generation of coarse scale continuum flow models from detailed fracture characterizations 1 a procedure for developing coarse scale continuum models from detailed fracture descriptions is developed and applied the coarse models are in the form of a generalized dual porosity representation in which matrix rock and fractures exchange fluid locally while large scale flow occurs through the fracture network the methodology developed here introduces local subgrids to resolve dynamics within the matrix and provides appropriate coarse scale parameters describing fracture fracture matrix fracture and matrix matrix flow the geometry of the local subgrids as well as the required parameters for the coarse scale model are determined from local flow solutions using the underlying discrete fracture model the method is applied to two and three dimensional single phase and two phase flow problems and the accuracy of the coarse models is assessed relative to fully resolved discrete fracture simulations for the cases considered it is shown that the technique is capable of generating highly accurate coarse models with many fewer unknowns than the detailed characterizations and speedups of about a factor of 100 are achieved

multiple reflection and transmission phases in complex layered media using a multistage fast marching method traditional grid based eikonal schemes for computing traveltimes are usually confined to obtaining first arrivals only however later arrivals can be numerous and of greater amplitude making them a potentially valuable resource for practical applications such as seismic imaging the aim of this paper is to introduce a grid based method for tracking multivalued wavefronts composed of any number of reflection and refraction branches in layered media a finite difference eikonal solver known as the fast marching method fmm is used to propagate wavefronts from one interface to the next by treating each layer that the wavefront enters as a separate computational domain one obtains a refracted branch by reinitializing fmm in the adjacent layer and a reflected branch by reinitializing fmm in the incident layer to improve accuracy a local grid refinement scheme is used in the vicinity of the source where wavefront curvature is high several examples are presented which demonstrate the viability of the new method in highly complex layered media even in the presence of velocity variations as large as 8 1 and interfaces of high curvature wavefronts composed of many reflection and transmission events are tracked rapidly and accurately this is because the scheme retains the two desirable properties of a single stage fmm computational speed and stability local grid refinement about the source also can increase accuracy by an order of magnitude with little increase in computational cost

analogy between approximate reasoning and the method of interpolation abstract in this paper we present an analogy between approximate reasoning and the method of interpolation for a large class of problems we first describe the analogy and then illustrate it through several simple yet concrete examples the new results obtained through the method of interpolation are compared with those obtained by the application of the existing method of approximate reasoning thus we show that approximate reasoning can also be realized effectively by the method of interpolation

a model for steady fluid flow in random three dimensional networks of disc shaped fractures a model for steady fluid flow in three dimensional random networks of fractures has been developed in this model the fractures are disc shaped discontinuities in an impermeable matrix the fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture radius orientation and density thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature after the boundary conditions and the desired fractures are specified the intersections nodes between these discs elements are identified then steady flow through the network is calculated using a mixed analytical numerical technique in each fracture analytic equations for flow into or out of each node as a function of the average head at each node are developed the equations are based on image theory and the assumption that each node is a source or sink of uniform strength a set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture these equations are solved for the average head at each node and flux between fractures can then be calculated by substituting the average head values back into the analytical equations the model has been successfully checked against analytical results for several cases of two and three intersecting fractures we plan to use these techniques to measure the permeability of fracture networks

investigations on the applicability of fuzzy interference abstract this paper investigates the applicability of some fuzzy implication operators which were evaluated in the literature and are considered to be very good operators we show that iin 1 1 a a b b has the best performance in the cases examined some new fuzzy implication operators are also investigated and found comparable in all cases to the operator given above

a review and comparison of six reasoning methods abstract five fuzzy reasoning methods are reviewed and their performance is compared with respect to a fuzzy control system model developed by an objective method based on three sets of real life data it is found from the investigation that the reasoning precision the calculation time and the number of possible input states to which a given reasoning method responds differ according to each reasoning method generally the point valued reasoning methods which are based on the assumption that connectives are crisp give better precision and shorter calculation time when the connectives are assumed to be linguistic reasoning with interval valued fuzzy sets are more appropriate to represent linguistic uncertainty for this reason type ii fuzziness generated with interval valued fuzzy sets are better handled with interval valued reasoning methods

