single variable term semi latticized fuzzy relation geometric programming with max product operator considering the practical application background in peer to peer network system we investigate the single variable term semi latticized fuzzy relation geometric programming with max product operator in this paper based on the characteristics of the objective function and feasible domain we develop a matrix approach to deal with the proposed problem a step by step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint two examples are given to illustrate the feasibility and efficiency of the algorithm

control problems in fuzzy systems abstract this paper deals with some problems of the control of fuzzy systems described by means of a relational equation of the type x 1 u x r the basic aspects such as mutual identification and control stabilization control control with constraints generation of control rules of a fuzzy logic controller important from the theoretical and applicational point of view are discussed and illustrated by means of numerical examples

characterization of some fuzzy relation equations provided with one solution on a finite set abstract in this paper some fuzzy relation equations provided with one solution on a finite set are characterized we consider fuzzy relation equations h q t with q f x x y and card x card y after recalling the definition of equivalent fuzzy relation equations we introduce the definition of equivalent ones which allows us to constrain our research without loss of generality to fuzzy relation equations where t does not have zero components

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

comparative lagrangian formulations for localized buckling an energy functional for a strut on a nonlinear softening foundation is worked into two different lagrangian forms in fast and slow space respectively the developments originate independently of the underlying differential equation and carry some quite general features in each case the kinetic energy is an indefinite quadratic form in fast space this leads to an escape phenomenon with fractal properties in slow space kinetic energy is added to a potential contribution that is familiar from modal formulations together and in conjunction with a recent set of numerical experiments they illustrate the extra complexities of localized as opposed to distributed periodic buckling

resolution of a system of the max product fuzzy relation equations using lou factorization in this paper the lu factorization is extended to the fuzzy square matrix with respect to the max product composition operator called l u factorization equivalently we will find two fuzzy lower and upper triangular matrices l and u for a fuzzy square matrix a such that a l u where is the max product composition an algorithm is presented to find the matrices l and u furthermore some necessary and sufficient conditions are proposed for the existence and uniqueness of the l u factorization for a given fuzzy square matrix a an algorithm is also proposed to find the solution set of a square system of fuzzy relation equations fre using the l u factorization the algorithm finds the solution set without finding its minimal solutions and maximum solution it is shown that the two algorithms have a polynomial time complexity as o n 3 since the determination of the minimal solutions is an np hard problem the algorithm can be very important from the practical point of view

linear optimization with an arbitrary fuzzy relational inequality in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition the feasible solution set is determined and compared with some common results in the literature a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem it is shown that in general a lower bound is always attainable for the optimal objective value moreover we prove that the optimal solution of the problem is obtained if the problem is defined by a non decreasing or non increasing function an algorithm is presented to summarize the process and an example is described to illustrate the algorithm

about macroscopic models of instability pattern formation abstract various macroscopic models to describe instability pattern formation are discussed in this paper they are similar to the ginzburg landau envelope equation but they can remain valid away from the bifurcation and are based on the technique of fourier series with slowly varying coefficients we focus on two questions the need to take phase changes into account and the boundary conditions to be associated with macroscopic models the analysis is carried out on the basis of numerical simulations for the problem of a compressed beam on a nonlinear foundation that is quite similar to the well known swift hohenberg equation the first macroscopic model involves a real envelope so that the phase is assumed to be constant the second model is also macroscopic and it is a sort of ginzburg landau equation with a complex envelope the third one follows from a multi scaled approach with a numerical bridging between the full model near the boundary and a macroscopic model in the bulk

fuzzy relational equations and the inverse problem abstract the inverse problem concerned with fuzzy relations is investigated the conditions for the existence of a solution are shown and an analytical solution is given a method for the improvement of the solution is proposed

numerical and applicational aspects of fuzzy relational equations we discuss numerical methods leading to a resolution of fuzzy relational equations which create a formal description of ill defined systems an applicability of the numerical approach is shown in solving some problems in fuzzy systems such as identification and control an idea of fuzzy discretization fuzzy chopping as a meaningful tool for handling various problems is also investigated

fuzzy linear optimization in the presence of the fuzzy relation inequality constraints with max min composition in this paper we study the new linear objective function optimization with respect to the fuzzy relational inequalities defined by max min composition in which fuzzy inequality replaces ordinary inequality in the constraints fuzzy inequalities enable us to attain the optimal points that are better solutions than those resulting from the resolution of the similar problems with ordinary inequality constraints denoted by x o i in this paper we have presented an algorithm to generate such optimal solutions also two examples are given to illustrate the algorithm presented and some real application of this work

