comprehensive analysis of a new fuzzy rule interpolation method the first published result in fuzzy rule interpolation was the spl alpha cut based fuzzy rule interpolation termed as kh fuzzy rule interpolation originally devoted for complexity reduction a modified version of the kh approach has been presented by yam et al 1999 which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method this paper presents a comprehensive analysis of the new method which includes detailed comparison with the original kh fuzzy rule interpolation method concerning the explicit functions of the methods preservation of piecewise linearity and stability the fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques all these comparisons shows that the new method preserves the advantageous properties of the kh method and alleviates its most significant disadvantage the problem of subnormality

fuzzy interpolative reasoning via scale and move transformations interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible this paper presents an interpolative reasoning method by means of scale and move transformations it can be used to interpolate fuzzy rules involving complex polygon gaussian or other bell shaped fuzzy membership functions the method works by first constructing a new inference rule via manipulating two given adjacent rules and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions this method has three advantages thanks to the proposed transformations 1 it can handle interpolation of multiple antecedent variables with simple computation 2 it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets and 3 it suggests a variety of definitions for representative values providing a degree of freedom to meet different requirements comparative experimental studies are provided to demonstrate the potential of this method

a review of algebraic multigrid abstract since the early 1990s there has been a strongly increasing demand for more efficient methods to solve large sparse unstructured linear systems of equations for practically relevant problem sizes classical one level methods had already reached their limits and new hierarchical algorithms had to be developed in order to allow an efficient solution of even larger problems this paper gives a review of the first hierarchical and purely matrix based approach algebraic multigrid amg amg can directly be applied for instance to efficiently solve various types of elliptic partial differential equations discretized on unstructured meshes both in 2d and 3d since amg does not make use of any geometric information it is a plug in solver which can even be applied to problems without any geometric background provided that the underlying matrix has certain properties

an adaptive algebraic multigrid for reactor criticality calculations an effective algorithm for reactor criticality calculations has been developed based on shift and invert iterations with an algebraic multigrid solver and wachspress rebalancing use of rebalancing makes it possible to transform the system into the natural basis in which a sequence of levels and intergrid operators are effectively calculated the main problem is to make such a procedure robust with respect to the error of approximation of the main eigenfunction without loss of efficiency this is achieved by coordinating the shift value with the value of the error of the current approximation of the main eigenfunction used in the rebalancing procedure

closed form fuzzy interpolation fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity although a number of important fuzzy rule interpolation approaches have been proposed in the literature most of these approaches cannot be expressed in a closed form this is usually caused by the effort to avoid possible invalid interpolated results this paper proposes a different fuzzy rule interpolation approach it not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets this approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems the mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation this approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages the results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation

an assumption based tms abstract this paper presents a new view of problem solving motivated by a new kind of truth maintenance system unlike previous truth maintenance systems which were based on manipulating justifications this truth maintenance system is in addition based on manipulating assumption sets as a consequence it is possible to work effectively and efficiently with inconsistent information context switching is free and most backtracking and all retraction is avoided these capabilities motivate a different kind of problem solving architecture in which multiple potential solutions are explored simultaneously this architecture is particularly well suited for tasks where a reasonable fraction of the potential solutions must be explored

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on bm alpha cuts and transformations techniques in sparse fuzzy rule based systems the fuzzy rule bases are usually incomplete in this situation the system may not properly perform fuzzy reasoning to get reasonable consequences in order to overcome the drawback of sparse fuzzy rule based systems there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule based systems it can produce more reasonable results than the existing methods the proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

simulating bosonic baths with error bars we derive rigorous truncation error bounds for the spin boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths for the numerical simulation of such baths the truncation of both the number of modes and the local hilbert space dimensions is necessary we derive superexponential lieb robinson type bounds on the error when restricting the bath to finitely many modes and show how the error introduced by truncating the local hilbert spaces may be efficiently monitored numerically in this way we give error bounds for approximating the infinite system by a finite dimensional one as a consequence numerical simulations such as the time evolving density with orthogonal polynomials algorithm tedopa now allow for the fully certified treatment of the system environment interaction

fuzzy interpolation and extrapolation a practical approach fuzzy interpolation does not only help to reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible it has been successfully applied to systems control but limited work exists for its applications to tasks like prediction and classification almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation and that such rules must flank the observation for each attribute also some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes to avoid such limitations and develop a more practical approach this paper extends the work of huang and shen the result enables both interpolation and extrapolation which involve multiple fuzzy rules with each rule consisting of multiple antecedents two realistic applications namely truck backer upper control and computer activity prediction are provided in this paper to demonstrate the utility of the extended approach experiment based comparisons to the most commonly used mamdani fuzzy reasoning mechanism and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on the areas of fuzzy sets fuzzy interpolative reasoning is an inference technique for dealing with the sparse rules problem in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the areas of fuzzy sets the proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results and has the following advantages 1 it holds the normality and the convexity of the fuzzy interpolative reasoning result 2 it can deal with fuzzy interpolative reasoning with complicated membership functions 3 it can deal with fuzzy interpolative reasoning when the fuzzy sets of the antecedents and the consequents of the fuzzy rules have different kinds of membership functions 4 it can handle fuzzy interpolative reasoning with multiple antecedent variables 5 it can handle fuzzy interpolative reasoning with multiple fuzzy rules and 6 it can handle fuzzy interpolative reasoning with logically consistent properties with respect to the ratios of fuzziness we use some examples to compare the fuzzy interpolative reasoning results of the proposed method with those of the existing fuzzy interpolative reasoning methods in terms of the six evaluation indices the experimental results show that the proposed method performs more reasonably than the existing methods the proposed method provides us a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