minimum traveltime calculation in 3 d graph theory traveltime calculation is a crucial part of seismic migration schemes especially prestack migration there are many different ways to compute traveltimes these methods can be divided into three categories 1 ray tracing julian and gubbins 1977 cerven et al 1977 these treat the problem as a initial value problem by shooting rays from the source to the receivers or they can also treat the problem as a two point boundary value problem an initial raypath is bent using perturbation theory until fermat s principle is satisfied nichols 1994 also computed traveltimes with the amplitude information attached to it in two dimensions 2 finite difference methods reshel and kosloff 1986 vidale 1988 van trier and symes 1991 these solve the eikonal equation directly by using different numerical schemes such as the runge kutta method wavefront expansion or upwind finite difference 3 graph theory moser 1991 fisher and lees 1993 meng et al 1994 this method recasts the traveltime prob

study on stability of fuzzy closed loop control systems abstract the problem of stability of fuzzy closed loop control systems has long been unsolved through analyzing the max min composition operator in fuzzy systems this paper presents a reasonable analytical model of fuzzy closed loop systems and then proposes a method to analyze the stability of control systems by the relational matrix of fuzzy systems an example is given to show the method available

shortest path calculation of seismic rays like the traveling salesman who wants to find the shortest route from one city to another in order to minimize his time wasted on traveling one can find seismic raypaths by calculating the shortest traveltime paths through a network that represents the earth the network consists of points that are connected with neighboring points by connections as long as the traveltime of a seismic wave along it the shortest traveltime path from one point to another is an approximation to the seismic ray between them by fermat s principle the shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously there are no restrictions of classical ray theory diffracted raypaths and paths to shadow zones are found correctly there are also no restrictions to the complexity or the dimensionality of the velocity model furthermore there are no problems with convergence of trial raypaths toward a specified receiver nor with ray

fuzzy expert systems for ie or ms abstract fuzzy expert systems can be developed for the effective use of management within the domains of concern associated with industrial engineering ie operations research or and management science ms these models are designed with 1 expressive powers of representation embedded in linguistic variables and their linguistic values in natural language expressions and 2 improved methods of inference based on fuzzy logic which is a generalization of multi valued logic the results of these fuzzy expert system models are either 1 approximately good in comparison with their classical counterparts i e within a few percentage points of the optimal results of classical models as for example for the cases of production and spare parts planning or 2 much better than their counterparts as for example for the cases of job shop scheduling and consumer preference prediction in market share analysis in order to establish a sound basis for the preceding claims basic issues of representation and inference are first reviewed and then several prototype case studies are presented to support these claims

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

block modeling and segmentally iterative ray tracing in complex 3d media we propose using a set of blocks to approximate geologically complex media that cannot be well described by layered models interfaces between blocks are triangulated to prevent overlaps or gaps often produced by other techniques such as b splines and to speed up the calculation of intersection points between a ray and block interfaces we also use a smoothing algorithm to make the normal vector of each triangle continuous at the boundary so that ray tracing can be performed with stability and accuracy based on fermat s principle we perturb an initial raypath between two points generally obtained by shooting with a segmentally iterative ray tracing sirt method intersection points on a ray are updated in sequence instead of simultaneously because the number of new intersection points may be increased or decreased during the iteration process to improve convergence speed we update the intersection points by a first order explicit formula instead of traditional iterative methods only transmitted and reflected waves are considered numerical tests demonstrate that the combination of block modeling and segmentally iterative ray tracing is effective in implementing kinematic two point ray tracing in complex 3d media

searching for basic properties obtaining robust implication operators in fuzzy control abstract this paper deals with the problem of searching basic properties for robust implication operators in fuzzy control we use the word robust in the sense of good average behavior in different applications and in combination with different defuzzification methods we study the behavior of the two main families of implication operators in the fuzzy control inference process these two families are composed by those operators that extend the boolean implication implication functions and those ones that extend the boolean conjunction t norms and force implications in order to develop the comparative study we will build different fuzzy controllers by means of these implication operators and will apply them to the fuzzy modeling of the real function y x and two three dimensional surfaces we analyze whether one of these two properties extension of the boolean implication and extension of the boolean conjunction is sufficient for obtaining a good implication operator or whether some complementary properties are necessary next we analyze whether we can get basic properties for good implication operators presenting three basic properties for the so called robust implication operators