solutions of fuzzy relation equations based on continuous t norms this study is concerned with fuzzy relation equations with continuous t norms in the form atr b where a and b are the fuzzy subsets of x and y respectively email protected xxy is a fuzzy relation and t is a continuous t norm the problem is how to determine a from r and b first an if and only if condition of being solvable is presented novel algorithms are then presented for determining minimal solutions when x and y are finite the proposed algorithms generate all minimal solutions for the equations making them efficient solving procedures

convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing abstract this paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form x k 2 x k r y k k 1 2 k where x k and y k denote fuzzy sets r and 2 fuzzy relations the sup min compositional operator the inf max one and a fuzzy convex combinator whose complement is furthermore we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations focusing our attention on the modeling of fuzzy input output systems normality of fuzzy sets characterizing fuzzy input fuzzy logical aspects of systems and association between fuzzy information finally it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems

fuzzy relational equations with generalized connectives and their applications the idea of fuzzy relational equation with generalized connectives is introduced and algorithms of resolution of this class equations are presented in details it is clearly shown that some types of well known fuzzy relational equations sup min inf max can be treated as special cases of a wise class of equations under discussion applicational aspects are carefully investigated presenting the advantages of the proposed approach

multi objective optimization with a max t norm fuzzy relational equation constraint in this paper we consider minimizing multiple linear objective functions under a max t norm fuzzy relational equation constraint since the feasible domain of a max archimedean t norm relational equation constraint is generally nonconvex traditional mathematical programming techniques may have difficulty in yielding efficient solutions for such problems in this paper we apply the two phase approach utilizing the min operator and the average operator to aggregate those objectives to yield an efficient solution a numerical example is provided to illustrate the procedure

solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations abstract in this paper we introduce a fuzzy operator constructed by the convex combination of two known operators max min and max average compositions h j zimmermann fuzzy set theory and it s application kluwer academic publishers boston dordrecht london 1999 this operator contains some properties of the two known compositions when it generates the feasible region for linear optimization problems we investigate linear optimization problems whose feasible region is the fuzzy sets defined with this operator thus firstly the structure of these fuzzy regions is considered and then a method to solve the linear optimization problems with fuzzy equation constraints regarding this operator is presented

minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations this paper considers the following optimization problem minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations using max product composition we first show some properties of minimal solutions of a system of fuzzy relation equations with max product composition and present some rules for reducing the original problem then we derive an algorithm which enables us to find all the optimal solutions for solving the optimization problem and provide some numerical examples to illustrate

a double expansion method for the frequency response of finite length beams with periodic parameters abstract a double expansion method for the frequency response of finite length beams with periodic distribution parameters is proposed the vibration response of the beam with spatial periodic parameters under harmonic excitations is studied the frequency response of the periodic beam is the function of parametric period and then can be expressed by the series with the product of periodic and non periodic functions the procedure of the double expansion method includes the following two main steps first the frequency response function and periodic parameters are expanded by using identical periodic functions based on the extension of the floquet bloch theorem and the period parametric differential equation for the frequency response is converted into a series of linear differential equations with constant coefficients second the solutions to the linear differential equations are expanded by using modal functions which satisfy the boundary conditions and the linear differential equations are converted into algebraic equations according to the galerkin method the expansion coefficients are obtained by solving the algebraic equations and then the frequency response function is finally determined the proposed double expansion method can uncouple the effects of the periodic expansion and modal expansion so that the expansion terms are determined respectively the modal number considered in the second expansion can be reduced remarkably in comparison with the direct expansion method the proposed double expansion method can be extended and applied to the other structures with periodic distribution parameters for dynamics analysis numerical results on the frequency response of the finite length periodic beam with various parametric wave numbers and wave amplitude ratios are given to illustrate the effective application of the proposed method and the new frequency response characteristics including the parameter excited modal resonance doubling peak frequency response and remarkable reduction of the maximum frequency response for certain parametric wave number and wave amplitude the results have the potential application to structural vibration control

resolution of composite interval valued fuzzy relation equations abstract in this study we investigate the properties and the solution procedure of composite interval valued fuzzy relation equations with max min operator this is a generalization of existing constant valued fuzzy relation problems the study includes both theoretical development and numerical analyses it is concluded that our proposed methodology not only solves the existing fuzzy relation equations but also reveals the necessary and sufficient conditions for more general problems therefore this study facilitates the understanding of solution structure and wider applications

some theoretical aspects of fuzzy relation equations describing fuzzy systems abstract this paper contains some theoretical results on fuzzy relation equations and applications to analysis of fuzzy systems as well as identification and control problems if ai 1 i k are fuzzy inputs b is a fuzzy output and r is a fuzzy relation describing the system the above problems are illustrated by means of a max min multidimensional equation of type b a 1 a k r furthermore we investigate some properties of fuzzy systems described by fuzzy relation equations focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion

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

on pseudo transitive approximations of fuzzy relations abstract in the present paper we consider a generalization of the well known notion of transitive fuzzy relations this may be useful for preference relations or similarity relations describing butterfly like configurations where the widely used transitive closure is rather different from the original relation moreover the proposed concept enables us to determine relations which are transitive only for a part of the elements under consideration some examples demonstrate the usefulness of our approach

on the quasi analytic treatment of hysteretic nonlinear response in elastic wave propagation microscopic features and their hysteretic behavior can be used to predict the macroscopic response of materials in dynamic experiments preisach modeling of hysteresis provides a refined procedure to obtain the stress strain relation under arbitrary conditions depending on the pressure history of the material for hysteretic materials the modulus is discontinuous at each stress strain reversal which leads to difficulties in obtaining an analytic solution to the wave equation numerical implementation of the integral preisach formulation is complicated as well under certain conditions an analytic expression of the modulus can be deduced from the preisach model and an elementary description of elastic wave propagation in the presence of hysteresis can be obtained this approach results in a second order partial differential equation with discontinuous coefficients classical nonlinear representations used in acoustics can be found as limiting cases the differential equation is solved in the frequency do

discriminating linear from nonlinear elastic damage using a nonlinear time reversal dort method the dort method is a selective detection and focusing technique originally developed to detect defects and damages which induce linear changes of the elastic moduli it is based on the time reversal tr where a signal collected from an array of transducers is time reversed and then back propagated into the medium to obtain focusing on selected targets tr is based on the principle of spatial reciprocity attenuation dispersion multiple scattering mode conversion etc do not break spatial reciprocity the presence of defects or damage may cause materials to show nonlinear elastic wave propagation behavior that will break spacial reciprocity therefore the dort method will not allow focusing on nonlinear elastic scatterers this paper presents a new method for the detection and identification of multiple linear and nonlinear scatterers by combining nonlinear elastic wave spectroscopy time reversal and dort method in the presence of nonlinear hysteretic elastic scatterers forcing the solid with a harmonic excitation the time reversal operator can be obtained not only at the fundamental frequency of excitation but also at the odd harmonics at the fundamental harmonic either inhomogeneities and linear damages can be individually selected but only at odd harmonics nonlinear hysteretic elastic damages exist a procedure was developed where by decomposing the operator at the odd harmonics it was possible to focus on nonlinear scatterers and to differentiate them from the linear inhomogeneities a complete mathematical nonlinear dort formulation for 1 and 2d structures is presented to model the presence of nonlinear elastic hysteretic scatterers a preisach mayergoyz pm material constitutive model was used results relative to 1 and 2 dimensional structures are reported showing the capability of the method to focus and discern selectively linear and nonlinear scatterers furthermore an analysis was conducted to study the influence of the number of sources and their location on the imaging process showing that using a higher numbers of sensors does not automatically bring to a minor uncoupled behaviour between the nonlinear targets

increasing continuous operations in fuzzy max equations and inequalities abstract in this paper solutions of fuzzy systems of equations a x b and systems of inequalities a x b a x b are considered where a 0 1 m n b 0 1 m stands for max product and x 0 1 n is an unknown vector in this paper the families of all solutions are described during the last thirty years this problem was considered by many authors our goal is to achieve the most general assumptions for which sets of solutions systems of equations and inequalities are the union of lattice intervals especially a method of determination of all minimal solutions in such systems is indicated as a result the families of all solutions of fuzzy systems of inequalities a x b and a x b are described as the main part of these results the method of determination of the family of all minimal solutions in max system of equations with an increasing operation continuous on the second argument is presented

