computing real solutions of fuzzy polynomial systems abstract this paper presents an efficient algorithm called solvefuzzysystem or sfs for finding real solutions of polynomial systems whose coefficients are symmetrical l r fuzzy numbers with bounded support for which the spread functions l and r are bijective the real solutions of such a system are deduced from solutions of some polynomial systems with real coefficients this algorithm is based on new results that are universal because they are independent from the spread functions these theoretical results include the management of the fuzzy system s solutions signs an implementation in the fuzzy package of the free computer algebra software sagemath and a parallel version of the algorithm are described

resolution of a system of fuzzy polynomial equations using the grobner basis the occurrence of imprecision in the real world is inevitable due to some unexpected situations the imprecision is often involved in any engineering design process the imprecision and uncertainty are often interpreted as fuzziness fuzzy systems have an essential role in the uncertainty modelling which can formulate the uncertainty in the actual environment in this paper a new approach is proposed to solve a system of fuzzy polynomial equations based on the grobner basis in this approach first the h cut of a system of fuzzy polynomial equations is computed and a parametric form for the fuzzy system with respect to the parameter of h is obtained then a grobner basis is computed for the ideal generated by the h cuts of the system with respect to the lexicographical order using faugere s algorithm i e f 4 algorithm the grobner basis of the system has an upper triangular structure therefore the system can be solved using the forward substitution hence all the solutions of the system of fuzzy polynomial equations can easily be obtained finally the proposed approach is compared with the current numerical methods some theorems together with some numerical examples and applications are presented to show the efficiency of our method with respect to the other methods

numerical solution of a system of fuzzy polynomials by fuzzy neural network in this paper a new approach for solving systems of fuzzy polynomials based on fuzzy neural network fnn is presented this method can also lead to improve numerical methods in this work an architecture of fuzzy neural networks is also proposed to find a real root of a system of fuzzy polynomials if exists by introducing a learning algorithm finally we illustrate our approach by numerical examples

variational problems with fractional derivatives invariance conditions and nother s theorem abstract a variational principle for lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases necessary and sufficient conditions for an infinitesimal transformation group basic nother s identity are obtained these conditions extend the classical results valid for integer order derivatives a generalization of nother s theorem leading to conservation laws for fractional euler lagrangian equation is obtained as well results are illustrated by several concrete examples finally an approximation of a fractional euler lagrangian equation by a system of integer order equations is used for the formulation of an approximated invariance condition and corresponding conservation laws

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

lie symmetry analysis and some new exact solutions of the wu zhang equation the lie symmetry analysis and the basic similarity reductions are performed for the wu zhang equation a 2 1 dimensional nonlinear dispersive wave equation some new exact solutions generated from the similarity transformation are provided they demonstrate some new three dimensional features of a single solitary wave and two interacting solitary waves

suppression of time aliasing in the solution of the equations of motion of an impacted beam with partial constrained layer damping abstract signal processing issues encountered when an analytical spectrum is converted in the time domain with an inverse discrete fourier transform are investigated in the analytical model of the transient time response of an impacted beam with partial constrained layer damping pcld developed in ref d granger a ross effects of partial constrained viscoelastic layer damping parameters on the initial transient response of impacted cantilever beams experimental and numerical results journal of sound and vibration 321 1 2 2009 45 64 doi 10 1016 j jsv 2008 09 039 noncausal effects were observed for lightly damped structures as discussed in the present paper the noncausal effects were due to time aliasing occurring when continuous frequency spectra were discretized to suppress such errors the numerical laplace transform is introduced and applied to the previous model which was based on fourier transforms the equations of motion of the system and the viscoelastic properties of the core are formulated in the laplace domain a window is used in the laplace domain to avoid amplification of the gibbs oscillations that are caused by the truncation of the spectrum the new solution technique is compared to the previous method it is shown that noncausal effects appearing in the first milliseconds of time signals with the use of discrete fourier transforms are avoided with the laplace transform solution method numerical results are validated for transient responses using experimental impact force signals the results are in good agreement with experimental data

