiers used for comparison especially for noisy classification problems

global continuous riemann solver for nonlinear elasticity we consider in this paper an isothermal model of nonlinear elasticity this model is described by two conservation laws that define a problem of mixed type both elliptic and hyperbolic we restrict ourselves to the linearly degenerate case and consider riemann data that lies in the hyperbolic regions the lack of uniqueness of the riemann problem is solved by the introduction of a so called kinetic relation used to narrow the set of admissible subsonic phase transitions in this situation we consider the riemann problem for any data lying in the hyperbolic region using either explicit computations or geometric arguments this construction allows us to give sufficient conditions on the kinetic relation in order that the generated riemann solver possesses properties of uniqueness globality and continuous dependence on the initial data in the l 1 distance

multiobjective optimization and comparison of nonsingleton type 1 and singleton interval type 2 fuzzy logic systems singleton interval type 2 fuzzy logic systems flss have been widely applied in several real world applications where it was shown that the singleton interval type 2 flss outperform their singleton type 1 counterparts in applications with high uncertainty levels however one of the main criticisms of singleton interval type 2 flss is the fact that they outperform singleton type 1 flss solely based on their use of extra degrees of freedom extra parameters and that type 1 flss with a sufficiently large number of parameters may provide the same performance as interval type 2 flss in addition most works on type 2 flss only compare their results with singleton type 1 flss but fail to consider nonsingleton type 1 systems in this paper we aim to directly address and investigate this criticism in order to do so we will perform a comparative study between optimized singleton type 1 nonsingleton type 1 and singleton interval type 2 flss under the presence of noise we will also present a multiobjective evolutionary algorithm moea for the optimization of singleton type 1 nonsingleton type 1 and singleton interval type 2 fuzzy systems for function approximation problems the moea will aim to satisfy two objectives to maximize the accuracy of the fls and minimize the number of rules in the fls thus improving its interpretability furthermore we will present a methodology to obtain optimal consequents for the flss hence this paper has two main contributions first it provides a common methodology to learn the three types of flss i e singleton type 1 nonsingleton type 1 and singleton interval type 2 flss from data samples the second contribution is the creation of a common framework for the comparison of type 1 and type 2 flss that allows us to address the aforementioned criticism we provide details of a series of experiments and include statistical analysis showing that the type 2 fls is able to handle higher levels of noise than its nonsingleton and singleton type 1 counterparts

an interval type 2 neural fuzzy system for online system identification and feature elimination we propose an integrated mechanism for discarding derogatory features and extraction of fuzzy rules based on an interval type 2 neural fuzzy system nfs in fact it is a more general scheme that can discard bad features irrelevant antecedent clauses and even irrelevant rules high dimensional input variable and a large number of rules not only enhance the computational complexity of nfss but also reduce their interpretability therefore a mechanism for simultaneous extraction of fuzzy rules and reducing the impact of or eliminating the inferior features is necessary the proposed approach namely an interval type 2 neural fuzzy system for online system identification and feature elimination it2nfs sife uses type 2 fuzzy sets to model uncertainties associated with information and data in designing the knowledge base the consequent part of the it2nfs sife is of takagi sugeno kang type with interval weights the it2nfs sife possesses a self evolving property that can automatically generate fuzzy rules the poor features can be discarded through the concept of a membership modulator the antecedent and modulator weights are learned using a gradient descent algorithm the consequent part weights are tuned via the rule ordered kalman filter algorithm to enhance learning effectiveness simulation results show that it2nfs sife not only simplifies the system architecture by eliminating derogatory irrelevant antecedent clauses rules and features but also maintains excellent performance