duality of optimization problems with generalized fuzzy relation equation and inequality constraints abstract a generalization of fuzzy relation equations and inequalities is introduced an explicit method for solving optimization problems the feasible set of which is described by a system of generalized fuzzy relation equations and inequalities is considered the objective function of the problems is equal to the maximum of continuous increasing functions of one variable a duality concept for such problems is proposed the problems are considered in a finitely dimensional space

some results on fuzzy relation equations provided with one solution in a previous paper 3 we characterized the fuzzy relation equations h q t where q f x y provided with one solution on a finite set considering card x card y or card x card y in this paper we settle the same question for card x card y and s q t o moreover we show that every fuzzy relation equation provided with one solution is equivalent to a fuzzy relation sub equation of it

solving interval valued fuzzy relation equations solving systems of fuzzy relation equations is an important topic in fuzzy set theory this paper studies the composite interval valued fuzzy relation equations after analyzing the properties of its solution set we convert the fuzzy relation equations into a fuzzy relation inequality system and propose an efficient computational procedure to generate the whole solution set examples are included to illustrate the idea and algorithm

sets of solution set invariant coefficient matrices of simple fuzzy relation equations abstract a set of coefficient matrices which are invariant to a solution set of a simple fuzzy relation equation is considered the equipollency of the cardinal numbers of solution sets of simple fuzzy relation equations for two constant vectors is also shown

an alternative approach to the resolution of fuzzy relation equations abstract in this paper we propose a solution procedure by means of a quasi characteristic matrix the matrix is so defined that not only the solution set can be determined but also the type of solution set such as the non empty set full set unique minimal solution and unique solution can be identified before the solution set is determined therefore it provides an insight into the structure of fuzzy relation equations

fuzzy relation equations theory as a basis of fuzzy modelling an overview abstract we give a wide overview on the applications of fuzzy relation equations theory to decision making processes to the construction of preference relations and to knowledge engineering mainly fuzzy control and fuzzy pattern recognition general theoretical results and methodological aspects are pointed out

on the relation between fuzzy max archimedean t norm relational equations and the covering problem the problem of solving a system of fuzzy relational equations with max archimedean t norm composition is studied it is shown that this problem is closely related to the covering problem which belongs to the class of np hard problems it is proved that there is a one to one correspondence between the minimal solutions of the equations and the irredundant coverings as previously discovered by markovskii on the relation between equations with max product composition and the covering problem fuzzy sets and systems 153 2005 261 273 for fuzzy relational equations with max product composition since max product composition is a special case of max archimedean t norm composition this work extends markovskii s work to fuzzy relational equations with max archimedean t norm composition an extension of markovskii s algorithm is implemented yielding a processing time linearly proportional to the square of the number of minimal solutions

nonlinear wave propagation in damaged hysteretic materials using a frequency domain based pm space formulation abstract in this work a new and simple numerical approach to simulate nonlinear wave propagation in purely hysteretic elastic solids is presented conversely to classical time discretization method which fully integrates the nonlinear equation of motion this method utilizes a first order approximation of the nonlinear strain in order to separate linear and nonlinear contributions the problem for the nonlinear displacements is then posed as a linear one in which the solid is enforced with nonlinear forces derived from the linear strain in this manner a frequency analysis can be easily conducted leading directly to a well known frequency spectrum for the nonlinear strain a mesoscale approach known as preisach mayergoyz space pm space is used for the chacterization of the nonlinear elastic region of the solid a meshless element free galerkin method is implemented for the discretized equations of motion nevertheless a mesh based method can be still used as well without loss of generality results are presented for bidimensional isotropic plates both in plane stress and in plane strain subjected to harmonic monotone excitation

solving fuzzy relation equations with a linear objective function abstract an optimization model with a linear objective function subject to a system of fuzzy relation equations is presented due to the non convexity of its feasible domain defined by fuzzy relation equations designing an efficient solution procedure for solving such problems is not a trivial job in this paper we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0 1 integer programming with a branch and bound solution technique after presenting our solution procedure a concrete example is included for illustration purpose

min max programming problem subject to addition min fuzzy relation inequalities a bittorrent like peer to peer file sharing system can be reduced into a system of addition min fuzzy relation inequalities addition min is a new composition and the solution set of addition min fuzzy relation inequalities differs much from that of general max t norm fuzzy relation inequalities or equations in order to avoid network congestion and improve the stability of data transmission a min max programming problem is proposed subject to addition min fuzzy relation inequalities in this paper based on some relevant theorems on resolution a novel algorithm is developed step by step to find an optimal solution of the proposed problem moreover an application example is given to illustrate the feasibility and efficiency of the algorithm finally some further discussions are made concerning the optimal solution of the proposed problem

