fuzzy measures on metric spaces abstract the aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces among other results we shall give lusin s theorem and egoroff s theorem we shall also prove the singleton characterization of atom of fuzzy measure and an algorithm to evaluate the fuzzy integrals of non negative measurable functions over an atom and a union of finite disjoint atoms

monotone measures and universal integrals in a uniform framework for the scientific impact assessment problem the choquet sugeno and shilkret integrals with respect to monotone measures as well as their generalization the universal integral stand for a useful tool in decision support systems in this paper we propose a general construction method for aggregation operators that may be used in assessing output of scientists we show that the most often currently used indices of bibliometric impact like hirsch s h woeginger s w egghe s g kosmulski s maxprod and similar constructions may be obtained by means of our framework moreover the model easily leads to some new very interesting functions

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

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

measures of fuzzy sets and measures of fuzziness abstract the measures presented in this paper are defined by using weber s concept of decomposable measures m of crisp sets having in particular the archimedean decomposable operations in view section 2 measures m of fuzzy sets are introduced as integrals with respect to m for the archimedean cases weber s integral will be used as alternative to sugeno s and choquet s concepts section 3 what fuzziness means will be described by functions of fuzziness f another name entropy n functions with respect to a negation in addition to the types of functions of fuzziness which are induced by concave functions we discuss also the ones which are induced by fuzzy connectives section 4 now using m for measuring the importance of items and f for the fuzziness of the possible values of a fuzzy set m f serves us as a measure of the fuzziness f of the concepts of de luca and termini capocelli and de luca kaufmann knopfmacher loo gottwald dombi and under the restriction to the archimedean cases also the concepts of trillas and riera and yager turn out to be special cases section 5

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

generalized incompressible flows multi marginal transport and sinkhorn algorithm starting from brenier s relaxed formulation of the incompress ible euler equation in terms of geodesics in the group of measure preserving diffeomorphisms we propose a numerical method based on sinkhorn s algorithm for the entropic regularization of optimal transport we also make a detailed comparison of this entropic regular ization with the so called bredinger entropic interpolation problem see 1 numerical results in dimension one and two illustrate the feasibility of the method

the smallest semicopula based universal integrals iii topology determined by the integral abstract motivated by the recent results on topology determined by the prominent sugeno and choquet integrals we study the topology on the space of measurable functions for a non additive measure which is determined by the universal integral based on a semicopula we define a family of pseudo metrics on the set of measurable functions parameterized by a semicopula and study their properties we show that for a semicopula without zero divisors the convergence in the constructed pseudo metric is equivalent to convergence in non additive measure as well as other two types of convergences of measurable functions for each such a pseudo metric we construct a family of subsets of measurable functions and we provide sufficient conditions for this family to be a topology on the set of measurable functions moreover we show that for some natural class of semicopulas the corresponding topological spaces are all equivalent being equivalent to the topology determined by the choquet integral

on fuzzy measures defined by seminormed fuzzy integrals and semiconormed fuzzy integrals abstract in this paper we show that for the continuous t seminorms and continuous t semiconorms the properties of null addivity pseudo null addivity autocontinuity and pseudo autocontinuity of fuzzy measures g can be preserved by the fuzzy measures g h and g h defined by seminormed fuzzy integrals and semiconormed fuzzy integrals respectively at most under the conditions that x y 0 x y 0 and x y x y g can be preserved by the fuzzy measures g h under the condition that x y 0 x y 0

a unified approach to the monotone convergence theorem for nonlinear integrals abstract we present a unified approach to the monotone convergence theorem for nonlinear integrals such as the choquet the sipos the sugeno and the shilkret integral a nonlinear integral may be viewed as a nonlinear functional defined on a set of pairs of a nonadditive measure and a measurable function we thus formulate our general type of monotone convergence theorem for such a functional the key tool is a perturbation of functional that manages not only the monotonicity of the functional but also the small change of the functional value arising as a result of adding small amounts to a measure and a function in the domain of the functional our approach is also applicable to the lebesgue integral when a nonadditive measure is additive