dynamical error bounds for continuum discretisation via gauss quadrature rules a lieb robinson bound approach instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics often the continua are approximated by a discrete set of modes we derive error bounds on expectation values of system observables that have been time evolved under such discretised hamiltonians these bounds take on the form of a function of time and the number of discrete modes where the discrete modes are chosen according to gauss quadrature rules the derivation makes use of tools from the field of lieb robinson bounds and the theory of orthonormal polynomials

open systems with error bounds spin boson model with spectral density variations in the study of open quantum systems one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density however in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data consequently some uncertainty regarding its form and parameters is unavoidable this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density here we focus on the spin boson model as a prototypical open quantum system find two error bounds on predicted expectation values in terms of the spectral density variation considered and state a sufficient condition for the strongest one to apply we further demonstrate an application of our result by bounding the error brought about by the approximations involved in the hierarchical equations of motion resolution method for spin boson dynamics

su 2 coherent state path integral the su 2 coherent state path integral is used to represent the matrix element of a propagator in the su 2 coherent state basis it is argued that the continuum representation of this integral is correct provided the necessary boundary term is taken into account in the case of the su 2 dynamical symmetry the path integral is explicitly computed by means of a change of variables the su 2 motion of the underlying phase space the correct stationary phase expansion for the propagator in terms of the total action including boundary term and classical trajectories is obtained

adaptive fuzzy interpolation fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems complexity however after a series of interpolations it is possible that multiple object values for a common variable are inferred leading to inconsistency in interpolated results such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations this paper presents a novel approach for identification and correction of defective rules in interpolative transformations thereby removing the inconsistencies in particular an assumption based truth maintenance system atms is used to record dependences between interpolations and the underlying technique that the classical general diagnostic engine gde employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations from this an algorithm is introduced to allow for the modification of the original linear interpolation to become first order piecewise linear the approach is applied to a realistic problem which predicates the diarrheal disease rates in remote villages to demonstrate the potential of this study

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

adaptive fuzzy interpolation based on general representative values of polygonal fuzzy sets and the shift and modification techniques abstract adaptive fuzzy interpolative reasoning afir can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning fir results in order to ensure that the derived fir results are consistent in this paper we propose a new afir method to solve the inconsistencies occurring after the fir process the proposed afir method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques the proposed afir method includes a new contradictions solving method to get a higher similarity degree between the afir results in order to demonstrate the higher consistency of the afir results obtained by the proposed afir method we apply the proposed afir method to deal with the diarrheal disease prediction problem the experimental results show that the proposed afir method outperforms yang and shen s afir method 2011 and cheng et al s afir method 2016 in terms of the degree of similarity between the afir results

weighted fuzzy interpolative reasoning systems based on interval type 2 fuzzy sets abstract in this paper we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on interval type 2 fuzzy sets we also apply the proposed weighted fuzzy interpolative reasoning method to deal with the truck backer upper control problem the proposed method satisfies the seven evaluation indices for fuzzy interpolative reasoning the experimental results show that the proposed method outperforms the existing methods it provides us with a useful way for dealing with fuzzy interpolative reasoning in sparse fuzzy rule based systems

stability of interpolative fuzzy kh controllers the classical approaches in fuzzy control zadeh and mamdani deal with dense rule bases when this is not the case i e in sparse rule bases one has to choose another method fuzzy rule interpolation proposed first by koczy and hirota internat j approx reason 9 1993 197 225 offers a possibility to construct fuzzy controllers kh controllers under such conditions the main result of this paper shows that the kh interpolation method is stable it also contributes to the application oriented use of balazs shepard interpolation operators investigated extensively by researchers in approximation theory the numerical analysis aspect of the result contributes to the well known problem of finding a stable interpolation method in the following sense we would like to approximate a function that is only known at distinct points e g where it can be measured since measurement errors cannot be eliminated in practice it is a natural requirement that the interpolation method should be stable independently from the selection of measurement points the classical interpolation methods generally do not fulfil this condition only with certain strong restrictions concerning the measurement points if we neglect the classical form of the approximating function polynomial and trigonometrical we can produce better behaving approximation the kh controller approximating function being a simple fractional function fulfils the stability condition this can also be interpreted as kh controllers are universal approximators in the space of continuous functions with respect to e g the supremum norm

