existence of a solution of the wave equation with nonlinear damping and source terms abstract we study the nonlinear wave equation involving the nonlinear damping term u t u t m 1 and a source term of type u u p 1 for 1 p m we prove a global existence theorem with large initial data for 1 m p a blow up result is established for sufficiently large initial data

energy decay for a damped nonlinear coupled system this paper proves the well posedness and uniform stabilization of a nonlinear coupled system we estimate the energy decay rate by using the multiplier method

convex combinations in terms of triangular norms a characterization of idempotent bisymmetrical and self dual compensatory operators it is observed that most of the well known compensatory operators are defined in terms of convex transformations of the values of triangular norms and conorms or other operators in this paper the characterization and the applicability of parametrized operators constructed again in terms of triangular norms and conorms but as transformations of their arguments are studied it turns out that these operators are closely related to the ordinary convex combination moreover when idempotency is required these operators can be characterized algebraically as bisymmetrical and self dual operators that satisfy the cancellation law

aggregation operators ordering and bounds standard ordering of aggregation operators in several distinguished classes is characterized lower and upper bounds of finite systems in those classes of aggregation operators are discussed several examples are given

weak limits of perturbed random walks and the equation y_t b_t alpha sup y_s colon s leq t beta inf y sb s colon s leq t let and be real numbers and f c o 0 we study the existence and uniqueness of solutions g of the equation g t f t sup o 8 t g s inf o 8 t g s carmona petit le gall and yor have shown existence or nonexistence and uniqueness for some we settle the remaining cases we study the nearest neighbor walk on the integers which behaves just like fair random walk unless one neighbor has been visited and the other has not when it jumps to the unvisited neighbor with probability p if p 2 3 we show these processes scaled converge to the solution of the equation above for brownian paths with 2p 1 p

aggregation of infinite sequences infinitary aggregation functions acting on sequences and possessing some a priori given properties as additivity comonotone additivity symmetry etc are investigated on the other side we discuss infinitary aggregation functions related to given extended aggregation functions where special attention is given to triangular norms triangular conorms and weighted means

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

generalized medians distance aggregation operators are introduced in the case of singleton based distance a well known class of k medians is recovered for interval based distance characterization of p r distance aggregation operators is given in general as well as for idempotent operators based on the triangle of median factors medians are introduced owa operators are shown to be a linear convex combination of special j medians

on uniform decay of solutions for wave equation of kirchhoff type with nonlinear boundary damping and memory source term in this paper we prove the existence of solution to the mixed problem for wave equation of kirchhoff type with nonlinear boundary damping and memory term moreover we discuss the uniform decay of solution

yosida approximation and nonlinear hyperbolic equation we are concerned with the initial value problem for nonlinear evolution equations of the form u t m a 1 2 u t 2 au t u t f t on 0 u 0 u o u o u 1 here a is a nonnegative selfadjoint operator in a real hilbert space h 0 is a constant and m is a c 1 class function satisfying m r m o 0 for r 0 with m o constant the equation has its motivation in the mathematical description of small amplitude vibrations of an elastic string

aggregation operators and fuzzy systems modeling abstract a general class of aggregation operators called mica having the properties of monotonicity symmetry and an identity element are introduced we stress the significance of the choice of identity in characterizing the operator we show that the t norm and t conorm are special cases of these operators other classees of these operators are introduced notably an additive class which is very much in the spirit of the kind of aggregation used in neural networks it is shown how a general description of the fuzzy system modeling technique can be obtained using these operators

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

continuous generated associative aggregation operators continuous generated associative aggregation operators are discussed the only asymmetric solutions are the trivial operators of the projection to the first or the last coordinate respectively the only nontrivial convenient aggregation operators are necessarily symmetric and they are either continuous archimedean t norms and t conorms or generated nullnorms the latter may combine any nilpotent t conorm and any t norm with any prescribed annihilator k 0 1

some mathematical aspects of fuzzy sets triangular norms fuzzy logics and generalized measures abstract from a mathematical point of view the use of triangular norms as connectives in many valued in particular in 0 1 valued logics and fuzzy logics is discussed also an overview of some non additive generalizations of classical measures is given

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

criteria importances in median like aggregation an axiomatization of criteria importances appearing in a given aggregation operator is proposed some distinguished examples are recalled for the class of k medians an integral based approach for inclusion of criteria importances is introduced several examples are given the case of ordinal scales is also discussed

shift invariant binary aggregation operators when applying an information fusion method usually the output results are required to be a scalar value in multiple situations the application of the fusion method to input values shifted by a constant should result in an output that is shifted likewise in this paper we present a study of the shift invariance property of aggregation operators the relationship between shift invariant binary aggregation operators and 1 lipschitz aggregation operators is shown and a full description of shift invariant aggregation operators is given

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

compensatory operators in fuzzy linear programming with multiple objectives previously h j zimmermann 11 presented a fuzzy approach to solve the linear vectormaximum problem in the mentioned approach the author uses the minimum or the product operators to translate the semantic meaning of the and the aim of this paper is to reconsider this approach by using operators which allow some degree of compensation between aggregated membership functions firstly the c operator already defined in 12 is used to combine our fuzzy objectives it is shown that solutions obtained by this way are always efficient unfortunately the substitute problem is not generally computationally feasible we suggest then the min bounded sum operator which is a compensatory one has some desired properties and is supported by empirical arguments it allows a considerable decrease of the computational burden in the substitute problem and leads to a solution which is attractive from the stand point of efficiency

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

some nonlinear degenerate wave equations on etudie la resolubilite locale du probleme aux valeurs limites et initiales suivant 2 u t 2 m gradu x t 2 dx u 0 dans 0 u 0 sur w 0 u 0 0 u t 0 dans ou m r est une fonction c 1 non negative sur 0 un domaine borne de r n a frontiere lisse w

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

characterization of invariant aggregation operators abstract following the ideas of bartlomiejczyk and drewniak minimal invariant subsets of 0 1 n are investigated an equivalence relation on these subsets is introduced consequently invariant aggregation operators are characterized by means of choquet integral based representation there are exactly 68 binary invariant aggregation operators 4 among them are also continuous further there are 6 self dual invariant binary aggregation operators a recurrent method of constructing invariant aggregation operators for n 2 is proposed restriction of invariant aggregation operators to finite scales is also discussed

multi attribute aggregation operators this paper deals with the idea of aggregation a new enlarged notion of aggregation operator is given along with a classification of classical properties into some main groups the concept of multi attribute aggregation operator which incorporates many classical aggregation methods is provided an extension of different properties to multi attribute aggregation operators is proposed

k maxitive aggregation functions abstract inspired by the idea of k maxitive measures we introduce and study k maxitive aggregation functions in particular 1 maxitive aggregation functions are shown to be just maxitive aggregation functions i e maxima of distorted inputs we introduce among others a representation of symmetric k maxitive aggregation functions moreover we show that for any k maxitive capacity and the smallest universal integral based on an arbitrary fixed semicopula including the sugeno and shilkret integrals the resulting aggregation function is k maxitive