perturbed proximal point algorithms for general quasi variational like inclusions in this paper we introduce two new concepts of subdifferential and proximal mappings of proper functionals on hilbert spaces the existence and lipschitz continuity of proximal mapping of a proper functional are proved by applying these concepts we introduce and study a class of general quasi variational like inclusions and develop some new perturbed proximal point algorithms of mann and ishikawa type for finding the approximate solutions of the general quasi variational like inclusions the convergence criteria of the sequences of approximate solutions generated by these new algorithms are also discussed our algorithms and results improve and generalize many known results in the literature

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

interactions of solitons in nonintegrable systems direct perturbation method and applications abstract problems of approximate description of soliton interaction in nonintegrable systems are discussed it is shown that in an arbitrary lagrangian system in the first nontrivial order of the small parameter asymptotic scheme for a system of solitons with close velocities a lagrangian may be introduced analogous to that for classical particles with a pair interaction potential a classification of possible types of soliton interaction is given and criteria of the existence of bound states are formulated a possibility of generalization of approximated description of soliton interaction in the multidimensional case is noted

algorithm for solving a new class of generalized nonlinear implicit quasi variational inclusions in banach spaces abstract in this paper we introduce and study a new class of generalized nonlinear implicit quasi variational inclusions with general h monotone operator in banach spaces by using the proximal mapping and nadler s theorem we suggest and analyze a class of iterative algorithm for solving the generalized nonlinear implicit quasi variational inclusion first an existence theorem of solutions for the generalized nonlinear implicit quasi variational inclusion is proved under suitable assumptions then the convergence of the iterative sequences generated by the new algorithm is proved

revealing logical dependencies in fuzzy data with the aid of multilevel fuzzy relational equations in this paper the idea is discussed to connect given fuzzy input and output data via a hidden layer of intermediate data this idea is on the one hand treated using cascaded systems of fuzzy relational equations and is on the other hand approached from a numerical perspective

spectral methods in time for a class of parabolic partial differential equations in this paper we introduce a fully spectral solution for the partial differential equation u t uu x vu x x mu x x x lu x x x x 0 for periodic boundary conditions in space the use of fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a chebyshev series boundary conditions other than periodic may still be treated with reasonable though lesser efficiency for all cases very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time

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

solution of fuzzy equations with extended operations abstract assuming that is any operation defined on a product set x y and taking values on a set z it can be extended to fuzzy sets by means of zadeh s extension principle given a fuzzy subset c of z it is here shown how to solve the equation a b c or a b c when a fuzzy subset a of x or a fuzzy subset b of y is given the methodology we provide includes as a special case the resolution of fuzzy arithmetical operations i e when stands for or extended to fuzzy numbers fuzzy subsets of the real line the paper is illustrated with several examples in fuzzy arithmetic

iterative processes with errors for nonlinear set valued variational inclusions involving accretive type mappings abstract the purpose of this paper is to introduce a new class of nonlinear set valued variational inclusions in banach spaces and study the existence of solution and convergence of ishikawa iterative processes with errors for this class of nonlinear set valued variational inclusions involving accretive type mappings our results extend and improve the corresponding results of chang huang and yuan

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

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

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

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

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

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

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

chaotic behaviour of soliton lattice in an unstable dissipative dispersive nonlinear system abstract dynamical behaviours of a sequence of asymmetric soliton like pulses arising in an unstable dissipative dispersive non linear wave system are investigated in terms of a nonlinear lattice model it is found in a three pulse periodic system in which either periodic or chaotic motions which are consistent with the results of the numerical initial value problem occur when the individual interacting pulse has an asymmetric oscillatory tail structure the existence of oscillatory structure is found to be responsible for chaotic motions several general properties of the asymmetric lattice are also discussed in comparison with the symmetric lattices for the korteweg de vries kdv and the fifth order kdv solitons

h φ η monotone operators in banach spaces with an application to variational inclusions in this paper we introduce and study a new class of h f email protected operators in banach spaces we define a proximal mapping associated with the h f email protected operator and show its lipschitz continuity as an application we consider the solvability for a class of variational inclusions involving the h f email protected operators in banach spaces by using the technique of proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

a new class of variational inclusions with b monotone operators in banach spaces in this paper we introduce and study a new class of variational inclusions in banach spaces for solving such class of variational inclusions we introduce a new notion of b monotone operator and prove the lipschitz continuity of the proximal mapping associated with the b monotone operator by using the proximal mapping an iterative algorithm for solving such class of variational inclusions is constructed in banach spaces under some suitable conditions we prove the convergence of iterative sequence generated by the algorithm

algorithm for solving a new class of general mixed variational inequalities in banach spaces in this paper a new concept of h proximal mapping for a proper subdifferentiable functional which may not be convex on a banach space is introduced an existence and lipschitz continuity of the h proximal mapping are proved by using properties of the h proximal mapping a new class of general mixed variational inequalities is introduced and studied in banach spaces an existence theorem of solutions is established and a new iterative algorithm for solving the general mixed variational inequality is suggested a convergence criteria of the iterative sequence generated by the new algorithm is also given

