a boundary value problem for second order fuzzy differential equations abstract in this paper we interpret a two point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept we present a new concept of solutions and utilizing the generalized differentiability we investigate the problem of finding new solutions some examples are provided for which the new solutions are found

first order linear fuzzy differential equations under generalized differentiability first order linear fuzzy differential equations are investigated we interpret a fuzzy differential equation by using the strongly generalized differentiability concept because under this interpretation we may obtain solutions which have a decreasing length of their support which means a decreasing uncertainty in several applications the behaviour of these solutions better reflects the behaviour of some real world systems derivatives of the h difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations using different versions of the variation of constants formula some examples show the rich behaviour of the solutions obtained

approximation of pareto optima in multiple objective shortest path problems we study methods for approximating the set of pareto optimal paths in multiple objective shortest path problems known generalizations of standard shortest path methods will compute this set but can suffer from rapidly increasing computational and storage demands as problem size increases in an effort to avoid such difficulties we develop approximation methods that can estimate the pareto optima to any required degree of accuracy the approximation methods are fully polynomial that is they operate in time and space bounded by a polynomial in problem size and accuracy of approximation the greater the accuracy the more time required to reach a solution we show how approximation methods may be applied to yield fully polynomial approximation schemes for a variety of np complete single objective problems

periodic boundary value problems for first order linear differential equations with uncertainty under generalized differentiability we study the existence of solutions to a class of first order linear fuzzy differential equations subject to periodic boundary conditions from the point of view of generalized differentiability the objective of this paper is to show that fuzzy differential equations under generalized differentiability can be used in the study of periodic phenomena by considering a combination of two types of derivatives with a switching point we provide sufficient conditions which guarantee that the piecewise defined solutions match adequately and illustrate through some examples the process of construction and calculation of solutions

approximation schemes for the restricted shortest path problem this note contains two fully polynomial approximation schemes for the shortest path problem with an additional constraint the main difficulty in constructing such algorithms arises since no trivial lower and upper bounds on the solution value whose ratio is polynomially bounded are known in spite of this difficulty one of the algorithms presented here is strongly polynomial applications to other problems are also discussed

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

fuzzy fractional quadratic regulator problem under granular fuzzy fractional derivatives in this paper a class of uncertain linear dynamical systems called fuzzy fractional linear dynamical systems is investigated the aim is to find control inputs to keep the states of the fuzzy fractional dynamical systems near the zero in an optimal manner the optimality criterion is in a form of a granular fuzzy integral whose integrand is a quadratic function of the state variables and control inputs the fuzzy fractional dynamical system is described using fuzzy fractional differential equations ffdes in order to achieve the aim an effective approach for solving ffdes should be at disposal due to some restrictions imposed by the previous approaches dealing with ffdes a new approach is proposed the proposed approach is based on the granular derivative and the so called relative distance measure fuzzy interval arithmetic new definitions of fuzzy fractional derivatives and integral called left and right granular riemann liouville fuzzy fractional derivatives left and right granular caputo fuzzy fractional derivatives and the left and right granular fuzzy fractional integral are also presented in addition the concepts of granular fuzzy partial derivative and granular fuzzy chain rule are introduced by the approximations of the granular fuzzy fractional integral and the granular caputo fuzzy fractional derivative the approximation solution to the ffdes is obtained consequently based on the new concepts and theorems the solution to the fuzzy fractional quadratic regulator problem is given by a theorem this paper closes with an example of regulating the motion of boeing 747 in longitudinal direction with the presence of uncertainty in the initial conditions and the coefficients

using angular dispersion of gradient direction for detecting edge ribbons edges in a scene generally project to smooth continuous curves nearly everywhere in the image which results in low angular deviation of the intensity gradients in small neighborhoods straddling edges angular deviation is shown to be a measure of snr a theoretical analysis of angular deviation arising due to independent and identically distributed n 0 sigma sup 2 random noise is presented angular deviation thresholds for neighborhood sizes from 3 3 to 11 11 pixels are determined both from this analysis and numerical examples the proposed gradient angular dispersion detection algorithm detects edge elements by comparing the measured angular deviation with values computed for the minimum acceptable snr low values of deviation violate the no edge hypothesis the algorithm is shown to make good use of the limited dynamic range of the imaging system the sensitivity and selectivity of the strategy are both shown to be high

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

minimum stability control problem and time optimal control problem for fuzzy linear control systems abstract in this paper we give a new concept that is the minimum stability control problems for fuzzy linear control systems and our observations revolve around this object at the same time study the existence of solutions for some kinds of this problem by generalized hukuhara derivative in addition we present the time optimal fuzzy control problem for this problems an algorithm to find the time optimal is described and illustrated by a basic example

initial value problems for higher order fuzzy differential equations we consider nth order fuzzy differential equations with initial value conditions we prove the existence and uniqueness of solution for nonlinearities satisfying a lipschitz condition we apply the obtained results to the particular case of linear fuzzy problems

extracting straight lines this paper presents a new approach to the extraction of straight lines in intensity images pixels are grouped into line support regions of similar gradient orientation and then the structure of the associated intensity surface is used to determine the location and properties of the edge the resulting regions and extracted edge parameters form a low level representation of the intensity variations in the image that can be used for a variety of purposes the algorithm appears to be more effective than previous techniques for two key reasons 1 the gradient orientation rather than gradient magnitude is used as the initial organizing criterion prior to the extraction of straight lines and 2 the global context of the intensity variations associated with a straight line is determined prior to any local decisions about participating edge elements