on invariant analysis of some time fractional nonlinear systems of partial differential equations i an investigation of lie point symmetries for systems of time fractional partial differential equations including ito system coupled burgers equations coupled korteweg de vries equations hirota satsuma coupled kdv equations and coupled nonlinear hirota equations has been done using the obtained symmetries each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving erdelyi kober fractional differential operator depending on a parameter

improved predictor corrector method for solving fuzzy initial value problems in this paper an improved predictor corrector ipc method is proposed to solve the fuzzy initial value problem the ipc method is generated by combining an explicit three step method and an implicit two step method the methods are compared with the methods discussed in t allahviranloo n ahmady e ahmady numerical solution of fuzzy differential equations by predictor corrector method information sciences 177 7 2007 1633 1647 and are shown to be more accurate the convergence and stability of the proposed methods are also presented in detail these methods are illustrated by solving some examples

linear optimization with bipolar max min constraints we consider a generalization of the linear optimization problem with fuzzy relational in equality constraints by allowing for bipolar max min constraints i e constraints in which not only the independent variables but also their negations occur a necessary condition to have a non empty feasible domain is given the feasible domain if not empty is algebraically characterized a simple procedure is described to generate all maximizers of the linear optimization problem considered and is applied to various illustrative example problems

a robust transfer matrix formulation for the ultrasonic response of multilayered absorbing media an improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half space and problems associated with numerical stability are solved efficiently the formulation is applicable to longitudinal and shear input waves alike at arbitrary incidence angles and for any sequence of solid or fluid layers also allowance is made for viscoelastic behavior by means of relaxation functions in the laplace transform domain finally the response to arbitrary incident pulse shapes and beam profiles is described through application of two dimensional numerical laplace inversion

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

numerical solution of fuzzy differential equations by predictor corrector method in this paper three numerical methods to solve the fuzzy ordinary differential equations are discussed these methods are adams bashforth adams moulton and predictor corrector predictor corrector is obtained by combining adams bashforth and adams moulton methods convergence and stability of the proposed methods are also proved in detail in addition these methods are illustrated by solving two fuzzy cauchy problems

resolution of fuzzy relational equations method algorithm and software with applications analytical methods and algorithms for inverse problem resolution of fuzzy linear systems of equations in some bl algebras godel algebra in case of max min and min max compositions and goguen algebra in case of max product composition are presented algorithms with software realization for solving fuzzy linear systems of equations are proposed applications include fuzzy optimization with fuzzy linear systems of equation constraint fuzzy machines and covering problem

a new fractional operator of variable order application in the description of anomalous diffusion abstract in this paper a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of caputo type the properties in term of the laplace and fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed the new formulation is efficient in modeling a class of concentrations in the complex transport process

analysis of approximation of continuous fuzzy functions by multivariate fuzzy polynomials for the given fuzzy valued function j rn f0 r the fuzzy valued bernstein polynomial is introduced to show the fact that continuous fuzzy valued functions can be approximately represented as the fuzzy valued polynomials on any compact set u rn some equivalent condition for the continuous fuzzy function f f0 r n f0 r that can be approximated to any degree of accuracy by fuzzy polynomials on arbitrary compact set u f0 r n are presented

invariant analysis and conservation laws for the time fractional 2 1 dimensional zakharov kuznetsov modified equal width equation using lie group analysis abstract in this paper the invariance properties of the time fractional 2 1 dimensional zakharov kuznetsov modified equal width zk mew equation have been investigated using the lie group analysis method lie point symmetries of the time fractional 2 1 dimensional zk mew equation have been derived by using the lie group analysis method of fractional differential equations using the lie symmetry analysis the vector fields and the symmetry reduction of this equation are obtained it is shown that the time fractional 2 1 dimensional zk mew equation can be transformed to an equation with erdelyi kober fractional derivative finally using new conservation theorem with formal lagrangian the new conserved vectors are well constructed with a detailed derivation which constitutes the conservation analysis for the time fractional 2 1 dimensional zk mew equation