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

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

upscaling discrete fracture network simulations an alternative to continuum transport models 1 particle tracking through stochastically generated networks of discrete fractures provides an alternative to the conventional advection dispersion description of transport in fractured rock however discrete fracture network simulations are computationally intensive and usually limited to small scales an approach for direct upscaling of discrete fracture simulations is described trajectories for nonreacting tracer particles are first extracted from relatively small discrete fracture network simulations tracer rock interaction is represented by also calculating a cumulative reactivity parameter along each trajectory the residence time reactivity information is then used in a monte carlo simulation to construct artificial particle trajectories of any length thereby achieving the upscaling objective in its simplest form the procedure has the form of a random walk evolving in a two dimensional space tests using site specific and generic networks show that it is necessary to modify the random walk to produce sequential correlation along the trajectories we achieve this by using a discrete state markov process to direct the random walk the procedure is computationally efficient easily implemented and compares well with the network simulations

on numerically solving the complex eikonal equation using real ray tracing methods a comparison with the exact analytical solution the exact analytical solution of the complex eikonal equation describing p and s waves radiated by a point source situated in a simple type of isotropic viscoelastic medium was ascertained the velocity attenuation model is smoothly inhomogeneous with a constant gradient of the square of the complex slowness the resultant traveltime is complex its real part describes the wave propagation and its imaginary part describes the attenuation effects the solution was further used as a reference solution for numerical tests of the accuracy and robustness of two approximate ray tracing approaches solving the complex eikonal equation real elastic ray tracing and real viscoelastic ray tracing numerical modeling revealed that the real viscoelastic ray tracing method is unequivocally preferable to elastic ray tracing it is more accurate and works even in situations when the elastic ray tracing fails also the ray fields calculated by the real viscoelastic ray tracing are excellently reproduced even in the case when the elastic ray tracing yields completely distorted results compared with complex ray tracing which is limited to simple types of media the real viscoelastic ray tracing offers a fast and computationally straightforward procedure for calculating complex traveltimes in complicated 3d inhomogeneous attenuating structures

obtaining smooth solutions to large linear inverse problems it is not uncommon now for geophysical inverse problems to be parameterized by 10 4 to 10 5 unknowns associated with upwards of 10 6 to 10 7 data con straints the matrix problem defining the linearization of such a system e g m b is usually solved with a least squares criterion m t t b the size of the matrix however discourages the direct solution of the system and researchers often tum to iterative techniques such as the method of conjugate gradients to obtain an estimate of the least squares solution these iterative methods take advantage of the sparse ness of which often has as few as 2 3 percent of its elements nonzero and do not require the calculation or storage of the matrix t although there are usually many more data constraints than unknowns these problems are in general underdetermined and therefore require some sort of regularization to obtain a solution when the regularization is simple damping the conjugate gradients method tends to converge in relatively few iterations however when derivative type regularization is applied first derivative constraints to obtain the flattest model that fits the data second deriv ative to obtain the smoothest the convergence of parts ofthe solution may be drastically inhibited in a series of i d examples and a synthetic 2 d crosshole tomography example we demonstrate this problem and also suggest a method of accelerating the convergence through the preconditioning of the conjugate gradient search direc tions we derive a i d preconditioning operator for the case of first derivative regularization using a wkbj approximation we have found that preconditioning can reduce the number of iterations necessary to obtain satisfactory convergence by up to an order of magnitude the conclusions we present are also relevant to baye sian inversion where a smoothness constraint is im posed through an a priori covariance of the model

probabilistic sets and fuzzy reasoning for data analysis problems abstract this paper presents two methods based on probabilistic sets to achieve some problems in data analysis we are indebted to professor arnold kaufmann for the beginnings of these two methods some of the first ideas were found in his prolific work the first method is related to subjective data analysis the second one is an approach for establishing a relationship two data sets the first one having a subjective origin and the second one being objective the purpose of this paper is not to compete with improved data analysis methods but to propose if data can be taken into account as probabilistic fuzzy sets to use such a representation which loses very little information both methods were tested on real data and the results compared with those obtained with improved data analysis methods mainly those of the principal component analysis and multiple correspondence factor analysis

an on line identification algorithm for fuzzy systems abstract based on the pedrycz s reference fuzzy sets the paper presents an on line identification algorithm for fuzzy systems which can on line update the fuzzy model the method proposed is useful for further analysis and development of the fuzzy model an example is given to illustrate the on line identification of the fuzzy model

approximate reasoning for production planning abstract approximate reasoning for production planning could effectively be based on an interval valued representation of linguistic variables an interval valued representation provides a framework that i incorporates a dispersion about membership values and ii produces a robust result compared to classical results the proposed representation and inference is applied to a set of production problems in prototype studies the result of one such prototype study is summarized