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

a markov type inequality for seminormed fuzzy integrals in this paper we present a markov type inequality for seminormed fuzzy integrals and its connections with chebyshev s inequality and other fundamental properties of the classical integral

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

generalized fuzzy integrals part i fundamental concepts abstract in this paper we introduce a definition of fuzzy integral which is a generalization of both s fuzzy integral defined by m sugeno and n fuzzy integral due to zhao ruhuaiand discuss the fundamen tal properties of this kind of fuzzy integral

open problems from the 12th international conference on fuzzy set theory and its applications eighteen open problems posed during fsta 2014 liptovsk jan slovakia are presented these problems concern fuzzy logics fuzzy partitions copulas triangular norms and related aggregation functions some open problems concerning effect and mv algebras are also included

the solution of hutn ik s open problem in this note we give a solution to problem 9 2 which was presented by mesiar and stup v n anov a it open problems from the 12th international conference on fuzzy set theory and its applications fuzzy sets and systems 2014 this http url j fss 2014 07 012 we show that the class of semicopulas solving problem 9 2 contains only the l ukasiewicz t norm

the smallest semicopula based universal integrals remarks and improvements abstract we provide several improvements and corrections of results dealing with the smallest universal integral i s based on a semicopula s we deal with a transformation of the integral into another semicopula based universal integral for continuous and commutative semicopulas monotone convergence theorems with new proofs and frechet type mappings properties corrected during this way we discover several fine properties of the integral functional i s we also discuss further convergences of measurable functions and the corresponding integrals in the light of the newest results from the literature answering several open questions stated in our previous articles of the series

on the null additivity of the fuzzy measure abstract in this paper egoroff s theorem and other several results on fuzzy measure space of papers 1 and 4 are improved the importance of the concept of null additivity which was first introduced by wang in 1 is further shown

homogeneity properties of seminormed fuzzy integrals this paper is concerned with the maxitivity and homogeneity of integrals in a very general setting for the semi co normed fuzzy integrals we study the maxitivity minitivity and homogeneity homogeneity properties some necessary conditions for the fuzzy integrals to have such homogeneity properties are obtained

on the monotone convergence theorem for conormed seminormed fuzzy integral abstract in this paper under the condition that the t conorm and t seminorm are continuous we prove the monotone convergence theorem of conormed seminormed fuzzy integral for non decreasing monotone measurable function sequence also we show that the result cannot be extended to the case of the non increasing function sequence

the relationship between structural characteristics of fuzzy measure abstract in this paper some new concepts property s 1 property ps property ps 1 are introduced the converse problems of convergence theorems such as egoroff s theorem and riesz s theorem are discussed some new results about the relationship between structural characteristics of fuzzy measure and convergences of sequences of measurable functions are obtained

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

the smallest semicopula based universal integrals i properties and characterizations abstract in this article we provide a detailed study of basic properties of the smallest universal integral i s with s being the underlying semicopula and review some of the recent developments in this direction the class of integrals under study is also known under the name seminormed integrals and includes the well known sugeno and shilkret integrals as special cases we present some representations and equivalent formulations for i s further we discuss basic properties such as translatability linearity homogeneity and maxitivity in particular we provide the characterizations of the two prominent integrals of sugeno and shilkret we also raise and discuss some open questions

generalized compressible flows and solutions of the h div geodesic problem we study the geodesic problem on the group of diffeomorphism of a domain m rd equipped with the h div metric the geodesic equations coincide with the camassa holm equation when d 1 and represent one of its possible multi dimensional generalizations when d 1 we propose a relaxation a la brenier of this problem in which solutions are represented as probability measures on the space of continuous paths on the cone over m we use this relaxation to prove that smooth h div geodesics are globally length minimizing for short times we also prove that there exists a unique pressure field associated to solutions of our relaxation finally we propose a numerical scheme to construct generalized solutions on the cone and present some numerical results illustrating the relation between the generalized camassa holm and incompressible euler solutions

