on some advanced type inequalities for sugeno integral and t s evaluators in this paper strengthened versions of the minkowski chebyshev jensen and holder inequalities for sugeno integral and t s evaluators are given as an application some equivalent forms and some particular results have been established

vibration of arbitrarily shaped triangular plates with elastically restrained edges abstract a solution method is proposed for the vibration analysis of arbitrarily shaped triangular plates with elastically restrained edges an arbitrarily shaped triangular plate is first mapped into a right angled isosceles triangular plate and subsequently stretched to form a square plate by padding to it another right angled isosceles triangular plate of near zero thickness the displacement function is then expressed as a two dimensional fourier cosine series supplemented by several one dimensional series introduced to improve the convergence and accuracy of the displacement solution regardless of the shapes and boundary conditions of the triangular plate the final stiffness and mass matrices can always be calculated analytically which makes the current solution method highly efficient in implementations numerical examples are presented to verify the applicability of the proposed method to triangular plates of different shapes and perhaps more importantly different boundary conditions the current method can be easily extended to plates with heterogeneous material properties variable thickness non uniform elastic restraints etc

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

statistical analysis of parametric t norms theoretical aspects of aggregation functions particularly t norms have been deeply investigated a further step in the study of these functions is to consider statistical behavior of outputs this research approach has been initiated by the authors in a recent paper mainly focused on the compensatory functions such as averages now parametric t norms are especially studied in order to provide simply easy rules to be used by practitioners when choosing one parameter value a pairwise parametric comparison of several t norm families is provided by means of charts

generalizations of the chebyshev type inequality for choquet like expectation this paper proves generalizations of the chebyshev type inequality for choquet like expectation some previous results are obtained as corollaries

reversed version of a generalized sharp holder s inequality and its applications in this paper we give a reversed version of a generalized sharp holder s inequality which is due to wu the results are then used to improve beckenbach s inequality and minkowski s inequality moreover as an application in information theory we present a refinement of singh s inequality which is one generalized shannon s inequality

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

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

training ν support vector classifiers theory and algorithms the support vector machine svm for classification proposed by scholkopf smola williamson and bartlett 2000 has the advantage of using a parameter on controlling the number of support vectors in this article we investigate the relation between svm and c svm in detail we show that in general they are two different problems with the same optimal solution set hence we may expect that many numerical aspects of solving them are similar however compared to regular c svm the formulation of svm is more complicated so up to now there have been no effective methods for solving large scale svm we propose a decomposition method for svm that is competitive with existing methods for c svm we also discuss the behavior of svm by some numerical experiments

on the comonotonic property for sugeno integral the so called comonotonic property for sugeno integral is introduced and investigated where 0 2 0 is a binary operation under the assumption that lim b a email protected a and lim a a email protected b we prove that sugeno integral possesses comonotonic property if and only if equals to one of the four operators minimum maximum pf the first projection and pl the last projection we also discuss comonotonic property when this assumption does not hold

chebyshev type inequalities for general fuzzy integrals abstract in this article we first introduce a class of binary operation called g seminorm which generalizes the concept of t seminorm then we use the g seminorm to define a class of sugeno like integral finally we establish some new chebyshev type inequalities for this kind of integral

sugeno integral of monotone functions based on lebesgue measure roman flores et al h roman flores a flores franulic y chalco cano the fuzzy integral for monotone functions applied mathematics and computation 185 2007 492 498 gave some optimal upper bounds for the sugeno integral of continuous and strictly monotone functions and provided yong type inequalities for the sugeno integral these results are generalized to monotone functions in this paper two algorithms are given for calculating the sugeno integral of monotone functions based on lebesgue measure several illustrative examples are presented