flow simulation in three dimensional discrete fracture networks in fractured rocks fluid flows mostly within a complex arrangement of fractures both the fracture network structure and its hydraulic properties are determined at first order by the broad range of fracture lengths and densities to handle the observed wide variety of fracture properties and the lack of direct fracture visualization we develop a general and efficient stochastic numerical model for discrete fracture networks dfns in a three dimensional 3d computational domain we present an original conforming mesh generation method addressing the penalizing configurations stemming from close fractures and acute angles between fracture intersections flows are subsequently computed by using a mixed hybrid finite element mhfe method the lack of direct fracture knowledge is treated by monte carlo simulations requiring simulations with a large number of networks with various characteristics we analyze the complexity in size and in time for the computation of flow in 3d dfns meshed with our method and compare with the complexities for 2d rectangular domains meshed with a regular grid we find out that complexity in size is similar whereas complexity in time is slightly larger for dfns than for 2d regular domains

an improved mesh generation scheme for the wavefront construction method wavefront construction is an effective tool for the rapid calculation of ray fields in anisotropic media the method explicitly tracks the propagation of a wavefront through a model mapping it to a computational mesh that is interpolated when accuracy criteria based on paraxial ray methods are violated takeoff angles are used often to define the initial ray directions but uniform sampling in the two angles leads to oversampling of the ray field in the direction of the axis such sampling can lead also to numerical instability associated with vanishing derivatives with respect to the azimuthal angle we suggest a new wavefront mesh definition using the cubed sphere mesh which is a coordinate system used to solve partial differential equations in spherical geometries when using this mesh ray directions are assigned by mapping points on a regular discretization of the faces of a cube surrounding the source to corresponding rays this scheme produces a nearly uniform distribution of rays with minimal effort and using the cubed sphere coordinates as ray parameters to calculate partial derivatives completely eliminates the singularities that arise when takeoff angles are used as ray parameters numerical results for quantities related to seismic amplitudes confirm that this new mesh does provide more stable and reliable results

smoothing operators for waveform tomographic imaging the analytic kernel in the space time domain for the frechet derivative of acoustic waveform data with respect to changes in the slowness model is given by the born approximation solution to the integral equation of waveform scattering preconditioning operators in the solution of this forward problem which may incorporate a priori information and approximate solutions are smoothing operators in the imaging problem the first iteration of a nonlinear inversion for the slowness model some preconditioning operators are determined for solutions to the parabolic wave equation and then used to create new sensitivity functions that retain appropriate characteristics of the true frechet kernel in forward calculations the new sensitivity functions define near source near receiver and far field kernels as well as kernels that exhibit an amplitude decay off the ray yielding ray perpendicular sensitivity that scales with the fresnel zone size a sample calculation from a synthetic cross well imaging experimen

on equivalence of approximate reasoning results using different interpretations of fuzzy if then rules abstract initially an axiomatic approach to the definition of fuzzy implication has been recalled in this paper based on this definition several important fuzzy implications have been investigated with respect to the results obtained from inference system a specific type of equivalence of inference results under defuzzification using both logical implication interpretation and conjunctive interpretation of the fuzzy if then rules has been described the theoretical considerations are illustrated by means of numerical examples in the field of fuzzy modeling

scaling of production data obtained from random walk particle tracking simulations in highly fractured porous media abstract we modeled tracer injection through highly fractured media by random walk particle tracking simulations and observed that production curves for different r values distance between injection and production wells are similar to each other and can be scaled hence if we define p t as a probability of a particle to reach the production well within traveling time t and plot p t r vs t r we observe that production curves for different values of r overlaid we identified the dependencies of and parameters on fracture network parameters such as fracture spacing fracture density and the fractal characteristics of fracture network

strategies to identify fuzzy rules directly from certainty degrees a comparison and a proposal with identification methods that learn fuzzy rules directly from certainty degrees we refer to methods that select the most promising rules from the training examples in only one pass in order to do that these methods employ a certainty measure to assess the goodness of each rule this paper aims to analyze in depth the behaviors and features of two different strategies for identifying fuzzy models from certainty degrees each of both combined with one of two well known alternatives for measuring the certainty degrees of the rules with this aim the advantages and drawbacks of each method are analyzed experimentally by considering the model error when applied to several systems besides the robustness of the results is investigated by applying the methods to noisy data as a conclusion a new method combining the best components of the previously considered methods is proposed and its results are analyzed the achieved performance in accuracy and computational cost shows the benefit of this new method