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

on the generalized kramers problem with exponential memory friction abstract the time dependent transmission coefficient for the generalized kramers problem with exponential memory friction has recently been calculated by kohen and tannor d kohen d j tannor j chem phys 103 1995 6013 using a procedure based on the method of reactive flux and the phase space distribution function their analysis is restricted to the high friction regime or diffusion limited regime we recently developed a complementary theory for the low friction energy diffusion limited regime in the markovian limit j m sancho a h romero k lindenberg j chem phys 109 1998 9888 here we generalize our method to the case of an exponential dissipative memory kernel we test our results as well as those of kohen and tannor against numerical simulations

left right semi uninorms and coimplications on a complete lattice in this paper we firstly discuss the deresidual operations of left right semi uninorms and show which properties they satisfy then we investigate the left and right semi uninorms induced by a coimplication and give some conditions such that the operations induced by a coimplication constitute left or right semi uninorms finally we demonstrate that the meet semilattice of all disjunctive right left distributive left right semi uninorms is order reversing isomorphic to the join semilattice of all right distributive coimplications which satisfy the neutrality principle

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

translation invariant semicopula based integrals in this note we give a solution to problem 9 2 which was presented by mesiar and stup anova 2015 6 we show that the class of semicopulas solving problem 9 2 contains only the ukasiewicz t norm

the completion of a fuzzy measure and its applications this paper discusses first the completion of a fuzzy measure which is defined on a ring then as an application of the complete fuzzy measure both convergence almost everywhere and convergence in fuzzy measure egoroff s theorems are provided

property s of fuzzy measure and riesz s theorem abstract in this note a sufficient and necessary condition for riesz s theorem to hold in the fuzzy measure space is given

a behavioral foundation for fuzzy measures in savage 41 a behavioral foundation was given for subjective probabilities to be used in the maximization of expected utility this paper analogously gives a behavioral foundation for fuzzy measures to be used in the maximization of choquet expected utility this opens the way to empirical verification or falsification of fuzzy measures and frees them of their ad hoc character

a survey of weak connectives and the preservation of their properties by aggregations the aim of this paper is to choose diverse definitions of generalized logical connectives and to present them in a coherent order from the weakest to the richest such a rich list of notions allows us to consider the problem of admissible aggregations in the presented classes of unary and binary operations this gives a contribution to the discussion of tolerance analysis in soft computing decision making approximate reasoning and fuzzy control first we present a short survey of the development of mv logic s connectives next we discuss postulates used for generalized logical connectives finally we describe families of weak connectives and indicate the preservation of their properties by some aggregation functions

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

minimal geodesics along volume preserving maps through semidiscrete optimal transport we introduce a numerical method for extracting minimal geodesics along the group of volume preserving maps equipped with the l 2 metric which as observed by arnold ann inst fourier grenoble 16 1966 pp 319 361 solve the euler equations of inviscid incompressible fluids the method relies on the generalized polar decomposition of brenier comm pure appl math 44 1991 pp 375 417 numerically implemented through semidiscrete optimal transport it is robust enough to extract nonclassical multivalued solutions of euler s equations for which the flow dimension defined as the quantization dimension of brenier s generalized flow is higher than the domain dimension a striking and unavoidable consequence of thismodel a i shnirelman geom funct anal 4 1994 pp 586 620 our convergence results encompass this generalizedmodel and our numerical experiments illustrate it for the first time in two space dimensions