optimization models for the first arrival target distribution function in discrete time the study of expectation optimality criteria standard criteria has constituted most previous work in the area of markov decision processes mdps however the optimal policies obtained from such models are not reliable when considering a single or a few decision processes since only the average performance over many trials is guaranteed to be optimal in fact the expectation optimality criteria are insufficient to characterize the w x variability risk features of practical problems 1 5 a typical requirement for a long term application for example unmanned space flight and satellites is to have a 0 95 or greater probability of being operational at the end of a 10 year period whereas a typical requirement for space shuttle aircraft flight control and military systems is to have a reliability of 0 97 at the end of a 3 h time period likewise chemical reactions must

state space black box modelling via markov parameters based on evolving type 2 neural fuzzy inference system for nonlinear multivariable dynamic systems abstract in this paper an approach for state space interval type 2 neural fuzzy identification of multivariable dynamic systems in an evolving and incremental learning context is proposed in combination with type 2 fuzzy systems the adopted methodology regards the following aspects recursive learning of the footprint of uncertainty and recursive learning of the rule consequents part by a recursive linear state space approaches where markov parameters are incrementally and robustly learnt in sample wise manner the efficiency and applicability of the proposed methodology are demonstrated through experimental and computational results and compared with prominent learning algorithms of the literature

mean variance criteria in an undiscounted markov decision process abstract in the steady state of an undiscounted markov decision process we consider the problem of finding an optimal stationary probability distribution that minimizes the variance of the reward in a transition among the stationary probability distributions which give a mean not less than a specified value the problem consists of a mathematical program with linear constraints and a non linear objective the solution technique replaces the non linear part of the objective with a constant inserts the constant as a constraint and then parametrically analyzes the resulting linear program three numerical examples are discussed

minimum risk probability for finite horizon semi markov decision processes abstract this paper studies the risk probability criteria for finite horizon semi markov decision processes the goal is to find an optimal policy with the minimum risk probability that the total reward produced by a system during a finite horizon does not exceed a reward level where the optimality is over the class of all randomized historic policies which include states planning horizons and also reward levels under mild conditions the optimality equation and the existence of optimal policies are established and in addition an iteration algorithm for solving optimal policies is developed our main results are applied to a manufacturing system

an extension to fuzzy cognitive maps for classification and prediction fuzzy cognitive maps fcms as an illustrative causative representation of modeling and manipulation of complex systems can be used to model the dynamic behavior of the investigated systems however due to defects in expression and architecture the traditional fcms and most of their relevant extensions are not applicable to classification problems to solve this problem this paper presents an approach that directly extends the model by translating the reasoning mechanism of traditional fcms to a set of fuzzy if then rules moreover the proposed approach fully considers the contribution of the inputs to the activation of the fuzzy rules and quantifies the causalities using mutual subsethood which works in conjunction with volume defuzziflcation in a gradient descent learning framework in this manner our approach enhances the capability of the conventional fcms to automatically identify membership functions and quantify causalities despite the increase in the number of tunable parameters experimental results show that the proposed approach efficiently extends the application of the traditional fcms into classification problems while keeping the ability for prediction and approximation

the vanishing discount approach in markov chains with risk sensitive criteria in this paper stochastic dynamic systems are studied modeled by a countable state space markov cost reward chain satisfying a lyapunov type stability condition for an infinite planning horizon risk sensitive exponential discounted and average cost criteria are considered the main contribution is the development of a vanishing discount approach to relate the discounted criterion problem with the average criterion one as the discount factor increases to one i e no discounting in comparison to the well established risk neutral case our results are novel and reveal several fundamental and surprising differences other contributions made include the use of convex analytic arguments to obtain appropriately convergent sequences and a verification theorem for the case of unbounded solutions to the average cost poisson equation arising in the risk sensitive case also of importance is the fact that our developments are very much self contained and employ only basic probabilistic and analysis principles

value iteration methods in risk minimizing stopping problems we consider an optimal stopping problem with a discrete time markov process where the criterion function is a threshold probability we give the fundamental properties of optimal values and optimal stopping times but the optimal value and the optimal stopping time depend upon the threshold value we also obtain the properties of optimal values with respect to the threshold value and a value iteration method is given