time fractional 2 1 dimensional wu zhang system dispersion analysis similarity reductions conservation laws and exact solutions abstract this paper examines the time fractional 2 1 dimensional wu zhang system describing dispersive long waves the dispersion relation of waves has been obtained from linear analysis and used to find the phase and group velocity the dispersion relation shows an anomalous dispersion of waves lie symmetries and the corresponding similarity reductions are carried out using riemann liouville fractional derivative and the order of the system is reduced to lower dimension furthermore the system is analysed for nonlinear self adjointness and the conservation laws are obtained associated with infinitesimal symmetries by applying new conservation theorem the adjoint variables are used to convert conservation laws into original dependent variables the exponential rational function method is employed to find exact solutions revealing kink and bell type profiles the effect of fractional order on the wave profile of solutions is discussed graphically

forecasting methods using fuzzy concepts in this paper fuzzy concepts are applied in forecasting product price and sales in the semiconductor industry which is often conceived as a highly dynamic environment first two fuzzy forecasting methods including fuzzy interpolation fi and fuzzy linear regression flr are developed and discussed forecasts generated by these methods are fuzzy valued next the subjective beliefs about whether the industry is booming or slumping and the speed at which this change in prosperity takes place during a given period are also considered two subjective functions are defined and used to adjust fuzzy forecasts practically fuzzy forecasts are incorporated with fuzzy programming like fuzzy linear programming flp or fuzzy nonlinear programming fnp for mid term or long term planning advantages over traditional methods are shown in our examples

numerical approximation of fuzzy functions by fuzzy polynomials one of the interesting important and attractive problems in applied mathematics is how to best approximate a function in a given space in this paper the problem of best approximation is considered for fuzzy functions by optimization to obtain a fuzzy polynomial

effective medium equations for fractional fick s law in porous media abstract this paper studies reaction diffusion phenomena in disordered porous media with non fickian diffusion effects the aim is to obtain an effective medium equation of the concentration dynamics having a fractional fick s law description for the particles flux since the methodology is based on a volume averaging approach a fractional spatial averaging theorem is developed to interchange averaging integration and fractional differentiation model structure simplifications are made on the basis of an order of magnitude analysis from physical insights the closure problem associated with the effective diffusivity definition is also developed showing that the macroscale diffusion parameter is affected by i the scaling from mesoscales to macroscales and ii by the disordered structure of the porous medium

invariant analysis of time fractional generalized burgers and korteweg de vries equations abstract a systematic investigation to derive lie point symmetries to time fractional generalized burgers as well as korteweg de vries equations is presented using the obtained lie point symmetries we have shown that each of them has been transformed into a nonlinear ordinary differential equation of fractional order with a new independent variable the derivative corresponding to time fractional in the reduced equation is usually known as the erdelyi kober fractional derivative

a fuzzy lagrange interpolation theorem abstract the following problem was posed by l a zadeh suppose we are given n 1 points x0 xn in r and for each of these points a fuzzy value in r rather than a crisp one is it then possible to construct some function on r with range also a collection of fuzzy values which coincides on the given n a points with the given fuzzy values and which fulfills some natural smoothness condition in this paper we shall present a solution to this problem based on the fundamental and well known polynomial interpolation theorm of lagrange

constructing consistent fuzzy surfaces from fuzzy data given fuzzy data describing a three dimensional entity such as terrain we develop methods to construct surfaces that are consistent with the uncertainty in the data and surface model itself in particular surfaces generated from higher cut values of the fuzzy data are contained within the surfaces generated by lower cut values of the fuzzy data moreover the smoothness and continuity conditions of the surface generating method is maintained by each level surface we demonstrate the ideas by developing two and three dimensional surfaces from fuzzy data for cubic splines and digital terrain models generated from triangulation