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

sharp bounds of jensen type for the generalized sugeno integral abstract in this paper we provide two sided attainable bounds of jensen type for the generalized sugeno integral of any measurable function the results extend the previous results of roman flores et al for increasing functions and abbaszadeh et al for convex and concave functions we also give corrections of some results of abbaszadeh et al as a by product we obtain sharp inequalities for symmetric integral of grabisch to the best of our knowledge the results in the real valued functions context are presented for the first time here

transformation of the pseudo integral and related convergence theorems abstract in this paper a transformation of the pseudo integral into another pseudo integral is considered using the transformed pseudo integral monotone convergence theorems for the pseudo integral are obtained based on the reverse fatou s lemma for the pseudo integral the dominated convergence type theorem is proven

the camassa holm equation as an incompressible euler equation a geometric point of view the group of diffeomorphisms of a compact manifold endowed with the l 2 metric acting on the space of probability densities gives a unifying framework for the incompressible euler equation and the theory of optimal mass transport recently several authors have extended optimal transport to the space of positive radon measures where the wasserstein fisher rao distance is a natural extension of the classical l 2 wasserstein distance in this paper we show a similar relation between this unbalanced optimal transport problem and the hdiv right invariant metric on the group of diffeomorphisms which corresponds to the camassa holm ch equation in one dimension on the optimal transport side we prove a polar factorization theorem on the automorphism group of half densities geometrically our point of view provides an isometric embedding of the group of diffeomorphisms endowed with this right invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an l 2 type of cone metric this leads to a new formulation of the generalized ch equation as a geodesic equation on an isotropy subgroup of this automorphisms group on s1 solutions to the standard ch thus give particular solutions of the incompressible euler equation on a group of homeomorphisms of r 2 which preserve a radial density that has a singularity at 0 an other application consists in proving that smooth solutions of the euler arnold equation for the hdiv right invariant metric are length minimizing geodesics for sufficiently short times

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

a further investigation for fuzzy measures on metric spaces the pseudometric generating property of non additive set functions also plays an important role as the autocontinuity in fuzzy measure theory jiang ph d thesis chiba university 1996 wang and klir fuzzy measure theory plenum press new york 1992 a further research on this property has been presented in jiang et al fuzzy sets and systems 1998 the aim of this paper is to prove the egoroff s theorem and lusin s theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric generating property

new axiomatisations of discrete quantitative and qualitative possibilistic integrals necessity resp possibility measures are very simple min decomposable resp max decomposable representations of epistemic uncertainty due to incomplete knowledge they can be used in both quantitative and qualitative settings in the present work we revisit choquet and sugeno integrals as criteria for decision under uncertainty and propose new axioms when uncertainty is representable in possibility theory first a characterization of choquet integral with respect to a possibility or a necessity measure is proposed we respectively add an optimism or a pessimism axiom to the axioms of the choquet integral with respect to a general capacity this new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional it essentially assumes that the decision maker preferences only reflect the plausibility ordering between states of nature the obtained pessimistic resp optimistic criterion is an average maximin resp maximax criterion of wald across cuts of a possibility distribution on the state space the additional axiom can be also used in the axiomatic approach to sugeno integral and generalized forms thereof to justify possibility and necessity measures the axiomatization of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed we show that the new axiom justifying possibilistic choquet integrals can be expressed in this setting in the case of sugeno integral we correct a characterization proof for an existing set of axioms on acts and study an alternative set of axioms based on the idea of non compensation

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

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

fuzzy sets and their operations ii among the basic operations which can be performed on fuzzy sets are the operations of union intersection complement algebraic product and algebraic sum in addition to these operations new operations called bounded sum and bounded difference were defined by l a zadeh to investigate the fuzzy reasoning which provides a way of dealing with the reasoning problems which are too complex for precise solution this paper investigates the algebraic properties of fuzzy sets under these nex operations of bounded sum and bounded difference and the properties of fuzzy sets in the case where these new operations are combined with the well known operations of union intersection algebraic product and algebraic sum

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

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

on the jensen type inequality for generalized sugeno integral we prove necessary and sufficient conditions for the validity of jensen type inequalities for generalized sugeno integral our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators for several choices of operators we characterize the classes of functions for which the corresponding inequalities are satisfied