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

statistical analysis of the main parameters in the fuzzy inference process abstract as there are many possibilities to select the set of basic operators used in the fuzzy inference process the search for the fuzzy operators that are most suitable for the different steps of a fuzzy system their characterization and evaluation can be included among the most important topics in the field of fuzzy logic a better insight into the performances of the alternative operators would make it easier to develop a fuzzy application in the present paper the relevancy and relative importance of the operators involved in the fuzzy inference process are investigated by using a powerful statistical tool the analysis of the variance anova 8 the results obtained show that the defuzzifier and the t norm operator are the most relevant factors in the fuzzy inference process moreover this statistical analysis is able to establish a classification of the defuzzifiers and t norms according to their intrinsic characteristics the conclusions here obtained justify the present interest observed in many current papers in studying both operators 6 22 24 33 64 67 futhermore our results are confirmed by some experiments dealing with a real control application

probabilistic sets and fuzzy reasoning to build relation between subjective and objective variables sets abstract this paper presents a new approach for getting into relation two data sets the first one having a subjective origin and the second one being objective the purpose of this paper is not to compete with improved data analysis methods but to propose if data can be taken into account as probabilistic fuzzy sets to use fuzzy reasoning in order to get into relation the two data sets first the two probabilistic fuzzy sets coming from the raw data are built when considering complementary cumulative distribution functions then fuzzy reasoning on inference rules is considered it leads to linking the two obtained distribution functions through a conditional possibility measure in order to fit the generalized modus ponens a composition operator has to be considered too then having a possibility measure composition operator pair its ability to be applied on a given data sample is assessed through performance indexes the performances of 19 pairs are compared to get two sets of fictitious data into relation the results are compared with those of the statistical method of principal component analysis

a fuzzy rule based system for handwritten chinese characters recognition based on radical extraction abstract in this paper a fuzzy rule based system for handwritten chinese characters recognition hccr based on radical extraction is proposed since the writings of handwritten chinese characters vary a lot we adopt fuzzy set theory to deal with the recognition of these fuzzy patterns candidates of strokes are provided with confidence values to obtain more reliable and accurate results furthermore hierarchical fuzzy rule sets that represent the character structures are used to combine the extracted strokes into compound strokes or radicals the flexible expansion ability thus provided is very promising also since the number of rules in a fuzzy system is much less than that in a general rule based system the computation effort is not difficult an average of 99 63 recognition rate of 542 test categories that are selected from the 100th sample set of hccrbase character image database provided by ccl itri taiwan is obtained the experimental results not only verify the feasibility of the proposed system but also suggest that applying fuzzy set theory to hccr is an efficient and promising approach

conditional simulations of fluid flow in three dimensional networks of discrete fractures how to predict flow through a network of discrete fractures in a three dimensional domain is investigated fractures are modeled as circular discs of arbitrary size orientation transmissivity and location a fracture network is characterized by the statistical distributions of these quantities fracture traces observed on a wall form the basis for estimates of mean fracture radius fracture orientation parameters and fracture density fracture trace lengths are estimated with the scanline method and from areal sampling on circular regions the traces observed on the wall can also be used to condition the network this trace conditioning is achieved by forcing the network generator to always reproduce the observed traces conditioning might be a means of decreasing the variability of the fracture networks a numerical simulation model has been developed which is capable of generating a fracture network of desired statistical properties and solving for the steady state flow on each fracture disc the flow is discretized with the boundary element method a series of hypothetical examples are analyzed these examples consist of sets of monte carlo simulations of flow through a series of networks generated from the same statistical distributions the examples lead to the following conclusions large fractures and high fracture density implies good connectivity in the networks a high fracture density implies a small variance in the flow through the network trace conditioning decreases estimation variance only when the fracture network consists of large fractures fracture statistics can be estimated reasonably well from fracture traces observed on a wall

a finite difference scheme for solving the eikonal equation including surface topography for solving the eikonal equation in the regions near the curved earth s surface and the curved interface we find a second order upwind finite difference scheme that uses nonuniform grid spacing in the regions near the earth s surface and the interface respectively specifically in the direct neighborhood of the earth s surface and of the considered interface we replace the regular grid spacing in the vertical direction by the vertical distance between the surface interface point and the grid point under consideration for the horizontal direction however only the regular grid points are used as a result the conventional upwind finite difference formulas are changed into the ones with nonuniform grid spacing furthermore for capturing and propagating the local wavefront near the curved earth s surface interface we adapt the fast marching method by introducing new point types namely the surface point the point above the surface the interface point and the point under the interface if we u