optimal threshold probability in undiscounted markov decision processes with a target set we consider risk minimizing problems in undiscounted markov decisions processes with a target set we formulate the problem as an infinite horizon case with a recurrent class we show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy also we give several value iteration methods and a policy improvement method

discounted mdp s distribution functions and exponential utility maximization the present value of the rewards associated with a discrete time markov process has a probability distribution which depends on the initial state the first part of the paper applies fixed point theory to a system of equations for the distribution functions of the present value the second part of the paper expands the model to a markov decision process mdp and considers the maximization of the expected utility of the present value when the utility function is exponential

interval type 2 mutual subsethood fuzzy neural inference system it2msfunis this paper presents an interval type 2 mutual subsethood fuzzy neural inference system it2msfunis a mutual subsethood measure between two interval type 2 fuzzy sets it2 fs has been derived and has been used in determining the similarity between the it2 fs inputs and it2 fs antecedents the consequent weights are taken to be interval sets the inputs to the system are fuzzified into it2 fss with gaussian primary membership function having fixed center and uncertain variance aggregation of type 2 mutual subsethood based activation spreads is performed using product operator the output is obtained using simplified type reduction followed by defuzzification the system learns using memetic procedure involving differential evolution for global search and gradient descent for local exploitation in solution space the mathematical modeling and empirical studies of it2msfunis bring forth its efficacy in problems pertaining to function approximation time series prediction control and classification comparisons with other type 1 and type 2 neuro fuzzy systems verify that it2msfunis compares excellently with other models with a performance better than most of them both in terms of total number of trainable parameters and result accuracy empirical studies indicate the intelligent decision making capability of the proposed model the main contribution of this paper lies in the identification of mutual subsethood to find out the correlation between it2 fss and to find out its applicability in diverse application domains the improved performance of the proposed method can be attributed to the better contrast handling capacity of mutual subsethood method and uncertainty handling capacity of it2 fss the integration of mutual subsethood with interval type 2 fuzzy logic puts forth a novel model with various merits as demonstrated amply with the help of well known problems reported in the literature

stochastic optimization of forward recursive functions this note solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming the forward recursive criterion is wide it includes additive discounted multiplicative discounted risk sensitive minimum and terminal criteria the basic idea is to apply invariant imbedding method for the stochastic optimization the method incorporates recursive accumulation process into dynamics by expanding the original state space

a metacognitive complex valued interval type 2 fuzzy inference system this paper presents a complex valued interval type 2 neuro fuzzy inference system cit2fis and derive its metacognitive projection based learning pbl algorithm metacognitive cit2fis mc cit2fis consists of a cit2fis which realizes takagi sugeno kang type inference mechanism as its cognitive component a pbl with self regulation is its metacognitive component the rules of cit2fis employ interval type 2 q gaussian membership functions that can represent different radial basis functions for different values of q as each sample is presented to the network the metacognitive component monitors the hinge loss error and class specific knowledge potential of the current sample to efficiently decide on what to learn when to learn and how to learn it when a new rule is added or existing rules are updated the optimal parameters of cit2fis corresponding to the minimum of the hinge loss error function are computed using a pbl algorithm derived using the wirtinger calculus the performance of mc cit2fis is evaluated on a set of benchmark real valued classification problems from the uci machine learning repository a circular transformation is used to convert the real valued features to the complex valued features in these problems the performance comparison and statistical study clearly show the superior classification ability of mc cit2fis finally the proposed complex valued network is used to solve a practical human action recognition problem that is represented by complex valued optical flow based feature set and a human emotion recognition problem represented using complex valued gabor filter based features the performance results on these problems substantiate the superior classification ability of mc cit2fis