lie symmetry analysis conservation laws and exact solutions of the time fractional generalized hirota satsuma coupled kdv system abstract in the present paper lie point symmetries of the time fractional generalized hirota satsuma coupled kdv hs ckdv system based on the riemann liouville derivative are obtained using the derived lie point symmetries we obtain similarity reductions and conservation laws of the considered system finally some analytic solutions are furnished by means of the invariant subspace method in the caputo sense

matrix propagator method for layered porous media analytical expressions and stability criteria we fully expand the thomson haskell propagator matrix method to obtain closed form analytical expressions for the reflectivity and transmittivity of a horizontally stratified poroelastic biot type medium that is bounded from above and below by fluid half spaces stable and unstable regions of the propagator matrix method are determined by means of comparison with the inherently stable reflectivity method it was found that the stability is mainly determined by the imaginary part of the vertical wavenumber of the biot slow wave

numerical solution of fuzzy polynomials by fuzzy neural network in this paper an architecture of fuzzy neural networks is proposed to find a real root of fuzzy polynomials if exists by introducing a learning algorithm we proposed a learning algorithm from the cost function for adjusting of crisp weights finally we illustrated our approach by numerical examples

generalized lie symmetry approach for fractional order systems of differential equations iii the generalized lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables the efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the 2 1 dimensional asymmetric nizhnik novikov veselov system 3 1 dimensional burgers system and 3 1 dimensional navier stokes equations with the help of derived lie point symmetries the corresponding invariant solutions transform each of the considered systems into a system of lower dimensional fractional partial differential equations

a new approach to estimate the interpolation error of fuzzy data using similarity measures of fuzzy numbers in this article new error and similarity indexes to determine the accuracy of interpolation of fuzzy data by cubic spline functions are presented the measures introduced are based on the similarity measure of fuzzy numbers through experimental simulations with different examples we verify the homogeneity of the error and similarity indexes which provides a criterion for determining the accuracy of the interpolation method with fuzzy data the development of a criterion or an error or similarity index represents an important advancement because of the lack of qualitative measures to estimate the interpolation error using fuzzy numbers in order to compare the results from distinct fuzzy data sets

modeling uncertain data with fuzzy b splines abstract fuzzy numbers are an alternative solution to the problem uncertain data modeling the idea of fuzzy b spline is here introduced its power relies on the possibility of being used as approximating function both for fuzzy and crisp data the fuzzy modeling of large collections of noisy data described in this paper moreover achieves a very high degree of compression with a relatively low computational complexity both for maintenance and interrogation of the model itself an extensive description of the modeling technique is given together with methods for interrogating the model experimental results are shown to prove the effectiveness of the proposed approach

a travelling wave solution to the ostrovsky equation in this paper we consider a nonlinear evolution equation like ostrovsky equation by using the hyperbolic tangent method and an exponential function approach a travelling wave solution for the ostrovsky equation is presented it is observed that both methods lead to the same type of solution

legendre and laguerre polynomial approach for modeling of wave propagation in layered magneto electro elastic media a numerical method to compute propagation constants and mode shapes of elastic waves in layered piezoelectric piezomagnetic composites potentially deposited on a substrate is described the basic feature of the method is the expansion of particle displacement stress fields electric and magnetic potentials in each layer on different polynomial bases legendre for a layer of finite thickness and laguerre for the semi infinite substrate the exponential convergence rate of the method for propagation of love waves is numerically verified the main advantage of the method is to directly determine complex wave numbers for a given frequency via a matricial eigenvalue problem in a way that no transcendental equation has to be solved results are presented and the method is discussed

a new conservation theorem a general theorem on conservation laws for arbitrary differential equations is proved the theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables the new theorem does not require existence of a lagrangian and is based on a concept of an adjoint equation for non linear equations suggested recently by the author it is proved that the adjoint equation inherits all symmetries of the original equation accordingly one can associate a conservation law with any group of lie lie backlund or non local symmetries and find conservation laws for differential equations without classical lagrangians