generalized adaptive fuzzy rule interpolation as a substantial extension to fuzzy rule interpolation that works based on two neighboring rules flanking an observation adaptive fuzzy rule interpolation is able to restore system consistency when contradictory results are reached during interpolation the approach first identifies the exhaustive sets of candidates with each candidate consisting of a set of interpolation procedures which may jointly be responsible for the system inconsistency then individual candidates are modified such that all contradictions are removed and thus interpolation consistency is restored it has been developed on the assumption that contradictions may only be resulted from the underlying interpolation mechanism and that all the identified candidates are not distinguishable in terms of their likelihood to be the real culprit however this assumption may not hold for real world situations this paper therefore further develops the adaptive method by taking into account observations rules and interpolation procedures all as diagnosable and modifiable system components in addition given the common practice in fuzzy systems that observations and rules are often associated with certainty degrees the identified candidates are ranked by examining the certainty degrees of its components and their derivatives from this the candidate modification is carried out based on such ranking this study significantly improves the efficacy of the existing adaptive system by exploiting more information during both the diagnosis and modification processes

approximate reasoning on a basis of z number valued if then rules approximate reasoning is about reasoning with imperfect information nowadays a large diversity of approaches to approximate reasoning with fuzzy information and fuzzy type 2 information exists it should be stressed however that real world imperfect information is characterized by combination of fuzzy and probabilistic uncertainties which is referred to as bimodal information in view of this zadeh introduced the concept of a z number regarded as an ordered pair z a b of fuzzy numbers a and b where a is a linguistic value of a variable of interest and b is a linguistic value of probability measure of a playing a role of its reliability unfortunately up to day there is no research on approximate reasoning realized on the basis of if then rules with z number valued antecedents and consequents briefly z rules zadeh addressed this problem as related to an uncharted territory in this paper a new approach is developed to study approximate reasoning with z rules on a basis of linear interpolation we provide an application of the approach to job satisfaction evaluation and to students educational achievement evaluation problems related to psychological and perceptual issues naturally characterized by imperfect information the obtained results show applicability and validity of the proposed approach

weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques in this paper we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems the proposed method uses weighted increment transformation and weighted ratio transformation techniques to handle weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems it allows each variable that appears in the antecedent parts of fuzzy rules to associate with a weight between zero and one moreover we also propose an algorithm that automatically tunes the optimal weights of the antecedent variables appearing in the antecedent parts of fuzzy rules we also apply the proposed weighted fuzzy interpolative reasoning method to handle the truck backer upper control problem the proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system 2000 huang and shen s method 2008 and chen and ko s method 2008 the proposed method provides us with a useful way to deal with weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems

weighted fuzzy rule interpolation based on ga based weight learning techniques in this paper we propose a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems it is based on a genetic algorithm ga based weight learning technique the proposed method can deal with fuzzy rule interpolation with weighted antecedent variables it also can deal with fuzzy rule interpolation based on polygonal membership functions and bell shaped membership functions we also propose a ga based weight learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules furthermore we apply the proposed weighted fuzzy interpolative reasoning method and the proposed ga based weight learning algorithm to deal with the truck backer upper control problem the computer activity prediction problem multivariate regression problems and time series prediction problems based on statistical analysis techniques the experimental results show that the proposed weighted fuzzy interpolative reasoning method by the use of the optimally learned weights that were obtained by the proposed ga based weight learning algorithm has statistically significantly smaller error rates than the existing methods

fast non overlapping schwarz domain decomposition methods for solving the neutron diffusion equation studying numerically the steady state of a nuclear core reactor is expensive in terms of memory storage and computational time in order to address both requirements one can use a domain decomposition method implemented on a parallel computer we present here such a method for the mixed neutron diffusion equations discretized with raviart thomas nedelec finite elements this method is based on the schwarz iterative algorithm with robin interface conditions to handle communications we analyse this method from the continuous point of view to the discrete point of view and we give some numerical results in a realistic highly heterogeneous 3d configuration computations are carried out with the minos solver of the apollo3 r neutronics code

adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets after the fuzzy interpolative reasoning processes if two unequal fuzzy interpolative reasoning results are derived or one derived and another observed for a consequence variable of a fuzzy rule then it is called a contradiction in the fuzzy interpolative reasoning process in recent years some adaptive fuzzy interpolation methods for sparse fuzzy rule based systems have been presented to solve contradictions after fuzzy interpolative reasoning processes in this paper a new adaptive fuzzy interpolation method is proposed for sparse fuzzy rule based systems based on ranking values and similarity measures of polygonal fuzzy sets which can solve contradictions occurred in fuzzy interpolative reasoning processes we also apply the proposed adaptive fuzzy interpolation method to predict the diarrheal disease rates in roadless villages the diarrheal disease prediction problem focuses on the issue to measure how the construction of a new road or railway in a previously roadless area may affect the epidemiology of infectious diseases in northern coastal ecuador the experimental results show that the proposed adaptive fuzzy interpolation method can overcome the drawbacks of the existing methods