fuzzy rules interpolation for sparse fuzzy rule based systems based on interval type 2 gaussian fuzzy sets and genetic algorithms in this paper we present a new method for fuzzy rules interpolation for sparse fuzzy rule based systems based on interval type 2 gaussian fuzzy sets and genetic algorithms first we present a method to deal with the interpolation of fuzzy rules based on interval type 2 gaussian fuzzy sets we also prove that the proposed method guarantees to produce normal interval type 2 gaussian fuzzy sets then we present a method to learn optimal interval type 2 gaussian fuzzy sets for sparse fuzzy rule based systems based on genetic algorithms we also apply the proposed fuzzy rules interpolation method and the proposed learning method to deal with multivariate regression problems and time series prediction problems the experimental results show that the proposed fuzzy rules interpolation method using the optimally learned interval type 2 gaussian fuzzy sets gets higher average accuracy rates than the existing methods

an interval type 2 fuzzy neural network with support vector regression for noisy regression problems this paper proposes an interval type 2 fuzzy neural network with support vector regression it2fnn svr for noisy regression problems the antecedent part in each fuzzy rule of an it2fnn svr uses interval type 2 fuzzy sets and the consequent part is of the takagi sugeno kang tsk type the use of interval type 2 fuzzy sets helps improve the network s noise resistance the network inputs may be numerical values or type 1 fuzzy sets with the latter being used for further improvements in robustness it2fnn svr learning consists of both structure learning and parameter learning the structure learning algorithm is responsible for online rule generation the parameters are optimized for structural risk minimization using a two phase linear svr algorithm in order to endow the network with high generalization ability it2fnn svr performance is verified through comparisons with type 1 and type 2 fuzzy logic systems and other regression models on noisy regression problems

developing a local least squares support vector machines based neuro fuzzy model for nonlinear and chaotic time series prediction local modeling approaches owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models seem appealing for modeling identification and prediction applications in this paper we propose a local neuro fuzzy lnf approach based on the least squares support vector machines lssvms the proposed lnf approach employs lssvms which are powerful in modeling and predicting time series as local models and uses hierarchical binary tree hbt learning algorithm for fast and efficient estimation of its parameters the hbt algorithm heuristically partitions the input space into smaller subdomains by axis orthogonal splits in each partitioning the validity functions automatically form a unity partition and therefore normalization side effects e g reactivation are prevented integration of lssvms into the lnf network as local models along with the hbt learning algorithm yield a high performance approach for modeling and prediction of complex nonlinear time series the proposed approach is applied to modeling and predictions of different nonlinear and chaotic real world and hand designed systems and time series analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed lnf approach with the hbt learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series

an online self constructing neural fuzzy inference network and its applications a self constructing neural fuzzy inference network sonfin with online learning ability is proposed in this paper the sonfin is inherently a modified takagi sugeno kang tsk type fuzzy rule based model possessing neural network learning ability there are no rules initially in the sonfin they are created and adapted as online learning proceeds via simultaneous structure and parameter identification in the structure identification of the precondition part the input space is partitioned in a flexible way according to an aligned clustering based algorithm as to the structure identification of the consequent part only a singleton value selected by a clustering method is assigned to each rule initially afterwards some additional significant terms selected via a projection based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds the combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network a main feature of the sonfin in the parameter identification the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm to enhance the knowledge representation ability of the sonfin a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved

algorithmic aspects of mean variance optimization in markov decision processes we consider finite horizon markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward we show that either randomized or history based policies can improve performance we prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is np hard for some cases and strongly np hard for others we finally offer pseudopolynomial exact and approximation algorithms

a differential game for a multiclass queueing model in the moderate deviation heavy traffic regime we study a differential game that governs the moderate deviation heavy traffic asymptotics of a multiclass single server queueing control problem with a risk sensitive cost we consider a cost set on a finite but sufficiently large time horizon and show that this formulation leads to stationary feedback policies for the game several aspects of the game are explored including its characterization via a one dimensional free boundary problem the semi explicit solution of an optimal strategy and the specification of a saddle point we emphasize the analogy to the well known harrison taksar free boundary problem which plays a similar role in the diffusion scale heavy traffic literature