tomography of joint p wave traveltime and polarization data a simple approach for media with low to moderate velocity gradients an elastic wave tomography method utilizing joint traveltime and polarization data is proposed that is computationally simpler than the existing methods hu and menke geophys j int 110 63 1992 farra and begat geophys j int 121 371 1995 in the linearization problem for the use of polarization data we start with ray perturbation theory and assume that the medium is weakly inhomogeneous then the problem formulation for polarization data is approximately expressed as a linear integral of the gradient of the medium slowness perturbation along a reference ray we call this a quasi linear approximation which ignores the effect of the perturbation of the ray position on the first order perturbation of the ray slowness vector to efficiently obtain the solution for multi data sets a quadratic objective functional is constructed by including the data misfit terms and a model constraint term then a new conjugate gradient type of iterative reconstruction algorithm is developed to solve this minimization problem this algorithm is also an extension of the conjugate gradient approach for standard least squares problems the feasibility and capability of the proposed tomography method is illustrated by conducting both noise free and noisy synthetic experiments in a cross hole geometry the numerical results demonstrate that the additional use of polarization data not only improves the image quality but also has a stabilizing effect on the iterative tomography solution however the limitation of the method is that it becomes inaccurate if the velocity variations in the medium change rapidly with position

big ray tracing and eikonal solver on unstructured grids application to the computation of a multivalued traveltime field in the marmousi model this paper presents a numerical computation of the multivalued traveltime field generated by a point source experiment in the marmousi model two methods are combined to achieve this goal a method called big ray tracing used to compute multivalued traveltime fields and an eikonal solver designed to work on unstructured meshes big ray tracing is based on a combination of ray tracing and local solutions of the eikonal equation classical ray tracing first discretizes the phase space and defines local zones that possibly overlap where the traveltime field is multivalued then an eikonal solver computes traveltimes in these zones called big rays it acts as an exact interpolation process between rays associated with different branches of the traveltime field the geometry of big rays may be complicated and is better discretized using unstructured meshes an eikonal solver designed to work on unstructured meshes is used

parameterized r implications a residuated implication operator r implications is a fuzzy material implication operator defined in terms of its corresponding t norm this paper is concerned with a family of r implications derived from the schweizer sklar family of parameterized t norms analysis of fuzzy and defuzzified outputs from two and three rule systems includes proper and improper fuzzy set outputs and exact defuzzified solutions for important special cases such as godel brouwer goguen and lukasiewicz implications a rule can be characterized as strong or weak in its interaction with a neighboring rule if two rules both interact with one another weakly there exists a range of y values all of which are 100 compatible with both rules given any x in their domain of interaction the paper concludes with a discussion of the joint effect of the strength of rule interaction and the value of the sehweizer sklar parameter

3 d traveltime computation using huygens wavefront tracing traveltime computation is widely used in seismic modeling imaging and velocity analysis the two most commonly used methods are ray tracing and numerical solutions to the eikonal equation eikonal solvers are fast and robust but are limited to computing only the first arrival traveltimes ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers we propose a robust and complete method of traveltime computation it is based on a system of partial differential equations which is equivalent to the eikonal equation but formulated in the ray coordinates system we use a first order discretization scheme that is interpreted very simply in terms of the huygens s principle our explicit finite difference solution to the eikonal equation solved in the ray coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step the finite difference method has proven to be a robust alternative to conventional ray tracing while being faster and having a better ability to handle rough velocity media and penetrate shadow zones

exact solutions for interacting rules in generalized modus ponens with parameterized implication functions many authors have presented exact analyses of the behavior of an isolated fuzzy inference rule and many have presented empirical studies of the behavior of multiple rule systems this paper presents an exact analysis of the behavior of a class of two rule systems in which the antecedent and consequent membership functions are trapezoidal and the implication operator is a strong implication s implication or a residuated implication r implication formed by the schweizer sklar family of parameterized t norms the two rule system exhibits many emergent properties not found when a single rule is studied and much of the behavior of many rule systems is dominated by two rule interactions

similarity based inverse approximate reasoning this paper investigates the inverse problem of ap proximate reasoning to conclude a from b and a b from different angles we develop a method to and a solution to the inverse problem by the use of the law of contrapositive symme try in the process generalized modus ponens generalized modus tollens and their generating functions are studied extensively an attempt is made here to establish that the concept of similarity plays an important role in inverse approximate reasoning we apply the concept of similarity to model inverse approximate reasoning and develop a new methodology that is named similarity based inverse approximate reasoning for a solution to the problem algorithms are presented and illustrated with simple yet concrete examples we then use zadeh s compositional rule of inference cri as a combi nation of cylindrical extension and projection and thereby model generalized modus tollens in a different way we thus develop a third way to find a solution to the inverse problem of approximate reasoning a comparison between the result of application of our technique and the real static characteristic of a dc shunt motor is presented