invariant analysis and conservation laws of 2 1 dimensional time fractional zk bbm equation in gravity water waves abstract this paper intends to make an in depth study on the symmetry properties and conservation laws of the 2 1 dimensional time fractional zakharov kuznetsov benjamin bona mahony zk bbm equation with riemann liouville fractional derivative symmetry properties have been investigated here via lie symmetry analysis method in view of erdelyi kober fractional differential operator the reduction of 2 1 dimensional time fractional zk bbm equation has been done into fractional ordinary differential equation to analyse the conservation laws new theorem of conservation law has been proposed here for constructing the new conserved vectors for 2 1 dimensional time fractional zk bbm equation with the help of formal lagrangian

on fuzzy relational equations and the covering problem previous studies have shown that fuzzy relational equations fres based on either the max continuous archimedean t norm or the max arithmetic mean composition can be transformed into the covering problem which is an np hard problem exploiting the properties common to the continuous archimedean t norm and the arithmetic mean this study proposes a generalization of them as the u norm enabling fres that are based on the max continuous u norm composition also to be transformed into the covering problem this study also proposes a procedure for transforming the covering problem into max product fres consequently max continuous u norm fres can be solved by extending any procedure for solving either the covering problem or max product fres

note on fuzzy monotonic interpolating splines of odd degree in this paper we propose a hermite type monotonic fuzzy quintic spline for interpolating fuzzy data its monotonicity is proved and the corresponding interpolation error estimate is provided this fuzzy quintic spline is generalized to odd degree monotonic fuzzy splines the uniform approximation property of the corresponding fuzzy linear and positive operator is obtained the monotonicity is tested on a numerical experiment

chaotic attractors in incommensurate fractional order systems in this paper based on the stability theorems in fractional differential equations a necessary condition is given to check the existence of 1 scroll 2 scroll or multi scroll chaotic attractors in a fractional order system this condition is proposed for incommensurate order systems in general but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems though the presented condition is only a necessary and not sufficient condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system chaotic attractors can not be observed and for what parameters and orders the system may generate chaos it can also be used as a tool to confirm or reject results of a numerical simulation some of the numerical results reported in the previous literature are confirmed by this tool

an application of the fuzzy theory in surface interpolation and surface deformation analysis measurements can be considered to be fuzzy values from mathematical point of view their uncertainty is caused by an incomplete knowledge of absolute truth only value ranges can be proposed in this case in this sense measurements provide some raw material for further researches they can be interpolated over a grid and approximated by an analytical surface additionally it can be necessary to obtain some surface characteristics of higher order based on the grid it is clear that each characteristic which is derived from uncertain measurements is also uncertain in this paper we discuss a method of modelling the propagation of the uncertainty the so called fuzzy propagation of measurements to derived differential geometric characteristics and its application

perturbation analysis of fuzzy linear systems this paper deals with the perturbation analysis of fuzzy linear systems three cases of perturbation are considered a the right hand side is perturbed while the coefficient matrix remains unchanged b the coefficient matrix is perturbed while the right hand side remains unchanged and c both the coefficient matrix and the right hand side are perturbed for all of the three cases the respective relative error bounds for solutions of fuzzy linear system are derived the results are illustrated by numerical examples

a formulation of noether s theorem for fractional problems of the calculus of variations abstract fractional or non integer differentiation is an important concept both from theoretical and applicational points of view the study of problems of the calculus of variations with fractional derivatives is a rather recent subject the main result being the fractional necessary optimality condition of euler lagrange obtained in 2002 here we use the notion of euler lagrange fractional extremal to prove a noether type theorem for that we propose a generalization of the classical concept of conservation law introducing an appropriate fractional operator