data based system modeling using a type 2 fuzzy neural network with a hybrid learning algorithm we propose a novel approach for building a type 2 neural fuzzy system from a given set of input output training data a self constructing fuzzy clustering method is used to partition the training dataset into clusters through input similarity and output similarity tests the membership function associated with each cluster is defined with the mean and deviation of the data points included in the cluster then a type 2 fuzzy takagi sugeno kang if then rule is derived from each cluster to form a fuzzy rule base a fuzzy neural network is constructed accordingly and the associated parameters are refined by a hybrid learning algorithm which incorporates particle swarm optimization and a least squares estimation for a new input a corresponding crisp output of the system is obtained by combining the inferred results of all the rules into a type 2 fuzzy set which is then defuzzified by applying a refined type reduction algorithm experimental results are presented to demonstrate the effectiveness of our proposed approach

percentile performance criteria for limiting average markov decision processes addresses the following basic feasibility problem for infinite horizon markov decision processes mdps can a policy be found that achieves a specified value target of the long run limiting average reward at a specified probability level percentile related optimization problems of maximizing the target for a specified percentile and vice versa are also considered the authors present a complete and discrete classification of both the maximal achievable target levels and of their corresponding percentiles the authors also provide an algorithm for computing a deterministic policy corresponding to any feasible target percentile pair next the authors consider similar problems for an mdp with multiple rewards and or constraints this case presents some difficulties and leads to several open problems an lp based formulation provides constructive solutions for most cases

discounted markov decision processes with utility constraints we consider utility constrained markov decision processes the expected utility of the total discounted reward is maximized subject to multiple expected utility constraints by introducing a corresponding lagrange function a saddle point theorem of the utility constrained optimization is derived the existence of a constrained optimal policy is characterized by optimal action sets specified with a parametric utility

neuro fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets abstract this paper presents the results of using type 2 fuzzy sets to assist in the pre processing of data for use with neuro fuzzy clustering for classification of sports injuries in the lower leg this research is concerned with the analysis of bone scans from stress related injuries to the tibia of particular interest is whether neural network based clustering techniques can help the consultant in classifying the images the work was motivated by the situation where there is a relatively small amount of relevant data and difficulties are faced by consultants in classifying the various types of injuries for this particular problem the consultant s interpretation of the image lends itself to representation using type 2 fuzzy sets this research sets out to address whether with fuzzy neuro clustering techniques some insights may be provided to the consultant that they can use along with their experience and knowledge the results of this approach indicate that the use of neural clustering using a type 2 representation can improve the classification of shin images

a fuzzy system constructed by rule generation and iterative linear svr for antecedent and consequent parameter optimization this paper proposes a new fuzzy regression model i e the fuzzy system constructed by rule generation and iterative linear support vector regression fs rglsvr for structural risk minimization the fs rglsvr is composed of takagi sugeno ts type fuzzy if then rules these rules are automatically constructed by a self splitting rule generation algorithm that introduces the self splitting technique to the k means clustering algorithm this new algorithm regards a cluster as a fuzzy rule where no preassignment of the cluster rule number is necessary the cost function for parameter learning is defined based on structural risk instead of empirical risk minimization in order to achieve generalizability tuning all of the free parameters in the fs rglsvr using linear support vector regression svr is proposed to minimize the cost function each of the consequent and antecedent part parameters is expressed as a linear combination coefficient in a transformed input space so that the linear svr is applicable this paper introduces iterative linear svr to tune antecedent and consequent parameters this paper demonstrates the capabilities of fs rglsvr by two simulated and four practical regression examples comparisons with fuzzy systems with different types of learning algorithms verify the performance of the fs rglsvr