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

on the set of solutions of composite fuzzy relation equations in this paper we introduce some algorithms which have minimization properties about the fuzziness of solutions in the maxmin fuzzy relation equations

latticized linear programming subject to max product fuzzy relation inequalities with application in wireless communication in this paper we introduce the latticized linear programming problem subject to max product fuzzy relation inequalities with application in the optimization management model of wireless communication emission base stations resolution of max product fuzzy relation inequalities is studied by comparing with that of the corresponding max product fuzzy relation equations a solution matrix approach is developed for solving the proposed problem without finding all the quasi minimal solutions of the constraint for carrying out the solution matrix approach we provide a step by step algorithm illustrated by a numerical example

lower solutions of systems of fuzzy equations lower solutions of a system of fuzzy equations are determined by lower solutions of each equation the result is applied to fuzzy relation equations so that they are decomposed to simple fuzzy relation equations

a software routine to solve the generalized inverse problem of fuzzy systems abstract a software routine to produce the solution of the generalized inverse problem of fuzzy relational equations is presented given the fuzzy matrices r and b defined on u v and w v respectively the routine produces all fuzzy matrices a defined on the product space w u which satisfy a r b where denotes maxmin composition

finite fuzzy relation equations with unique solution in complete brouwerian lattices abstract we characterize finite fuzzy relation equations having a unique solution for sake of completeness we first recall some results already established in foregoing papers in the context of the linear lattices new results are established in the general setting of the complete brouwerian lattices suitable examples illustrate the theorems obtained

on the amplitude modulation and localization phenomena in interactive buckling problems the postcritical behavior of a 3d system of elastically restrained beams which can manifest overall and local modes is analyzed the secondary bifurcation in the overall postcritical range is studied by applying the multiple scale perturbation method it is found that the amplitude modulation phenomenon is governed by a differential equation of the second order an approximate analytical expression of the amplitude modulating function is obtained by the wkb asymptotic method the occurrence of a turning point which is responsible for the strong localization is revealed close analogies with localization of vibrations in imperfect systems are highlighted

cellular buckling from mode interaction in i beams under uniform bending beams made from thin walled elements while very efficient in terms of the structural strength and stiffness to weight ratios can be susceptible to highly complex instability phenomena a nonlinear analytical formulation based on variational principles for the ubiquitous i beam with thin flanges under uniform bending is presented the resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post buckling range can be portrayed the interaction between global lateral torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling snaking being predicted theoretically for the first time solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

an accelerated approach for solving fuzzy relation equations with a linear objective function in literature the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0 1 integer programming problem by fang and li 1999 they proposed a jump tracking branch and bound method to solve this 0 1 integer programming problem in this paper we propose an upper bound for the optimal objective value based on this upper bound and rearranging the structure of the problem we present a backward jump tracking branch and bound scheme for solving this optimization problem a numerical example is provided to illustrate our scheme furthermore testing examples show that the performance of our scheme is superior to the procedure in the paper by fang and li several testing examples show that our initial upper bound is sharp

localization and mode interaction in sandwich structures compressed sandwich structures comprising two stiff face plates separated by a softer core material while designed principally as efficient integral structures can lose this quality when faces buckle locally interaction between overall euler buckling and local buckling of one face suggests that failure will localize into the centre a variational formulation leading to a pair of nonlinear differential equations subject to integral constraints describes the post buckling response these are solved by a combination of numerical shooting and continuation techniques such that the response far into the unstable post buckling regime can be portrayed solutions with both linear and nonlinear constitutive core relations are compared with the results of an engineering body force approach and with those of earlier periodic rayleigh ritz analyses the latter demonstrate the extra destabilization that comes with localization

nonlinear mode interaction in equal leg angle struts susceptible to cellular buckling a variational model that describes the interactive buckling of a thin walled equal leg angle strut under pure axial compression is presented a formulation combining the rayleigh ritz method and continuous displacement functions is used to derive a system of differential and integral equilibrium equations for the structural component solving the equations using numerical continuation reveals progressive cellular buckling or snaking arising from the nonlinear interaction between the weak axis flexural buckling mode and the strong axis flexural torsional buckling mode for the first time the resulting behaviour being highly unstable physical experiments conducted on 10 cold formed steel specimens are presented and the results show good agreement with the variational model