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

the sugeno integral with respect to α preinvex functions abstract in this paper we establish the left hand side of the hermite hadamard inequality for preinvex functions and illustrate that the hermite hadamard inequality for preinvex functions is not valid for the sugeno integral moreover we give several upper bounds for the sugeno integral related to preinvex functions some examples are also provided to show the validity of our results

fast full search in motion estimation by hierarchical use of minkowski s inequality humi abstract in this paper we extend the idea of successive elimination algorithm sea to obtain a fast full search fs algorithm accelerating the block matching procedure of motion estimation based on the monotonic relation between the accumulated absolution distortions aad obtained for distinct layers of a pyramid structure the proposed method successfully rejects many impossible candidates considered in the fs the derivation of the monotonicity relation repeatedly uses in a four dimensional vector space the l 1 version of minkowski s inequality an inequality which is quite well known in the field of mathematics simulation results show that the processing speed is faster than that of several well known fast full search methods including the sea that uses just once the minkowski s inequality in a vector space of 256 dimension when the block size is 16 16 the processing speed of the proposed method is also competitive with that of the three step search tss which is often used for block matching in interframe video coding although the visual quality performance of tss is usually a little poorer than that of the fs

an inequality related to minkowski type for sugeno integrals an inequality related to minkowski type for the sugeno integral on abstract spaces is studied in a rather general form some previous results on chebyshev type inequality obtained by the authors are generalized several examples are given to illustrate the validity of this inequality the conditions such that this inequality becomes an equality are also discussed finally conclusions and some problems for further investigations are included

chebyshev type inequalities involving permanents and their applications abstract we extend the well known chebyshev s inequality to some new cases involving permanents under the proper hypotheses our main results are per a b n per a n per b n and per a i 1 n j 1 n a i j per b i 1 n j 1 n b i j as applications we consider the problem of finding bounds of the ratios of two functions involving permanents

chebyshev s inequality for choquet like integral abstract the chebyshev inequality for the choquet like integral is investigated as an application a markov s inequality for this type of integral is proven some previous results obtained by others are generalized

on stolarsky inequality for sugeno and choquet integrals recently flores franulic roman flores and chalco cano proved the stolarsky type inequality for sugeno integral with respect to the lebesgue measure l the present paper is devoted to generalize this result by relaxing some of its requirements moreover stolarsky inequality for choquet integral is added too

multi label core vector machine with a zero label abstract multi label core vector machine rank cvm is an efficient and effective algorithm for multi label classification but there still exist two aspects to be improved reducing training and testing computational costs further and detecting relevant labels effectively in this paper we extend rank cvm via adding a zero label to construct its variant with a zero label i e rank cvmz which is formulated as the same quadratic programming form with a unit simplex constraint and non negative ones as rank cvm and then is solved by frank wolfe method efficiently attractively our rank cvmz has fewer variables to be solved than rank cvm which speeds up training procedure dramatically further the relevant labels are effectively detected by the zero label experimental results on 12 benchmark data sets demonstrate that our method achieves a competitive performance compared with six existing multi label algorithms according to six indicative instance based measures moreover on the average our rank cvmz runs 83 times faster and has slightly fewer support vectors than its origin rank cvm

fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices this paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set it also presents basic ideas on fuzzy integrals defined using these fuzzy measures definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers several useful properties of fuzzy measures and fuzzy integrals are stated and proved definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

holder type inequality for sugeno integral two inequalities for the sugeno integral on abstract spaces are studied in rather general forms which generalize most of the results on the same topic obtained by other authors thus closing the series of papers on this topic as an application a holder type inequality is obtained finally some conclusions are drawn and some problems for further investigation are suggested

fuzzy integral based perceptron for two class pattern classification problems the single layer perceptron with single output node is a well known neural network for two class classification problems furthermore the sigmoid or logistic function is usually used as the activation function in the output neuron a critical step is to compute the sum of the products of the connection weights with the corresponding inputs which indicates the assumption of additivity among individual variables unfortunately because the input variables are not always independent of each other an assumption of additivity may not be reasonable enough in this paper the inner product can be replaced with an aggregation value obtained by a useful fuzzy integral by viewing each of the connection weights as a value of a l fuzzy measure for the corresponding variable a genetic algorithm is then employed to obtain connection weights by maximizing the number of correctly classified training patterns and minimizing the errors between the actual and desired outputs of individual training patterns the experimental results further demonstrate that the proposed method outperforms the traditional single layer perceptron and performs well in comparison with other fuzzy or non fuzzy classification methods