robust self organizing neural fuzzy control with uncertainty observer for mimo nonlinear systems this paper proposes a robust self organizing neural fuzzy control rsonfc scheme for a class of uncertain nonlinear multiple input multiple output mimo systems we first develop a self organizing neural fuzzy network sonfn with concurrent structure and parameter learning the fuzzy rules of sonfn are generated or pruned systematically the proposed rsonfc scheme comprises an sonfn identifier an uncertainty observer and a supervisory controller the sonfn identifier functions as the principal controller and the uncertainty observer is designed to oversee uncertainties within the compound system the supervisory controller combines sliding mode control smc and an adaptive bound estimation scheme with various weights to achieve h tracking performance with a desired level of attenuation projection type adaptation laws of network parameters developed using the lyapunov s synthesis approach guarantee the stability of the overall control system simulation studies on a single link flexible joint manipulator and a two link robot demonstrate the effectiveness of the proposed control scheme

t2fela type 2 fuzzy extreme learning algorithm for fast training of interval type 2 tsk fuzzy logic system a challenge in modeling type 2 fuzzy logic systems is the development of efficient learning algorithms to cope with the ever increasing size of real world data sets in this paper the extreme learning strategy is introduced to develop a fast training algorithm for interval type 2 takagi sugeno kang fuzzy logic systems the proposed algorithm called type 2 fuzzy extreme learning algorithm t2fela has two distinctive characteristics first the parameters of the antecedents are randomly generated and parameters of the consequents are obtained by a fast learning method according to the extreme learning mechanism in addition because the obtained parameters are optimal in the sense of minimizing the norm the resulting fuzzy systems exhibit better generalization performance the experimental results clearly demonstrate that the training speed of the proposed t2fela algorithm is superior to that of the existing state of the art algorithms the proposed algorithm also shows competitive performance in generalization abilities

simplified interval type 2 fuzzy neural networks this paper describes a self evolving interval type 2 fuzzy neural network fnn for various applications as type 1 fuzzy systems cannot effectively handle uncertainties in information within the knowledge base we propose a simple interval type 2 fnn which uses interval type 2 fuzzy sets in the premise and the takagi sugeno kang tsk type in the consequent of the fuzzy rule the tsk type consequent of fuzzy rule is a linear combination of exogenous input variables given an initially empty the rule base all rules are generated with on line type 2 fuzzy clustering instead of the time consuming k m iterative procedure the design factors ql and qr are learned to adaptively adjust the upper and lower positions on the left and right limit outputs using the parameter update rule based on a gradient descent algorithm simulation results demonstrate that our approach yields fewer test errors and less computational complexity than other type 2 fnns

long term learning for type 2 neural fuzzy systems abstract the development of a new long term learning framework for interval valued neural fuzzy systems is presented for the first time in this article the need for such a framework is twofold to address continuous batch learning of data sets and to take advantage the extra degree of freedom that type 2 fuzzy logic systems offer for better model predictive ability the presented long term learning framework uses principles of granular computing grc to capture information knowledge from raw data in the form of interval valued sets in order to build a computational mechanism that has the ability to adapt to new information in an additive and long term learning fashion the latter is to accommodate new input output mappings and new classes of data without significantly disturbing existing input output mappings therefore maintaining existing performance while creating and integrating new knowledge rules this is achieved via an iterative algorithmic process which involves a two step operation iterative rule base growth capturing new knowledge and iterative rule base pruning removing redundant knowledge for type 2 rules the two step operation helps create a growing but sustainable model structure the performance of the proposed system is demonstrated using a number of well known non linear benchmark functions as well as a highly nonlinear multivariate real industrial case study simulation results show that the performance of the original model structure is maintained and it is comparable to the updated model s performance following the incremental learning routine the study is concluded by evaluating the performance of the proposed framework in frequent and consecutive model updates where the balance between model accuracy and complexity is further assessed

neuro fuzzy systems for function approximation abstract we present a neuro fuzzy architecture for function approximation based on supervised learning the learning algorithm is able to determine the structure and the parameters of a fuzzy system the approach is an extension to our already published nefcon and nefclass models which are used for control or classification purposes the proposed extended model which we call nefprox is more general and can be used for any application based on function approximation