fuzzy inference and its applicability to control systems abstract two fuzzy reasoning methods the linguistic synthesis method and a new model are studied by being applied to construct fuzzy controllers to a second order nonlinear system cart pole system in the former method several implication operators are used in order to investigate the applicabilities and robustnesses of these two methods the parameters of the controlled process are changed the advantages of the new model are shown through the procedure of generating the fuzzy controller and the results of fuzzy control system

fuzzy sets and their operations ii among the basic operations which can be performed on fuzzy sets are the operations of union intersection complement algebraic product and algebraic sum in addition to these operations new operations called bounded sum and bounded difference were defined by l a zadeh to investigate the fuzzy reasoning which provides a way of dealing with the reasoning problems which are too complex for precise solution this paper investigates the algebraic properties of fuzzy sets under these nex operations of bounded sum and bounded difference and the properties of fuzzy sets in the case where these new operations are combined with the well known operations of union intersection algebraic product and algebraic sum

epicardial boundary detection using fuzzy reasoning a fully automated system for detecting the endocardial and epicardial boundaries in a two dimensional echocardiography by using fuzzy reasoning techniques is proposed the image is first enhanced by applying the laplacian of gaussian edge detector second the center of the left ventricle is determined automatically by analyzing the original image next a search process radiated from the estimated center is performed to locate the endocardial boundary by using the zero crossing points after this step the estimation of the range of radius of a possible epicardial boundary is carried out by comparing the high level knowledge of intensity changes along all directions with the actual image intensity changes the high level knowledge of global intensity change in the image is acquired from experts in advance and is represented in the form of fuzzy linguistic descriptions and relations knowledge of local intensity change can therefore be deduced from the knowledge of global intensity change through fuzzy reasoning

finite difference solution of the eikonal equation using an efficient first arrival wavefront tracking scheme first break traveltimes can be accurately computed by the finite difference solution of the eikonal equation using a new corner node discretization scheme it offers accuracy advantages over the traditional cell centered node scheme a substantial efficiency improvement is achieved by the incorporation of a wavefront tracking algorithm based on the construction of a minimum traveltime tree for the traditional discretization scheme an accurate average value for the local squared slowness is found to be crucial in stabilizing the numerical scheme for models with large slowness contrasts an improved method based on the traditional discretization scheme can be used to calculate traveltimes in arbitrarily varying velocity models but the method based on the corner node discretization scheme provides a much better solution

some considerations on input and output partitions to produce meaningful conclusions in fuzzy inference abstract a large number of papers have been devoted to point out which combinations of the several fuzzy implication composition and aggregation operators are necessary to satisfy a natural requirement for meaningful reasoning that is given a system observation which matches the antecedent of a rule the conclusion of the inference process matches the consequent of that rule nevertheless only few of these papers have analysed once fixed a combination which constraints on the reciprocal position of input and output fuzzy sets should be satisfied in this paper we consider fuzzy implication operators which are extensions of the two valued logic implication operator and are non decreasing with respect to their second argument generic sup t composition operators and minimum as aggregation operator first we analyse some features namely uniform level of indetermination perfect matching with the consequent of a rule and complete indetermination of the conclusions inferred by those fuzzy implication operators with regard to fuzzy reasoning with one rule then as regards approximate reasoning with multiple rules we demonstrate that if the fundamental requirement for fuzzy reasoning is satisfied then the fuzzy sets which partition the input and output universes have to meet appropriate constraints finally we provide a sufficient condition defined on input fuzzy sets to obtain a reasonable inference result

hypersingular integrals in boundary element fracture analysis a new general purpose boundary element method for domains with cracks has been recently developed this technique avoids the use of a multi domain decomposition by including an additional integral equation expressing the boundary condition on the crack the principal requirement of this technique is the analytic determination of certain hypersingular integrals of the green s function which arise from this equation in order to establish the applicability of this method for fracture these integrals are evaluated herein for the kelvin solution of the three dimensional navier equations of linear elasticity numerical results for fracture problems using the single domain boundary element analysis are also presented

robustness of fuzzy reasoning via logically equivalence measure abstract in this paper we discuss robustness of fuzzy reasoning after proposing the definition of perturbation of fuzzy sets based on some logic oriented equivalence measure we present robustness results for various fuzzy logic connectives fuzzy implication operators inference rules and fuzzy reasoning machines and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators the robustness results are presented in terms of equalities of fuzzy sets based on some logic oriented equivalence measure and the maximum of which ensures the corresponding equality holds is derived

seepage flow with free surface in fracture networks 1 crystalline rocks are often heterogeneous geological materials that contain numerous fractures of various attitudes and scales although considerable advances have been made in simulation of fluid flow through fractured media our knowledge of seepage flow with free surfaces in fracture networks remains to be an outstanding issue in this paper the partial differential equations pdes defined on the whole fracture network domain are formulated for free surface seepage flow problems by an extension of darcy s law a variational inequality vi formulation is then presented and the proof of the equivalence between the pde and vi formulations is given since the boundary conditions involving the flux components in the pde formulation become the natural conditions in the vi formulation the difficulty of choosing the trial functions for numerical solutions is significantly reduced and the locations of seepage points can be easily determined on the basis of the discrete vi the corresponding numerical procedure for unconfined seepage analysis of discrete fracture network has been developed the results from three typical examples demonstrate the validity and capability of the procedure for unconfined seepage problems involving complicated fracture networks

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

a new model of fuzzy reasoning abstract a new model of fuzzy reasoning is proposed a comparison of inference results using the new model and the linguistic synthesis approach is given

robustness of fuzzy reasoning and spl delta equalities of fuzzy sets fuzzy reasoning methods or approximate reasoning methods are extensively used in intelligent systems and fuzzy control in this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning that is he discusses the robustness of fuzzy reasoning after reviewing his previous work 1996 he presents robustness results for various implication operators and inference rules all the robustness results are formulated in terms of spl delta equalities of fuzzy sets two fuzzy sets are said to be spl delta equal if they are equal to an extent of spl delta

fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras in the paper we shall examine the fuzziness measure fm of terms or of complete and linear hedge algebras of a linguistic variable the notion of semantically quantifying mappings sqms previously examined by the first author will be redefined more generally and a closed relation between the fm of linguistic terms and a family of sqms with the parameters to be the fm of primary terms and linguistic hedges will be established a semantics based topology of hedge algebras and a closed and interesting relation between this topology the fm and the above family of sqms will be discovered and examined an applicability of the fm and sqms will be shown by an examination of some application examples

applicability of some fuzzy implication operators this paper examines the maximal errors of seventy two implication operators with various membership functions in several typical cases and shows five operators which have very good performance in fuzzy inference

hierarchical scheduling based on approximate reasoning a comparison with isis abstract a hierarchical scheduling problem is considered the hierarchy consists of five levels each level has an associated rule base there are six basic input factors 1 the priority of a job 2 the earliness of the due date of a job 3 the likelihood of the availability of resources for the work station w s s 4 the capability of w s s to meet physical constraints 5 the capability of w s s to meet quality requirements and 6 work in progress inventory costs there are five consequents one for each level 1 suggested place of a job in the order of jobs 2 the suggested place of w s s in the order of w s s 3 the current suggested place of a w s s in the order of w s s 4 the next current suggested place of w s s in the order of w s s and 5 the suggested place of the queue arrangements both the input factors antecedents and the output factors consequents take on linguistic terms to express the qualitative assessments of a scheduling expert within the context of the specific factor an approximate reasoning framework based on interval valued fuzzy sets and a search tree heuristic with similarity measures is executed for the analysis of the hierarchical scheduling problem using a fuzzy tool box coded in lisp that interacts with kee for the representation of the knowledge base in a frame structure the software model is tested with real life data used in m fox s isis model a comparison of the two models based on tardiness measure shows that there are slight advantages to fuzzy set representation and approximate reasoning with respect to tardiness measure above and beyond the user friendly nature of knowledge representation available with fuzzy sets

linguistic stability analysis of fuzzy closed loop control systems abstract a linguistic analysis method for fuzzy closed loop control systems where both fuzzy controller and controlled processes are described by linguistic rules is proposed in this paper first a linguistic relation model of a fuzzy closed loop control system is deduced from the linguistic rule models of the fuzzy controller and the controlled process then the linguistic stability of the fuzzy closed loop system is discussed by a linguistic relation matrix finally an example is given to illustrate the proposed method