fuzzy spline interpolation with optimal property in parametric form in this paper we propose a new fuzzy interpolation procedure that uses cubic splines with an optimal property obtained in parametric form this fuzzy interpolation operator is also a linear operator of uniform approximation that preserves the monotonicity moreover by integrating this fuzzy cubic spline we obtain the trapezoidal quadrature rule for fuzzy henstock integrable functions

forward projection of transient sound pressure fields radiated by impacted plates using numerical laplace transform forward propagation of the transient sound pressure radiated by an impacted plate is presented it is shown that direct and inverse time domain discrete fourier transforms involved in fourier transform based near field acoustical holography nah lead to aliasing errors in the reconstructed time signals adding trailing zeros to the initial time signals is an inefficient way to reduce time aliasing errors hence the numerical laplace transform is introduced and a fourier transform based transient nah tnah approach is formulated an error measure is introduced to compare both nah and tnah with respect to the propagation distance and the location of the observation point in the projection plane the percentage of error with tnah is reduced by more than a factor of 10 without adding trailing zeros to the initial signals simulation results are validated experimentally using a free plexiglas plate impacted at its center

a new computational approach for solving nonlinear local fractional pdes abstract in this article we propose a new factorization technique for nonlinear odes involving local fractional derivatives for the first time by making use of the traveling wave transformation the exact solutions for nonlinear local fractional fitzhugh nagumo and newell whitehead equations are given the obtained results illustrate that the proposed method is efficient and accurate for finding the exact solutions for a class of local fractional pdes occurring in mathematical physics

interpolation of fuzzy data abstract we will consider the interpolation of fuzzy data by a continuous fuzzy valued function and give some numerical methods for calculating the fuzzy interpolant

symmetries and exact solutions of the time fractional harry dym equation with riemann liouville derivative abstract in this paper group analysis of the time fractional harry dym equation with riemann liouville derivative is performed its maximal symmetry group in lie s sense and the corresponding optimal system of subgroups are determined similarity reductions of the equation under study are performed as a result the reduced fractional ordinary differential equations are deduced and some group invariant solutions in explicit form are obtained as well

the hyperspace of fuzzy sets a natural nontopological fuzzy topological space let x be a uniform topological space then on the family ix resp d x of all nonzero functions resp nonzero uppersemicontinuous functions from x to the unit interval i a fuzzy uniform topology is constructed such that 2x resp 61 x the family of all nonvoid resp nonvoid closed subsets of x equipped with the hausdorff bourbaki structure is isomorphically injected in ix resp i x the main result of this paper is a complete description of convergence in ix by means of a notion of degree of incidence of members of ix immediate consequences are that first it can be shown that this notion of convergence refines some particular useful notions of convergence of fuzzy sets used in applications and that second it follows from its construction and properties that for each ordinary uniform topological space x there exists a natural nontopological fuzzy uniform topology on ix

approximation of uncertain functional relationships in this paper we consider methods for the linguistic modelling of vague functional relationships where the linguistic model is supposed to be given as a set of rules two approaches for deriving a fuzzy valued function from such models are proposed it is argued that both approaches can be interpreted as a generalization of ordinary methods for the interpolation and approximation of functions mathematical properties of fuzzy functions associated with a set of rules are investigated particularly for the second approach a universal approximation property is shown

nonlinear self adjointness and conservation laws the general concept of nonlinear self adjointness of differential equations is introduced it includes the linear self adjointness as a particular case moreover it embraces the strict self adjointness definition 1 and quasi self adjointness introduced earlier by the author it is shown that the equations possessing nonlinear self adjointness can be written equivalently in a strictly self adjoint form by using appropriate multipliers all linear equations possess the property of nonlinear self adjointness and hence can be rewritten in a nonlinear strictly self adjoint form for example the heat equation ut u 0 becomes strictly self adjoint after multiplying by u 1 conservation laws associated with symmetries are given in an explicit form for all nonlinearly self adjoint partial differential equations and systems