riemann problem for gasdynamic combustion abstract the riemann problem for gasdynamic combustion is considered existence and uniqueness are obtained constructively for arbitrary riemann data under the following restrictions the solutions are selfsimilar and piecewise smooth the lax entropy condition is satisfied at the discontinuity points except at the front sides of deflagration waves where the temperatures are assumed to be ignition point the number of detonation waves in the solutions is as small as possible the number of times of oscillation of temperature around the ignition point is also as small as possible and last the number of deflagration waves is as large as possible using the riemann problem we analyzed the overtaking of shocks and combustion waves a shock always accelerates detonation whereas it transforms deflagration into detonation when it is strong enough transition from deflagration to detonation in the ignition problem is also investigated

threshold probability of non terminal type in finite horizon markov decision processes abstract we consider a class of problems concerned with maximizing probabilities given stage wise targets which generalizes the standard threshold probability problem in markov decision processes the objective function is the probability that at all stages the associatively combined accumulation of rewards earned up to that point takes its value in a specified stage wise interval it is shown that this class reduces to the case of the nonnegative valued multiplicative criterion through an invariant imbedding technique we derive a recursive formula for the optimal value function and an effective method for obtaining the optimal policies

an evolving interval type 2 neurofuzzy inference system and its metacognitive sequential learning algorithm in this paper we propose an evolving interval type 2 neurofuzzy inference system it2fis and its fully sequential learning algorithm it2fis employs interval type 2 fuzzy sets in the antecedent part of each rule and the consequent realizes takagi sugeno kang fuzzy inference mechanism in order to render the inference fast and accurate we propose a data driven interval reduction approach to convert interval type 1 fuzzy set in antecedent to type 1 fuzzy number in the consequent during learning the sequential algorithm learns a sample one by one and only once the it2fis structure evolves automatically and adapts its network parameters using metacognitive learning mechanism concurrently the metacognitive learning regulates the learning process by appropriate selection of learning strategies and helps the proposed it2fis to approximate the input output relationship efficiently an evolving it2fis employing a metacognitive learning algorithm is referred to as mcti2fis performance of metacognitive interval type 2 neurofuzzy inference system mcit2fis is evaluated using a set of benchmark time series problems and is compared with existing type 2 and type 1 fuzzy inference systems finally the performance of the proposed mcit2fis has been evaluated using a practical stock price tracking problem the results clearly highlight that mcit2fis performs better than other existing results in the literature

minimizing a threshold probability in discounted markov decision processes necessary and sufficient conditions are found for the characteristic functions of a finite number of given sets to be linearly independant

minimizing risk models in markov decision processes with policies depending on target values abstract this paper studies the minimizing risk problems in markov decision processes with countable state space and reward set the objective is to find a policy which minimizes the probability risk that the total discounted rewards do not exceed a specified value target in this sort of model the decision made by the decision maker depends not only on system s states but also on his target values by introducing the decision maker s state we formulate a framework for minimizing risk models the policies discussed depend on target values and the rewards may be arbitrary real numbers for the finite horizon model the main results obtained are i the optimal value functions are distribution functions of the target ii there exists an optimal deterministic markov policy and iii a policy is optimal if and only if at each realizable state it always takes optimal action in addition we obtain a sufficient condition and a necessary condition for the existence of finite horizon optimal policy independent of targets and we give an algorithm computing finite horizon optimal policies and optimal value functions for an infinite horizon model we establish the optimality equation and we obtain the structure property of optimal policy we prove that the optimal value function is a distribution function of target and we present a new approximation formula which is the generalization of the nonnegative rewards cases an example which illustrates the mistakes of previous literature shows that the existence of optimal policy has not been proved really in this paper we give an existence condition which is a sufficient and necessary condition for the existence of an infinite horizon optimal policy independent of targets and we point out that whether there exists an optimal policy remains an open problem in the general case