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

the smallest semicopula based universal integrals ii in this paper we continue studying the smallest universal integral i s having s as the underlying semicopula we present convergence theorems for i s integral sequences including monotone almost everywhere almost uniform in measure and in mean converging sequences of measurable functions respectively it emerges that these convergences characterize the underlying measure properties such as null additivity monotone autocontinuity and autocontinuity we provide many examples and counter examples as well as a few interesting open problems

general hardy type inequality for seminormed fuzzy integrals hardy type inequality for seminormed fuzzy integrals based on an aggregation function is studied in a rather general form the main results of this paper generalize some previous results also some conclusions are drawn and some problems for further investigations are given

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

on s homogeneity property of seminormed fuzzy integral we give an answer to problem 9 3 stated by mesiar and stup anova 8 we show that the class of semicopulas solving this problem contains any associative semicopula s such that for each a 0 1 the function x s a x is continuous and increasing on a countable number of intervals

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

problems of classification in a fuzzy environment this paper presents a classification model in a fuzzy environment by using possibility distributions and fuzzy measures optimal in bayes sense membership functions are induced these functions are similar to decision rules used in classical discriminant analysis the relations between fuzzy measures and possibility measures are also discussed to formulate a classification model where sugeno s fuzzy measures and integrals are used

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

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

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

a concept of duality for multivariate exchangeable survival models in some past works by the author and collaborators the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed generally the ageing function turns out to be a semi copula here we focus attention on the special class of survival models whose ageing function is actually a copula for pairs of models in this class we define a notion of duality such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula the formulation of the notion of duality presented here came out some years ago in the frame of research activity in collaboration with bruno bassan

holder minkowski type inequality for generalized sugeno integral abstract we give a necessary and sufficient condition for validity of the holder minkowski type inequality for the generalized sugeno integral any monotone measure and the class of associated functions we also show a connection between integral inequalities and the problem of finding binary operations satisfying the distributivity inequalities we characterize all semicopulas satisfying holder and minkowski inequalities for the seminormed fuzzy integral one result has been obtained for the recently introduced q integral we describe the relationships among the existing sufficient conditions and show that our result generalizes most known holder minkowski type inequalities for comonotone functions in the available literature we also provide two other methods to get the above mentioned inequality for the sugeno integral and the class of m subadditive functions as well as for the sugeno integral of 0 1 valued functions using a duality approach we point out some flaws and correct the corresponding false statements appearing in the literature at the end we pose several problems and questions for further research

beyond the scope of super level measures abstract we expand the theoretical background of the recently introduced outer measure spaces theory of do and thiele in harmonic and time frequency analysis context in the context of non additive measures and integrals we propose a certain framework for a natural extension of the basic ingredients of the theory i e the concept of size outer essential supremum and the corresponding super level measure which besides the covering the previously considered cases permits us to introduce a further substantial extension of a class of non additive integrals all these notions are studied in detail and exemplified

on comonotone commuting and weak subadditivity properties of seminormed fuzzy integrals abstract in the paper we characterize the class of all the binary operators commuting with the generalized sugeno integral generated by a strict t norm for the sugeno integral this problem was solved by ouyang and mesiar we also present the necessary and sufficient conditions for the weak subadditivity of the generalized sugeno integral

further discussions on convergence theorems for seminormed fuzzy integrals and semiconormed fuzzy integrals abstract in this paper a convergence in fuzzy measure resp pseudo in fuzzy measure theorem for seminormed resp semiconormed fuzzy integrals is proved provided that the fuzzy measure is autocontinuous resp pseudo autocontinuous furthermore an almost everywhere resp pseudo almost everywhere convergence theorem for seminormed resp semiconormed fuzzy integrals is showed provided that the fuzzy measure is null additive resp pseudo null additive

admissibility of the observation operators for volterra systems with exponential kernels we study admissibility of the observation operators for volterra systems in hilbert spaces with exponentially decaying kernels sufficient conditions for infinite time admissibility of the observation operators are established and some illustrating examples are given