solving linear optimization problems with max star composition equation constraints in this paper an optimization model with a linear objective function subject to a system of fuzzy relation composition equations is presented since the non empty feasible solution set of the fuzzy relation equations is generally a non convex set the conventional linear programming method will not be suitable for solving such a problem therefore an efficient solution procedure for such problems appears to be necessary in this paper firstly we characterize the feasible solution set and then introduce two efficient procedures for solving the problem finally two concrete examples are included for more details

s norm aggregation of infinite collections abstract the aggregation of membership values by means of the iterate application of an s norm is of cardinal relevance for the development of any general theory of approximate reasoning which relies on a sup t model for relation composition here we present a definition of s norm aggregation for possibly infinite collections which can be demonstrated to generalize previous approaches consistently it provides a common framework in which classical sup t and finite s t compositions can be analyzed as well as other significant cases general properties of the s norm aggregation concept its specialization for the class of continuous s norms and its relationship with fuzzy measure theory are discussed

an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition abstract fuzzy sets as the feasible region for optimization problems is an interesting and on going research topic s c fang g li solving fuzzy relations equations with a linear objective function fuzzy sets syst 103 1999 107 113 7 j lu s c fang solving nonlinear optimization problems with fuzzy relation constraints fuzzy sets syst 119 2001 1 20 16 e khorram a ghodpusian linear objective function optimization with fuzzy relation constraints regarding max av composition appl math comput in press doi 10 1016 j amc 2005 04 021 in this paper we focus on these kind problems in which the solutions region is the fuzzy relation equation with max prod composition and the objective function is linear whereas one of the major difficulties in such problems is non convexity of the feasible region it is preferable to study these regions in the first step hence we have primarily investigated two methods and their relationship and then we have determined the feasible region via them after determining the feasible set we have given an algorithm to optimize the linear objective function on such these regions finally we have presented two examples to illustrate the methods and algorithms

addition min fuzzy relation inequalities with application in bittorrent like peer to peer file sharing system abstract the data transmission mechanism in bittorrent like peer to peer p2p file sharing systems may be reduced to some addition min fuzzy relation inequalities the solution set of addition min fuzzy relation inequalities plays an important role in the corresponding optimization problem in this paper we study some properties of the solutions to such system convexity of the solution set and number of minimal solutions are discussed with comparison to those of the classical max t fuzzy relation equations or inequalities besides vertex solution and variable ordering minimal solution are also investigated with application in bittorrent like p2p file sharing system two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable ordering solution

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

an efficient procedure for solving a fuzzy relational equation with max archimedean t norm composition in the literature a necessary condition for minimal solutions of a fuzzy relational equation with max product composition shows that each of its components is either zero or the corresponding component s value of the greatest solution in this paper we first extend this necessary condition to the situation with max archimedean triangular norm t norm composition based on this necessary condition we then propose rules to reduce the problem size so that the complete set of minimal solutions can be computed efficiently furthermore rather than work with the actual equations we employ a simple matrix whose elements capture all of the properties of the equations in finding the minimal solutions numerical examples with specific cases of the max archimedean t norm composition are provided to illustrate the procedure

a new fourier related double scale analysis for instability phenomena in sandwich structures abstract in this paper we present a new fourier related double scale analysis to study instability phenomena of sandwich structures by using the technique of slowly variable fourier coefficients a zig zag theory based microscopical sandwich model is transformed into a macroscopical one that offers three numerical advantages firstly only the envelopes of instability patterns are evaluated and this leads to a significant improvement on computational efficiency especially when dealing with high wavenumber wrinkling phenomena secondly the proposed macroscopical model allows one to select modal wavelength which makes easy to control non linear calculations thirdly in contrast to landau ginzburg envelope equations it may also remain valid away from the bifurcation point and the coupling between global and local instabilities can be accounted for the established non linear system is solved by asymptotic numerical method anm which is more reliable and less time consuming than other iterative classical methods the proposed double scale analysis yields accurate results with a significant reduced computational cost