fuzzy integral based information fusion for classification of highly confusable non speech sounds acoustic event classification may help to describe acoustic scenes and contribute to improve the robustness of speech technologies in this work fusion of different information sources with the fuzzy integral fi and the associated fuzzy measure fm are applied to the problem of classifying a small set of highly confusable human non speech sounds as fi is a meaningful formalism for combining classifier outputs that can capture interactions among the various sources of information it shows in our experiments a significantly better performance than that of any single classifier entering the fi fusion module actually that fi decision level fusion approach shows comparable results to the high performing svm feature level fusion and thus it seems to be a good choice when feature level fusion is not an option we have also observed that the importance and the degree of interaction among the various feature types given by the fm can be used for feature selection and gives a valuable insight into the problem

free vibration of shear deformable general triangular plates an analysis of free vibration of shear deformable general triangular plates with arbitrary combinations of boundary conditions is presented the reissner mindlin plate theory is used to incorporate shear deformation effects in the analysis the triangular plate is first mapped onto a basic square plate the rayleigh ritz method with an admissible displacement function expressed as a product of a two dimensional simple polynomial and a basic function is then used to obtain the governing eigenvalue equation the basic function is chosen as the product of boundary expressions of the basic square plate each raised to an appropriate power to satisfy the various geometric boundary conditions of the actual triangular plate gaussian quadrature is used for numerical evaluation of stiffness and mass matrices the natural frequencies of general triangular mindlin plates with different combinations of free simply supported and clamped conditions are determined wherever possible the results are verified by comparison with existing published solutions a comprehensive parametric study of natural frequencies of general triangular plates with all three edges clamped is presented graphically no previous results are known to exist for general triangular mindlin plates having arbitrary combinations of boundary conditions

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

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

multilabel classifiers with a probabilistic thresholding strategy in multilabel classification tasks the aim is to find hypotheses able to predict for each instance a set of classes or labels rather than a single one some state of the art multilabel learners use a thresholding strategy which consists in computing a score for each label and then predicting the set of labels whose score is higher than a given threshold when this score is the estimated posterior probability the selected threshold is typically 0 5 in this paper we introduce a family of thresholding strategies which take into account the posterior probability of all possible labels to determine a different threshold for each instance thus we exploit some kind of interdependence among labels to compute this threshold which is optimal regarding a given expected loss function we found experimentally that these strategies outperform other thresholding options for multilabel classification they provide an efficient method to implement a learner which considers the interdependence among labels in the sense that the overall performance of the prediction of a set of labels prevails over that of each single label

a jensen type inequality for fuzzy integrals in this paper we show a jensen type inequality for the sugeno integral we also discuss some conditions assuring the satisfaction of opposite inequality reverse jensen inequality

threshold optimisation for multi label classifiers many multi label classifiers provide a real valued score for each class a well known design approach consists of tuning the corresponding decision thresholds by optimising the performance measure of interest we address two open issues related to the optimisation of the widely used f measure and precision recall p r curve with respect to the class related decision thresholds on a given data set i we derive properties of the micro averaged f which allow its global maximum to be found by an optimisation strategy with a low computational cost so far only a suboptimal threshold selection rule and a greedy algorithm with no optimality guarantee were known ii we rigorously define the macro and micro p r curves analyse a previously suggested strategy for computing them based on maximising f and develop two possible implementations which can be also exploited for optimising related performance measures we evaluate our algorithms on five data sets related to three different application domains

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

h continuity of fuzzy measures and set defuzzification the purpose of this work is to analyze the continuity of fuzzy measures with respect to the hausdorff metric on k r n the class of all nonempty compact subsets of r n as an application we study the continuity of set defuzzification processes on r n which are defined by aumann integral methods

chebyshev type inequalities for pseudo integrals abstract chebyshev type inequalities for two classes of pseudo integrals are shown one of them concerning the pseudo integrals based on a function reduces on the g integral where pseudo operations are defined by a monotone and continuous function g another one concerns the pseudo integrals based on a semiring a b max where is generated moreover a strengthened version of chebyshev s inequality for pseudo integrals is proved

a chebyshev type inequality for fuzzy integrals abstract in this paper we prove a chebyshev type inequality for fuzzy integrals more precisely we show that 0 1 fg d 0 1 f d 0 1 g d where is the lebesgue measure on r and f g 0 1 0 are two continuous and strictly monotone functions both increasing or both decreasing also some examples and applications are presented