on the existence of solutions of systems of fuzzy equations abstract a necessary and sufficient condition for the existence of solutions of a fuzzy equation given by e sanchez is extended to systems of fuzzy equations

fuzzy relational structures the state of art fuzzy relational structures built with the aid of fuzzy sets and fuzzy relations constitute a fundamental class of constructs arising in fuzzy set theory they give rise to fuzzy relation equations in this paper we will develop the concepts of single and multilevel relational structures different logic operations will be discussed in detail aspects of the knowledge representation will be studied and illustrated with several schemes of applications

specificity shift in solving fuzzy relational equations abstract studied is a system of n fuzzy relational equations with a max t composition x k r y k where the input output fuzzy sets x k and y k are available while the fuzzy relation r needs to be determined the solution to these equations is derived through a new paradigm of specificity shift the main objective is to modify a level of specificity of the fuzzy sets relational constraint so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable in more detail the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets the optimization of the specificity levels is discussed in detail numerical studies are also included finally the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient based techniques

a fuzzy approach to stability of fuzzy controllers this paper deals with stability analysis of fuzzy controllers a new definition embedding the notion of stability into fuzzy set theory is suggested in this context the introduction of a gradual stability is discussed investigating stability needs a model of the process one of the essential assumptions for the model used here is that the process has an approximatively linear structure within a sufficiently small time interval t possible deviations between the model and the real system are taken into account by specifying fuzzy parameters for the sake of simplicity however only a simple version of the model is considered in the present paper moreover some facts about the influence of the defuzzifier and the inference engine on the stability statement are presented by using this model and the suggested definition of stability some criteria ensuring stability are derived

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

on various eigen fuzzy sets and their application to image reconstruction in this study we formulate and solve a problem of image reconstruction using eigen fuzzy sets treating images as fuzzy relations we propose two algorithms of generating eigen fuzzy sets that are used in the reconstruction process the first one corresponds to a convex combination of eigen fuzzy set equations i e fuzzy relational equations involving convex combination of max min and min max compositions in the case of the first algorithm various eigen fuzzy sets can be generated by changing the parameter controlling the convex combination of the corresponding equations the second algorithm generates various eigen fuzzy sets with respect to the original fuzzy relation using a permutation matrix a thorough comparison of the proposed algorithms and a conventional algorithm which reconstructs an image using the greatest and smallest eigen fuzzy sets is presented as well in the experiments 10 000 artificial images of size 5x5 pixels the approximation error in the case of the first second algorithm is decreased to 68 2 97 9 of that of the conventional algorithm respectively furthermore through the experimentation using real images extracted from standard image database sidba it is confirmed that the approximation error of the first algorithm is decreased to 41 5 of that of the conventional one

general algorithm of solutions for nonlinear variational inequalities in banach space abstract in this paper we shall study a class of general nonlinear variational inequalities in reflexive banach spaces by applying a minimax inequality obtained by the author some existence uniqueness theorems of solutions for the general nonlinear variational inequalities are proved next by applying the auxiliary problem technique we suggest an innovative iterative algorithm to compute the approximate solutions of the general nonlinear variational inequality finally the convergence criteria is also discussed

mann and ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi variational inclusions abstract in this paper we introduce a new class of generalized nonlinear implicit quasi variational inclusions and prove its equivalence with a class of fixed point problems by making use of the properties of maximal monotone we also prove the existence of solutions for this generalized nonlinear implicit quasi variational inclusions and the convergence of iterative sequences generated by the perturbed algorithms

sets of solution set equivalent coefficient matrices of fuzzy relation equations abstract a set of coefficient matrices which are equivalent to the solution set of a fuzzy relation equation is considered it is also shown that the cardinal numbers of solution sets of fuzzy relation equations for two constant vectors with the same partition on the index set are equal to each other

fuzzy set framework for development of a perception perspective abstract the question of perception attracts a lot of investigation concerning fundamental issues of knowledge representation and particularly application oriented techniques we clearly indicate the context dependent character of information processed in cognitive processes as opposed to statistical analysis in which no context is taken into account the problem being addressed here is translated into an optimization scheme under which algorithms of data analysis are worked out a general class of techniques dedicated to linguistic analysis of records of numerical data is introduced its essence relies on determining the level of data and fuzzy labels

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

h monotone operator and resolvent operator technique for variational inclusions in this paper we introduce a new class of monotone operators h monotone operators the resolvent operator associated with an h monotone operator is defined and its lipschitz continuity is presented we also introduce and study a new class of variational inclusions involving h monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique

intrinsic stochasticity with many degrees of freedom we study a simple model equation describing a system with an infinity of degrees of freedom which displays an intrinsically chaotic behavior some concepts of fully developed turbulence are discussed in relation to this model we also develop an approach based on lyapunov exponent measurements numerical results on the distribution of lyapunov numbers and the power spectrum of the associated lyapunov vectors are presented and briefly discussed