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

identification of fuzzy relational equations by fuzzy neural networks abstract although the identification of a fuzzy system by a feedforward neural network is obviously possible whenever the system was continuous however when we use fuzzy max min neural network some problems on the learning of the network arise in this paper we present a method to identify a fuzzy relation by a fuzzy max min neural network we adapt the learning algorithm backpropagation to learning of max min neural network by using one which we will denote as smooth derivative finally we present some examples and a comparison with a similar method

a nodal discontinuous galerkin finite element method for nonlinear elastic wave propagation a nodal discontinuous galerkin finite element method dg fem to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented this dg fem method combines the geometrical flexibility of the finite element method and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method required for nonlinear elastodynamics simulations in order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications the equations of nonlinear elastodynamics have been written in a conservative form the adopted formalism allows the introduction of different kinds of elastic nonlinearities such as the classical quadratic and cubic nonlinearities or the quadratic hysteretic nonlinearities absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate when needed semi infinite or infinite media the developed dg fem scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations lamb s problem and plane wave nonlinear propagation

fuzzy phoneme recognition abstract first a scheme for pattern recognition is given in a learning step a relation between acoustic characteristics and the corresponding phoneme is computed using an inference rule next the phonemes are recognised as result of a fuzzy relation equation then the recognition quality is analysed by means of uncertainty measures specially sugeno s and possibility measures

equations in classes of fuzzy relations abstract particular solutions of fuzzy relation equations are examined in diverse classes of fuzzy relations the main results concern the existence of solutions and the description of the family of all desired solutions

finite fuzzy relation equations with a unique solution in linear lattices abstract we characterize fuzzy relation equations possessing a unique solution the equations presented here involve fuzzy sets and fuzzy relations assuming values in a linear lattice and defined on finite sets a suitable example also shows that our main result generally does not hold if the fuzzy equations are assigned on complete brouwerian lattices not necessarily linear

on solving relational equations in brouwerian lattices abstract the problems of finding generic and minimal solutions of a fuzzy relational equations in brouwerian lattices are considered

smoothing and accelerated computations in the element free galerkin method two topics in the formulation and implementation of meshless methods are considered the smoothing of the approximating functions at concave boundaries and the speedup of the calculation of the approximating functions and their derivatives these techniques are described in the context of the element free galerkin method but they are applicable to other meshless methods results are presented for some elastostatic problems which show a moderate improvement in the accuracy of the smoothed interpolant the speedup in calculating the shape functions is about a factor of two

on matrix equations in a class of complete and completely distributive lattices matrix equations of the form ax b and ya b are considered in a class of complete and completely distributive lattices where the multiplication operation of matrices is defined either by the max min or by the min max way necessary and sufficient conditions for the solvability of the equations are obtained and for the solvable case the entire solution set and the largest solution are determined by using relative pseudo or relative lower pseudocomplements in lattices the results are seen to be a generalization of 4 5 6 and in a sense also an extension of 3 as an application the g inverse and thierrin vagner inverses of matrices are considered

some results in the setting of fuzzy relation equations theory abstract in this paper we point out certain theoretical aspects of fuzzy relation equations connecting some known results between composite and o fuzzy equations several theorems are obtained and some examples are provided too

fuzzy relation equations and inequalities abstract this paper generalizes a method of solution of fuzzy relation equations introduced by sanchez 1976 and developed by pedrycz 1982 we find the greatest or the least solution of a composite l fuzzy relation equation with arbitrary monotone composition

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

a fixed charge model with fuzzy inequality constraints composed by max product operator abstract a fixed charge model subject to a system of fuzzy relation inequalities with max product composite operator is presented the feasible domain of the model is first investiged of which the necessary and sufficient condition is proposed if it is infeasible a minimum calibration procedure is provided to have at least one solution due to the nonconvexity of its feasible domain a solution procedure is designed to have a minimum objective value of which the initial cost is considered an illustrative example is presented

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

an efficient solution procedure for fuzzy relation equations with max product composition we study a system of fuzzy relation equations with max product composition and present an efficient solution procedure to characterize the whole solution set by finding the maximum solution as well as the complete set of minimal solutions instead of solving the problem combinatorially the procedure identifies the nonminimal solutions and eliminates them from the set of minimal solutions

approximately solving fuzzy relation equations some mathematical results and some heuristic proposals abstract fuzzy relation equations are intimately connected with the approach toward fuzzy control unfortunately systems of such equations are solvable only under quite restrictive conditions therefore a notion of approximate solution is discussed which applied also in cases where such systems do not have solutions for some types of fuzzy equations best possible approximate solutions are known for other types some strategies are considered to suitably guess approximate solutions furthermore that approach is applied to some types of cascaded fuzzy relation equations which are connected with ideas to join neural network structures with fuzzy control

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure