componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

pseudo integral and generalized choquet integral abstract due to many applications the choquet integral as a powerful tool for modeling non deterministic problems needs to be further extended therefore the paper is devoted to a generalization of the choquet integral as a basis the pseudo integral for bounded integrand is extended to the case for nonnegative integrands at first and then the generalized choquet integral is defined as special cases pseudo choquet stieltjes integrals pseudo fuzzy stieltjes integrals g choquet integrals pseudo n fuzzy integrals and pseudo s fuzzy integrals are obtained and various kinds of properties and convergence theorems are shown meanwhile markov jensen minkowski and holder inequalities are proved in the end the generalized discrete choquet integral is discussed the obtained results for the generalized choquet integral cover some previous results on different types of nonadditive integrals

decomposable measures and nonlinear equations abstract using integrals based on decomposable measures with respect to a pseudo addition related to a semiring a b a b a unified method is given for solving some nonlinear differential ordinary and partial difference and optimization equations for that purpose important tools as pseudo superposition principle and pseudolaplace transform are used

stable computation of multiquadric interpolants for all values of the shape parameter abstract spectrally accurate interpolation and approximation of derivatives used to be practical only on highly regular grids in very simple geometries since radial basis function rbf approxima ions permit this even for multivariate scattered data there has been much recent interest in practical algorithms to compute these approximations effectively several types of rbfs feature a free parameter e g c in the multiquadric mq case f r r 2 c 2 the limit of c increasingly flat basis functions has not received much attention because it leads to a severely ill conditioned problem we present here an algorithm which avoids this difficulty and which allows numerically stable computations of mq rbf interpolants for all parameter values we then find that the accuracy of the resulting approximations in some cases becomes orders of magnitude higher than was the case within the previously available parameter range our new method provides the first tool for the numerical exploration of mq rbf interpolants in the limit of c the method is in no way specific to mq basis functions and can without any change be applied to many other cases as well

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

regularity aspects of non additive set multifunctions abstract in this paper continuity properties of set multifunctions such as regularity and continuity from above and below as well as others are introduced by way of a wijsman topology some of the relationships between them are established different examples counterexamples and applications are provided

convergences and topology via sequences of multifunctions in this paper we define different types of convergences for sequences of multifunctions and establish relationships among them using the convergence in fuzzy measure we obtain a topological structure on a space of multifunctions

l additive measures on measure spaces abstract in his thesis sugeno has introduced a class of non additive set functions g which have been called additive measures he has printed out that g can be represented by a density function if it is defined on the power set of a finite set in this article this concept is generalized for arbitrary measure spaces moreover it is shown that any density function on a measure space determines a unique parameter 1 as in the finite case additive measures are belief functions iff 0 and plausibility functions iff 0 the proof of this statement is achieved by a generally applicable reduction of the problem to finite algebras

a fuzzy gould type integral in this paper we introduce and study a set valued gould type integral of a real function with respect to a fuzzy multimeasure taking values in the family of all nonempty closed subsets of a banach space x some classical properties of the integral are obtained only using the hypothesis of monotonicity for the set valued fuzzy measure

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

enhancing the approximation order of local shepard operators by hermite polynomials we show how to combine local shepard operators with hermite polynomials on the simplex c k chui m j lai multivariate vertex splines and finite elements j approx theory 60 1990 245 343 so as to raise the algebraic precision of the shepard taylor operators r farwig rate of convergence of shepard s global interpolation formula math comp 46 1986 577 590 that use the same data and contemporaneously maintain the interpolation properties at each sample point derivative data included and a good accuracy of approximation numerical results are provided

an interval for the shape parameter in radial basis function approximation the radial basis functions rbfs depend on an auxiliary parameter called the shape parameter great theoretical and numerical efforts have been made to find the relationship between the accuracy of the rbf approximations and the value of the shape parameter in many cases the numerical approaches are based on minimization of an estimation of the error function such as rippa s approach and its modifications these approaches determine a value for the shape parameter in this paper we propose a practical approach to determine an interval instead of a value without any minimization and estimation of error function the idea is based on adding a loop on the shape parameter but not to minimize an error norm suitable values of the shape parameter are determined by take into account the practical convergence behavior of the problem the proposed method is applied to some illustrative examples including one and two dimensional interpolation and partial differential equations the results of the method are compared with those of some other approaches to confirm the reliability of the method furthermore numerical stability of the method of line respect to the shape parameter is considered for time dependent pdes the results show that the proposed method can be used as an independent method to find a shape parameter and also as an alternative for investigating the validity of the values of the other methods

integrals of set valued functions for decomposable measures abstract in this paper based on weber s 1984 integrals for archimedean t conorms decomposable measures integrals of set valued functions for archimedean t conorms decomposable measures are established some results similar to aumann s set valued integrals are given these include convexity closedness convergence theorems etc all these are the generalization of aumann s results

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

a meshless interpolation algorithm using a cell based searching procedure in this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets it is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell based searching procedure more precisely we construct a cell structure which partitions the domain and strictly depends on the dimension of the subdomains thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in allasia et al 2011 and cavoretto and de rossi 2010 2012 in fact this efficient algorithm and in particular the new searching procedure enable us a fast computation also in several applications where the amount of data to be interpolated is often very large up to many thousands or even millions of points analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm this is also supported by numerical experiments

probabilistically weighted owa aggregation in decision making under uncertainty we have a collection of alternatives from which we must choose one associated with each alternative is an uncertainty profile consisting of the set of possible outcomes that can occur if we choose this alternative along with some indication of the uncertainty associated with the outcomes since it is difficult to compare these uncertainty profiles one commonly used approach is to obtain a representative value an aggregation of the information in the uncertainty profile and use these to compare the alternatives the method that we use to aggregate the information in the uncertainty profile must reflect aspects of the decision attitude of the decision maker here we look at the role that the ordered weighted averaging owa can play in the aggregation process used to obtain these representative values since an uncertainty profile can involve a discrete set of possible outcomes or an interval of possible outcomes we provide the owa operator with the capability to perform aggregations in either of these environments in addition we provide the owa operator with the ability to perform aggregations in situations where the arguments being aggregated the potential outcomes have an associated uncertainty probability of occurrence particularly notable is the extension the owa operator to perform aggregation with arguments consisting of a continuum of values with an associated probability density function we also look at the cases where the uncertainty is modeled with a belief structure as well a possibility distribution

a trivariate interpolation algorithm using a cube partition searching procedure in this paper we propose a fast algorithm for trivariate interpolation which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions the partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube partition searching procedure more precisely we construct a cube structure which partitions the domain and strictly depends on the size of its subdomains so that the new searching procedure and accordingly the resulting algorithm enable us to efficiently deal with a large number of nodes complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

indicators for the characterization of discrete choquet integrals ordered weighted averaging owa operators and their extensions are powerful tools used in numerous decision making problems this class of operator belongs to a more general family of aggregation operators where each operator of this family is understood as a discrete choquet integral aggregation operators are usually characterized by indicators in this article four indicators usually associated with the owa operator are extended to the discrete choquet integral namely the degree of balance the divergence the variance indicator and renyi entropies all of these indicators are considered from a local and a global perspective linearity of indicators for linear combinations of capacities is investigated and to illustrate the usefulness of results indicators of the probabilistic ordered weighted averaging powa operator are derived finally a numerical example is provided to discuss the results in a specific context

on the representation of choquet integrals of set valued functions and null sets in this paper we consider the definition of set valued choquet integrals we obtain some properties and the representation of set valued choquet integrals and also we discuss some fundamental relations between null sets and set valued choquet integrals

an analytical study of sound transmission through unbounded panels of functionally gradedmaterials the problem of sound transmission and reflection from unbounded panels of functionally graded materials is studied using an analytical approach by means of matrix manipulation and fourier component analysis the three dimensional 3 d governing equations of elastodynamics are converted into a system of ordinary differential equations with variable coefficients in the frequency and wavenumber domain integration of the ordinary differential equation system across the panel thickness leads to a closed form solution for the transfer matrix analytical expressions are then obtained for sound reflection and transmission coefficients for panels of functionally graded materials the present model is used to predict sound transmission losses for various panel examples the results compare well with published data from other methods thereby validating the accuracy of the formulation developed in this study

regularity and autocontinuity of set multifunctions in this paper we study different types of regularity for monotone uniformly autocontinuous set multifunctions defined on a ring of subsets of a locally compact hausdorff space t and taking values in the family of closed nonvoid sets of a real normed space x

efficient computation of partition of unity interpolants through a block based searching technique in this paper we propose a new efficient interpolation tool extremely suitable for large scattered data sets the partition of unity method is used and performed by blending radial basis functions rbfs as local approximants and using locally supported weight functions in particular we present a new space partitioning data structure based on a partition of the underlying generic domain in blocks this approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points leading to an optimized searching routine complexity analysis and numerical experiments in two and three dimensional interpolation support our findings some applications to geometric modelling are also considered moreover the associated software package written in matlab is here discussed and made available to the scientific community

coupling finite element method with meshless finite difference method in thermomechanical problems this paper focuses on coupling two different computational approaches namely finite element method fem and meshless finite difference method mfdm in one domain the coupled approach is applied in solving thermomechanical initialboundary value problem where the heat transport in the domain is non stationary in this method the domain is divided into two subdomains for fem and mfdm respectively contrary to other coupling techniques the approach presented in this paper is defined in terms of mathematical problem formulation rather than at the approximation level in the weak form of thermomechanical initialboundary value problem variational principle the appropriate additional coupling integrals are defined a priori subsequently the fem and the mfdm approximations which may differ from each other are provided to the formulation it is assumed that there exists a very thin layer of material between the subdomains which is not spatially discretized the width of this layer may be considered the coupling parameter and it is the same for both thermal and mechanical parts similar approach is applied to essential boundary conditions e g prescribed temperature and displacements consequently the consistent formulation of the mixed problem for the coupled femmfdm method is derived the analysis is illustrated with two and three dimensional examples of mechanical and thermomechanical problems

a gould type integral of fuzzy functions abstract in this paper a new type of integral of a fuzzy valued function relative to a non negative set function is proposed as a new useful tool in modeling uncertainties various properties of this new type of integral are established concerning the behavior with respect to the fuzzy function or to the set function several examples linking our integral with birkhoff and lebesgue integrals are provided also problems related to atomicity are addressed

pseudo atoms and darboux property for set multifunctions in this paper we introduce and study the concepts of pseudo atom and darboux property for set multifunctions we establish relationships between the darboux property and non atomicity in the multivalued case we also prove that the range of a multimeasure having the darboux property is a convex set

a lusin type theorem for regular monotone uniformly autocontinuous set multifunctions in this paper we continue our study concerning monotone uniformly autocontinuous regular set multifunctions as an application a lusin type theorem under a suitable type of measurability is obtained and several applications for finitely purely atomic multisubmeasures are proved

inequalities of holder and minkowski type for pseudo integrals with respect to interval valued measures abstract in the present paper the holder and minkowski type of inequality for the pseudo integral of a real valued function with respect to the interval valued pseudo additive measure is proven two cases of semirings are considered in the first case pseudo operations pseudo addition and pseudo multiplication are set by a strictly monotone continuous function in the second case the pseudo addition is the idempotent operation sup and pseudo multiplication is specified by a strictly monotone continuous function as in the first case trivial and nontrivial examples of interval valued pseudo additive measures are provided as well as holder and minkowski type of inequalities with respect to those measures

lusin s theorem for monotone set valued measures on topological spaces abstract on a topological space the inner regularity outer regularity and regularity of a monotone set valued measure are considered their properties are discussed based on these the versions of egoroff s theorem and lusin s theorem for monotone set valued measures on a topological space are shown respectively

radial basis functions for the multivariate interpolation of large scattered data sets an efficient method for the multivariate interpolation of very large scattered data sets is presented it is based on the local use of radial basis functions and represents a further improvement of the well known shepard s method although the latter is simple and well suited for multivariate interpolation it does not share the good reproduction quality of other methods widely used for bivariate interpolation on the other band radial basis functions which have proven to be highly useful for multivariate scattered data interpolation have a severe drawback they are unable to interpolate large sets in an efficient and numerically stable way and maintain a good level of reproduction quality at the same time both problems have been circumvented using radial basis functions to evaluate the nodal function of the modified shepard s method this approach exploits the flexibility of the method and improves its reproduction quality the proposed algorithm has been implemented and numerical results confirm its efficiency

on the transformation of fuzzy measures to the power set and its role in determining the measure of a measure we are interested in developing a framework for determining the degree of satisfaction of some imprecisely stated conditions by some relevant variables whose value itself may be imprecise or uncertain we particularly focus on the use of fuzzy measures as they can provide a unified representation of various types of uncertainty and imprecision starting with set measures mappings from crisp sets into the unit interval we first discuss the extension of these to provide measures of fuzzy subsets we next consider the issue of allowing measures to assign values to other measures this requires the transformation of the set measure to be a measure on the power set we then look at some methods for transforming measures to the power set

stable computations with gaussian radial basis functions radial basis function rbf approximation is an extremely powerful tool for representing smooth functions in nontrivial geometries since the method is mesh free and can be spectrally accurate a perceived practical obstacle is that the interpolation matrix becomes increasingly ill conditioned as the rbf shape parameter becomes small corresponding to flat rbfs two stable approaches that overcome this problem exist the contour pade method and the rbf qr method however the former is limited to small node sets and the latter has until now been formulated only for the surface of the sphere this paper focuses on an rbf qr formulation for node sets in one two and three dimensions the algorithm is stable for arbitrarily small shape parameters it can be used for thousands of node points in two dimensions and still more in three dimensions a sample matlab code for the two dimensional case is provided

a least squares radial basis function partition of unity method for solving pdes recently collocation based radial basis function rbf partition of unity methods pums for solving partial differential equations have been formulated and investigated numerically and theoretically when combined with stable evaluation methods such as the rbf qr method high order convergence rates can be achieved and sustained under refinement however some numerical issues remain the method is sensitive to the node layout and condition numbers increase with the refinement level here we propose a modified formulation based on least squares approximation we show that the sensitivity to node layout is removed and that conditioning can be controlled through oversampling we derive theoretical error estimates both for the collocation and least squares rbf pums numerical experiments are performed for the poisson equation in two and three space dimensions for regular and irregular geometries the convergence experiments confirm the theoretical estimates and the least squares formulation is shown to

atoms of weakly null additive monotone measures and integrals in this paper we prove some properties of atoms of weakly null additive monotone measures by using the regularity and weak null additivity a sin gleton characterization of atoms of monotone measures on a metric space is shown it is a generalization of previous results obtained by pap the calculation of the sugeno integral and the choquet integral over an atom is also presented respectively similar results for recently introduced universal integral are also given following these results it is shown that the sugeno integral and the choquet integral over an atom of monotone measure is maxitive linear and standard linear respectively convergence theorems for the sugeno integral and the choquet integral over an atom of a monotone measure are also shown

pseudo additive measures and integrals abstract we suggest pseudo additive measures based on a pseudo addition and discuss integrals with respect to pseudo additive measures a pseudo additive measure is a special type of fuzzy measures to define an integral a multiplication corresponding to a pseudo addition is introduced the resulting integral is an extension of the lebesgue integral in this context radon nikodym like theorems are shown

a special class of fuzzy measures choquet integral and applications abstract we model a space of agents as a product space x x 0 1 and discuss the choquet integral with respect to a fuzzy measure on this space we introduce a fubini like and a lyapunov like theorems and based on these results core of economy and walras equilibria are studied

rbf pu method for pricing options under the jump diffusion model with local volatility abstract meshfree methods based on radial basis functions rbfs are of general interest for solving partial differential equations pdes because they can provide high order or spectral convergence for smooth solutions in complex geometries for global rbf methods one of the major disadvantages is the computational cost associated with the dense linear systems that arise therefore this paper is currently directed toward localized rbf approximations known as the rbf partition of unity rbf pu method for partial integro differential equation pide arisen in option pricing problems in jump diffusion model rbf pu method produces algebraic systems with sparse matrices which have small condition number also for comparison some stable time discretization schemes are combined with the operator splitting method to get a fully discrete problem numerical examples are presented to illustrate the convergence and stability of the proposed algorithms for pricing european and american options with merton and kou models

some properties of choquet integrals of set valued functions abstract in this paper we will define choquet integrals of set valued functions then we show some properties of choquet integrals of set valued functions

general chebyshev type inequalities for sugeno integrals chebyshev type inequalities for the sugeno integral on abstract spaces are studied in a rather general form thus closing the series of papers on the topic dealing with special cases restricted to the real line and product operation

pseudo optimal measures based on a pseudo addition on 0 pseudo optimal measures related to non negative set functions vanishing at the empty set non negative games are introduced for a fixed pseudo addition an equivalence on non negative set functions is studied a special stress is given to pure pseudo optimal measures admitting no other equivalent set function

atoms of monotone set valued measures and integrals abstract this paper first introduces the concept of a monotone set valued measure and then focuses on the atoms and pseudo atoms of the monotone set valued measure space moreover the paper proposes an integral which is the integral of real valued function with respect to the monotone set valued measure and shows some properties of this integral particularly the paper gives the representations of integrals defined on atoms and pseudo atoms some classical results are extended to the case of the monotone set valued measure

fast and accurate interpolation of large scattered data sets on the sphere in this paper a new efficient algorithm for spherical interpolation of large scattered data sets is presented the solution method is local and involves a modified spherical shepard s interpolant which uses zonal basis functions as local approximants the associated algorithm is implemented and optimized by applying a nearest neighbour searching procedure on the sphere specifically this technique is mainly based on the partition of the sphere in a suitable number of spherical zones the construction of spherical caps as local neighbourhoods for each node and finally the employment of a spherical zone searching procedure computational cost and storage requirements of the spherical algorithm are analyzed moreover several numerical results show the good accuracy of the method and the high efficiency of the proposed algorithm

propagation properties of acoustic waves inside periodic pipelines abstract this paper presents a new method to model and to simulate the propagation properties of the acoustic wave in periodic pipelines first an ideal model of pipeline and its dispersion equations of acoustic waves are constructed and described in detail in order to implement this method subsequently the classical finite difference method is applied to determine the boundary conditions of the pipelines in addition the transfer matrix method is used to simulate the propagation process of the acoustic waves inside the pipelines finally by conducting length limited periodic drill string experiments it is shown that this model and algorithm can be used to obtain the acoustic wave spectrum distribution and impulse response characteristics inside periodic pipelines under operational conditions this method provides a theoretical basis for the fault diagnosis of acoustic wave transmission systems for oil industry applications

on the regularities of fuzzy set multifunctions with applications in variation extensions and fuzzy set valued integrability problems in this paper we continue our studies 6 7 concerning regularity in this sense we obtain extension results by preserving regularity and we establish basic properties and continuity properties for the variation of fuzzy set multifunctions this enables us to get relationships among different types of regularity and also to point out regularity properties of the fuzzy set valued integral 20

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

atoms of fuzzy measures and fuzzy integrals abstract some analytical properties of sugeno s fuzzy measures especially of atoms of fuzzy measures are investigated a fuzzy integral of riemann type is defined through atoms and it is proved that a continuous function is fuzzy integrable in the sense of riemann and has the same integral as that of sugeno

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

scattered and track data interpolation using an efficient strip searching procedure abstract a new local algorithm for bivariate interpolation of large sets of scattered and track data is presented the method which changes partially depending on the kind of data is based on the partition of the interpolation domain in a suitable number of parallel strips and starting from these on the construction for any data point of a square neighbourhood containing a convenient number of data points then the well known modified shepard s formula for surface interpolation is applied with some effective improvements the proposed algorithm is very fast owing to the optimal nearest neighbour searching and achieves good accuracy computational cost and storage requirements are analyzed moreover the efficiency and reliability of the algorithm are shown by several numerical tests also performed by renka s algorithm for a comparison

on fuzzy measures defined by fuzzy integrals on definit une mesure floue comme une fonction ensemble sur 7b f qui est une algebre de sous ensembles de l ensemble x

continuity properties and alexandroff theorem in vietoris topology in several previous papers we introduced and studied various continuity properties in the set valued case precisely we established results concerning increasing decreasing convergence exhaustivity order continuity and regularity in hausdorff topology for closed set valued monotone set multifunctions on a real normed space in this paper taking as starting point of a previous work we introduce and study from another point of view corresponding continuity properties in vietoris topology for more general monotone set multifunctions on a hausdorff linear topological space thus we obtain generalizations of some previous results which in turn generalize to the set valued case well known results from classical fuzzy i e monotone measure theory an alexandroff theorem in vietoris topology and its converse are also established

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

fuzzy measures and integrals in evaluation of strategies artificial intelligence ai techniques have been applied to games for a long time in this paper we will explore the use of fuzzy measures and integrals to evaluate strategies in games we will show their use in decision making when modeling auctions the paper describes the role of fuzzy measures and integrals in decision making and reviews some computational aspects which are important for building real applications

fuzzy integrals for set valued mappings in this paper we introduce the concept of fuzzy integrals for set valued mappings which is an extension of fuzzy integrals for single valued functions defined by sugeno we give some properties including convergence theorems on fuzzy integrals for set valued mappings

fuzzy valued fuzzy measures and generalized fuzzy integrals in this paper the concept of fuzzy valued fuzzy measures is introduced at first and then based on the generalized fuzzy integral given by wu et al fuzzy sets and systems 57 1993 219 the generalized fuzzy integral of fuzzy valued functions with respect to fuzzy valued fuzzy measures is defined and the properties and convergence theorems are given all these are extensions of the sugeno theory of fuzzy integrals and its applications ph d thesis tokyo institute of technology 1974 and wu et al 1993 theory

on set valued fuzzy integrals abstract in the paper we extend fuzzy integrals of point valued functions which were defined by ralescu and adams to set valued functions some properties similar to auman integrals are shown and these include convexity monotonicity fatou s lemma lebesgue convergence theorem etc

remarks on monotone interval valued set multifunctions in this paper motivated by the representation of uncertainty we discuss the problem of interval valued set multifunctions which are monotone with respect to guo and zhang order relation 7 we prove that a set multifunction m c p k c r is a multisubmeasure in this order relation if and only if for every email protected c m a m 1 a m 2 a m 1 m 2 c r being submeasures in the sense of drewnowski 5 as application related results concerning variation and continuity properties are established

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

choquet like integrals abstract integrals based on a pseudo addition and a pseudo multiplication with properties similar to those of the choquet and the sugeno integral respectively are introduced the structure of convenient pseudo arithmetical operations leading to a choquet like integral is studied

stable evaluation of gaussian radial basis function interpolants we provide a new way to compute and evaluate gaussian radial basis function interpolants in a stable way with a special focus on small values of the shape parameter i e for flat kernels this work is motivated by the fundamental ideas proposed earlier by bengt fornberg and his coworkers however following mercer s theorem an l 2 mathbb r d rho orthonormal expansion of the gaussian kernel allows us to come up with an algorithm that is simpler than the one proposed by fornberg larsson and flyer and that is applicable in arbitrary space dimensions d in addition to obtaining an accurate approximation of the radial basis function interpolant using many terms in the series expansion of the kernel we also propose and investigate a highly accurate least squares approximation based on early truncation of the kernel expansion

λ generalized sugeno integral and its application sugeno integral is a useful tool for many problems in several domains especially in game theory measure theory decision making probability image processing and finance in this paper we introduce the concept of generalized sugeno integral then we establish general versions of chebyshev type inequality for this kind of sugeno integral by using a monotone measure our results generalize and improve the corresponding ones in the literature finally some conclusions and problems for further investigations are given

pan operations structure abstract the structure of pan addition and pan multiplication of a commutative isotonic semiring r is analyzed we show that if v supremum then r is a g semiring i e a b g 1 g a g b and d a b g 1 g a g b conclusions for pan integrals with respect to a measure are shown

non atomicity for fuzzy and non fuzzy multivalued set functions in this paper we extend the concept of set valued fuzzy measures introduced and studied by guo and zhang 2004 on set valued fuzzy measures information sciences 160 2004 13 25 to the class of multivalued set functions taking values in the family of non empty closed subsets of a real normed space also we introduce the notions of atom and non atomicity of a multivalued set function and present some of their properties we also establish an extension result by preserving non atomicity for a fuzzy multisubmeasure multimeasure

set valued lusin type theorem for null null additive set multifunctions in a previous paper we presented a set valued egoroff type theorem for monotone set multifunctions in this paper a new version of this set valued egoroff type theorem is obtained it enables a set valued lusin type theorem for null null additive monotone continuous set multifunctions to be established several applications of this lusin type theorem are given pointing out some relationships among m measurability a measurability and totally measurability of real functions we also compare our new lusin type theorem with lusin s theorem previously obtained by the second author

elasticity solution for stresses in a sandwich beam with functionally graded core introduction w eight savingsofferedby sandwich constructionsfor structures that require high bending stiffness are signi cant however sandwich constructions have not been fully exploited in structuralapplicationsdue to damage toleranceconcerns the core face sheet delamination is a major concern in sandwich construction the stiffness discontinuityat the face sheet and core interface results in a large increase in shear stresses although the core material itself may be able to withstand very high shear stresses the bond or adhesive layer at the interface could be relativelyweaker resulting in interfacial delamination results from this study indicate that the interfacial shear stresses can be reduced by varying functionallygrading the core properties through the thickness this note presents the displacement and stress elds in a functionallygraded core for a one dimensionalsandwichplate and compares them to that in a uniformcore the objective is to demonstrate the signi cant reduction in shear stresses at the face sheet core interface in the sandwich panel achieved by functionally grading the core properties

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

autocontinuity of set valued fuzzy measures and applications the main object of this paper is to further the study of set valued fuzzy measures introduced by gavrilut in 2009 some asymptotic structural characteristics of set valued fuzzy measures such as null additivity and autocontinuity are investigated in terms of applications convergence theorems for sequences of measurable functions are established

fuzzy measures and measures of fuzziness abstract in this paper the fuzzy integral defined by z x wang fuzzy math wuhan china in press which is different from that defined by m sugeno theory of fuzzy integrals and its applications ph d tokyo inst of technology 1974 is further considered and it is shown that the fuzzy measures of ordinary sets and fuzzy sets can be determined by each other summing up the results on the measure of fuzziness by a deluca and s a termini inform and control 20 1972 301 312 z x wang op cit and r r yager internat j gen systems 5 1979 221 229 inform and control 44 1980 236 260 the axioms for measures of fuzziness are given furthermore as an application of the furry integrals a measure of fuzziness is defined inversely it is proven that a measure of fuzziness satisfying some conditions can surely be expressed as a fuzzy integral with respect to some fuzzy measure

complex structured decision making model a hierarchical frame work for complex structured data we introduce a hierarchical framework we call complex structured decision making model for complexly structured knowledge representation in intelligent decision making we show that our model extends non hierarchical flat decision making models to hierarchical decision making models that are similar to comprehensible human decision making processes further we make an argument that hierarchial representation of knowledge in a complex structured decision making model simplifies the approximation of aggregation functions to easily adapt to the underline relation of the system additionally using a real world complex structured data set we show that hierarchically organized fuzzy integrals e g choquet integral and sugeno integral and fuzzy signatures outperform these non hierarchical fuzzy integrals

wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions wave propagation through a layer of a material that is inhomogeneous in the thickness direction typically a functionally graded material fgm is investigated the material parameters and the displacement components are expanded in power series in the thickness coordinate leading to recursion relations among the displacement expansion functions these can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions and this can be done even if the layer is not thin this gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties for thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer thus completely replacing the layer by these effective boundary conditions numerical examples illustrate the convergence properties of the scheme for fg layers and the influence of different variations of the material parameters in the fg layer

strong integral of multifunctions relative to a fuzzy measure abstract in this paper we define and study an integral for measurable multifunctions taking values in the family of all nonvoid subsets of 0 with respect to a fuzzy measure unlike various ways of defining such an integral e g aumann way using different selections dunford way riemann way we use the sugeno method directly applied to multifunctions the originality of our definition is that the value of the integral is a real scalar and not usually a set some classical integral properties a convergence theorem and relationships with other integrals are presented