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

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral in this paper a hybrid approach for image recognition combining type 2 fuzzy logic modular neural networks and the sugeno integral is described interval type 2 fuzzy inference systems are used to perform edge detection and to calculate fuzzy densities for the decision process a type 2 fuzzy system is used for edge detection which is a pre processing applied to the training data for better use in the neural networks another type 2 fuzzy system calculates the fuzzy densities necessary for the sugeno integral which is used to integrate results of the neural network modules in this case fuzzy logic is shown to be a good methodology to improve the results of a neural system facilitating the representation of the human perception a comparative study is also made to verify that the proposed approach is better than existing approaches and improves the performance over type 1 fuzzy logic

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

high accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain summary based on the differential quadrature dq rule the gauss lobatto quadrature rule and the variational principle a dq finite element method dqfem is proposed for the free vibration analysis of thin plates the dqfem is a highly accurate and rapidly converging approach and is distinct from the differential quadrature element method dqem and the quadrature element method qem by employing the function values themselves in the trial function for the title problem the dqfem without using shape functions essentially combines the high accuracy of the differential quadrature method dqm with the generality of the standard finite element formulation and has superior accuracy to the standard fem and fdm and superior efficiency to the p version fem and qem in calculating the stiffness and mass matrices by incorporating the reformulated dq rules for general curvilinear quadrilaterals domains into the dqfem a curvilinear quadrilateral dq finite plate element is also proposed the inter element compatibility conditions as well as multiple boundary conditions can be implemented simply and conveniently as in fem through modifying the nodal parameters when required at boundary grid points using the dq rules thus the dqfem is capable of constructing curvilinear quadrilateral elements with any degree of freedom and any order of inter element compatibilities a series of frequency comparisons of thin isotropic plates with irregular and regular planforms validate the performance of the dqfem copyright q 2009 john wiley sons ltd

the fuzzy integral for monotone functions abstract in this paper we give some optimal upper bounds for the sugeno s integral of monotone functions more precisely we show that if g 0 0 is a continuous and strictly monotone function then the fuzzy integral value p 0 a g d with respect to the lebesgue measure verifies the following sharp inequalities a g a p p for the increasing case and b g p p for the decreasing case moreover we show that under adequate conditions these optimal inequalities provides a powerful tool for solving fuzzy integrals also some examples and application are presented

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

general minkowski type inequalities for sugeno integrals minkowski 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 pseudo additive operation

penalized partial least square discriminant analysis with l 1 norm for multi label data multi label data are prevalent in real world due to its great potential applications multi label learning has now been receiving more and more attention from many fields however how to effectively exploit the correlations of variables and labels and tackle the high dimensional problems of data are two major challenging issues for multi label learning in this paper we make an attempt to cope with these two problems by proposing an effective multi label learning algorithm specifically we make use of the technique of partial least square discriminant analysis to identify a common latent space between the variable space and the label space of multi label data moreover considering the label space of the multi label data is sparse a l1 norm penalty is further performed to constrain the y loadings of the optimization problem of partial least squares making them sparse the merit of our method is that it can capture the correlations and perform dimension reduction at the same time the experimental results conducted on eleven public data sets show that our method is promising and superior to the state of the art multi label classifiers in most cases highlightsa new and effective learning method for the multi label data is proposed the method exploits the sparse property of the label space fully the method captures the correlations of the variables by using partial least squares discriminant analysis dimension reduction has also applied to the high dimensional data the sparse purpose is achieved by performing the l1 norm penalty

core vector machines fast svm training on very large data sets standard svm training has o m3 time and o m2 space complexities where m is the training set size it is thus computationally infeasible on very large data sets by observing that practical svm implementations only approximate the optimal solution by an iterative strategy we scale up kernel methods by exploiting such approximateness in this paper we first show that many kernel methods can be equivalently formulated as minimum enclosing ball meb problems in computational geometry then by adopting an efficient approximate meb algorithm we obtain provably approximately optimal solutions with the idea of core sets our proposed core vector machine cvm algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m experiments on large toy and real world data sets demonstrate that the cvm is as accurate as existing svm implementations but is much faster and can handle much larger data sets than existing scale up methods for example cvm with the gaussian kernel produces superior results on the kddcup 99 intrusion detection data which has about five million training patterns in only 1 4 seconds on a 3 2ghz pentium 4 pc