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

complexity of the multicut problem in its vanilla partial and generalized versions in graphs of bounded treewidth abstract in the multicut problem the input consists of a graph and a set of pairs of terminal vertices that have to be disconnected by the removal of a set of edges with minimum total weight the partial multicut problem generalizes multicut by only requiring a given number of pairs of terminals to be disconnected by the removal of edges it has been shown that multicut remains apx hard if the treewidth t w g of its input graph g is bounded but that it is fpt w r t t w g h where h is the demand graph whose vertices are the terminals and whose edges are the pairs of terminals we prove that this also holds for partial multicut furthermore it has been proved that multicut also becomes polynomial time solvable if t w g is bounded and h is complete this is the multiterminal cut problem we extend this result in two directions by proving that multicut remains polynomial time solvable if t w g h is bounded and that this remains true for partial multicut finally we show that if we further generalize the problem to allow non unitary profits for pairs of terminals then the problem is weakly np hard and has an fptas if t w g h is bounded and becomes apx hard if t w g h is bounded

precision edge contrast and orientation estimation the contrast and orientation estimation accuracy of several edge operators that have been proposed in the literature is examined both for the noiseless case and in the presence of additive gaussian noise the test image is an ideal step edge that has been sampled with a square aperture grid the effects of subpixel translations and rotations of the edge on the performance of the operators are studied it is shown that the effect of subpixel translations of an edge can generate more error than moderate noise levels methods with improved results are presented for sobel angle estimates and the nevatia babu operator and theoretical noise performance evaluations are also provided an edge operator based on two dimensional spatial moments is presented all methods are compared according to worst case and rms error in an ideal noiseless situation and rms error under various noise levels

existence and uniqueness of fuzzy solution for semilinear fuzzy integrodifferential equations with nonlocal conditions abstract in this paper the existence and uniqueness of a fuzzy solution for the semilinear fuzzy integrodifferential equation is established via the banach fixed point analysis approach and using the fuzzy number whose values are normal convex upper semicontinuous and compactly supported interval in e n

a class of linear differential dynamical systems with fuzzy matrices abstract this paper investigates the first order linear fuzzy differential dynamical systems with fuzzy matrices we use a complex number representation of the level sets of the fuzzy system and obtain the solution by employing such representation it is applicable to practical computations and has also some implications for the theory of fuzzy differential equations we then present some properties of the 2 dimensional dynamical systems and their phase portraits some examples are considered to show the richness of the theory and we can clearly see that new behaviors appear we finally present some conclusions and new directions for further research in the area of fuzzy dynamical systems

nonlinear processing and analysis of angular signals physical quantities referring to angles like vector direction color hue etc exhibit an inherently periodic nature due to this periodicity digital filters and edge operators proposed for data on the line cannot be applied on such data we introduce filters for angular signals circular mean circular median circular a trimmed mean circular modified trimmed mean particular emphasis is given to the circular median filter for which some interesting properties are derived we also use estimators of circular dispersion to introduce edge detectors for angular signals three variations for the extension of quasirange to circular data are proposed and expressions for their output pdf are derived these circular quasiranges have good and user controlled properties as edge detectors in noisy angular signals the performance of the proposed edge operators is evaluated on angular edges using certain quantitative criteria finally a series of experiments featuring one dimensional 1 d angular signals and hue images is used to illustrate the operation of the new filters and edge detectors

variation of constant formula for first order fuzzy differential equations in this paper we study first order linear fuzzy differential equations by using the generalized differentiability concept and we present the general form of their solutions we also correct and complete some previous results finally some examples are given to illustrate our results

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

z differential equations this paper is devoted to make a framework for studying a class of uncertain differential equations called z differential equations in order to achieve the purpose we first introduce four basic operations on z numbers based on semigranular function then the limit and continuity concepts of a z number valued function are given under a definition of a metric on the space of z numbers moreover the concepts of z differentiability z integral and z laplace transform of a z number valued function are introduced in addition by giving some theories proved in this paper a basis for calculus z calculus is established we further give theories based on which existence and uniqueness of z differential equations are investigated a conceptual unity between z differential equations and z numbers is also shown the conceptual unity demonstrates that a z differential equation may be expressed as a bimodal differential equation combining a fuzzy differential equation fde and a random differential equation moreover the concept of a bimodal cut called s mu cut is introduced and its relation to other new concepts such as acceptable time and acceptable information area is explained using an example the application of z differential equations in medicine is clarified it is demonstrated that z differential equations outperform fdes in making a decision under uncertainty

image field categorization and edge corner detection from gradient covariance edges corners and vertices in an image correspond to 1d one dimensional and 2d discontinuities in the intensity surface of the underlying scene ridges and peaks correspond to 1d and 2d extrema in it all of them can be characterized by the distribution of gradients particularly by the dimensionality of it the approach to image field categorization here is to construct a covariance matrix of the gradient vector in each small window and apply the canonical correlation analysis to it schwarz s inequality on the matrix determinant and the related differential equation is the key to this analysis we obtain two operators p sub eg and q sub eg to categorize the image field into a unidirectionally varying region univar an omidirectionally varying region omnivar and a nonvarying region we investigate the conditions under which their absolute maximum response i e p sub eg 1 and q sub eg 1 occurs in the small window and show that they are respectively the desired 1d and 2d discontinuities extrema and omnivar is in many cases a 1d pattern in polar coordinates this leads to an algorithm to obtain further classification and accurate localization of them into edges ridges peaks corners and vertices through detailed analysis in the informative varying axis of them we examined and compared the performance of the operators and the localization algorithm on various types of images and various noise levels the results indicate that the proposed method is superior with respect to stability localization and resolution

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

a new approach for the optimal fuzzy linear time invariant controlled system with fuzzy coefficients in this article a new technique for solving the linear time invariant dynamical system with fuzzy parameters is proposed this approach is used to solve a fuzzy controlled system by using a cuts and presentation of numbers in a more compact form by moving to the field of complex numbers by considering a new feature of the hamiltonian function and using the pontryagin maximum principle the solution of the fuzzy optimal controlled system is considered

approximation schemes for a class of subset selection problems in this paper we develop an easily applicable algorithmic technique tool for developing approximation schemes for certain types of combinatorial optimization problems special cases that are covered by our result show up in many places in the literature for every such special case a particular rounding trick has been implemented in a slightly different way with slightly different arguments and with slightly different worst case estimations usually the rounding procedure depended on certain upper or lower bounds on the optimal objective value that have to be justified in a separate argument our easily applied result unifies many of these results and sometimes it even leads to a simpler proof we demonstrate how our result can be easily applied to a broad family of combinatorial optimization problems as a special case we derive the existence of an fptas for the scheduling problem of minimizing the weighted number of late jobs under release dates and preemption on a single machine the approximability status of this problem has been open for some time

numerical solution of some initial optimal control problems using the reproducing kernel hilbert space technique in this paper we present a general technique for solving a class of linear nonlinear optimal control problems in fact an analytical solution of the state variable is represented in the form of a

adaptive pseudo dilation for gestalt edge grouping and contour detection we consider the problem of detecting object contours in natural images in many cases local luminance changes turn out to be stronger in textured areas than on object contours therefore local edge features which only look at a small neighborhood of each pixel cannot be reliable indicators of the presence of a contour and some global analysis is needed we introduce a new morphological operator called adaptive pseudo dilation apd which uses context dependent structuring elements in order to identify long curvilinear structure in the edge map we show that grouping edge pixels as the connected components of the output of apd results in a good agreement with the gestalt law of good continuation the novelty of this operator is that dilation is limited to the voronoi cell of each edge pixel an efficient implementation of apd is presented the grouping algorithm is then embedded in a multithreshold contour detector at each threshold level small groups of edges are removed and contours are completed by means of a generalized reconstruction from markers the use of different thresholds makes the algorithm much less sensitive to the values of the input parameters both qualitative and quantitative comparison with existing approaches prove the superiority of the proposed contour detector in terms of larger amount of suppressed texture and more effective detection of low contrast contours

consistent gradient operators we propose optimal gradient operators based on a newly derived consistency criterion this criterion is based on an orthogonal decomposition of the difference between a continuous gradient and discrete gradients into the intrinsic smoothing effect and the self inconsistency involved in the operator we show that consistency assures the exactness of gradient direction of a locally 1d pattern in spite of its orientation spectral composition and sub pixel translation stressing that inconsistency reduction is of primary importance we derive an iterative algorithm which leads to accurate gradient operators of arbitrary size we compute the optimum 3 spl times 3 4 spl times 4 and 5 spl times 5 operators compare them with conventional operators and examine the performance for one synthetic and several real images the results indicate that the proposed operators are superior with respect to accuracy bandwidth and isotropy

gradient orientation pattern matching with the hamming distance abstract this paper presents a novel pattern matching technique that is robust to illumination changes and the occlusion problem the technique is based on the matching of gradient orientations in place of traditional image features such as intensities or gradients gradient orientations depend on the texture in an image they are known to be insensitive to changes of image intensities that are often caused by time varying illuminations or the auto gain control agc function of the camera moreover the proposed method employs a voting strategy in the process of matching gradient orientations the method works remarkably well even when a large part of the pattern is occluded with a foreign object consequently the proposed method is robust to both irregular lighting conditions and the occlusion problem

extracting image orientation feature by using integration operator this paper presents an orientation operator to extract image local orientation features we show that a proper employment of image integration leads to an unbiased orientation estimate based on which an orientation operator is proposed the resulting discrete operator has flexibility in the scale selection as the scale change does not violate the bias minimization criteria an analytical formula is developed to compare orientation biases of various discrete operators the proposed operator shows lower bias than eight well known gradient operators experiments further demonstrate higher orientation accuracy of the proposed operator than these gradient operators