general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

triangular norms position paper ii general constructions and parameterized families this second part out of three of a series of position papers on triangular norms for part i see triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press deals with general construction methods based on additive and multiplicative generators and on ordinal sums also included are some constructions leading to non continuous t norms and a presentation of some distinguished families of t norms

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

finite element approximation of incompressible navier stokes equations with slip boundary condition we consider mixed finite element approximations of the stationary incompressible navier stokes equations with slip boundary condition simultaneously approximating the velocity pressure and normal stress component the stability of the schemes is achieved by adding suitable consistent penalty terms corresponding to the normal stress component and to the pressure a new method of proving the stability of the discretizations allows us to obtain optimal error estimates for the velocity pressure and normal stress component in natural norms without using duality arguments and without imposing uniformity conditions on the finite element partition the schemes can easily be implemented into existing finite element codes for the navier stokes equations with standard dirichlet boundary conditions

statistical inference procedures for bivariate archimedean copulas abstract a bivariate distribution function h x y with marginals f x and g y is said to be generated by an archimedean copula if it can be expressed in the form h x y 1 f x g y for some convex decreasing function defined on 0 1 in such a way that 1 0 many well known systems of bivariate distributions belong to this class including those of gumbel ali mikhail haq thelot clayton frank and hougaard frailty models also fall under that general prescription this article examines the problem of selecting an archimedean copula providing a suitable representation of the dependence structure between two variates x and y in the light of a random sample x 1 y 1 x n y n the key to the estimation procedure is a one dimensional empirical distribution function that can be constructed whether the uniform representation of x and y is archimedean or not and independently of their marginals this semiparametric estimator based on a decomposition of kendall s tau statistic

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

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

on the asymptotic limit of the navier stokes system on domains with rough boundaries abstract we study the asymptotic behavior of solutions to the incompressible navier stokes system considered on a sequence of spatial domains whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non degenerate meaning not oriented in a single direction

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

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

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

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

triangular norms position paper iii continuous t norms this third and last part of a series of position papers on triangular norms for parts i and ii see e p klement r mesiar e pap triangular norms position paper i basic analytical and algebraic properties fuzzy sets and systems in press e p klement r mesiar e pap triangular norms position paper ii general constructions and parameterized families submitted for publication presents the representation of continuous archimedean t norms by means of additive generators and the representation of continuous t norms by means of ordinal sums with archimedean summands both with full proofs finally some consequences of these representation theorems in the context of comparison and convergence of continuous t norms and of the determination of continuous t norms by their diagonal sections are mentioned

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

representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples it is shown that the electromagnetic em field radiated or scattered by bounded sources can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded the number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field this result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain it is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry the case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered for these geometries precise and fast sampling algorithms of central type are presented which allow an efficient recovery of em fields from a nonredundant finite number of samples such algorithms are stable with respect to random errors affecting the data

meta theorems on inequalities for scalar fuzzy set cardinalities we present meta theorems stating general conditions ensuring that certain inequalities for cardinalities of ordinary sets are preserved under fuzzification when adopting a scalar approach to fuzzy set cardinality the conditions pertain to the commutative conjunctor used for modelling fuzzy set intersection in particular this conjunctor should fulfil a number of bell type inequalities the advantage of these meta theorems is that repetitious calculations can be avoided this is illustrated in the demonstration of the lukasiewicz transitivity of fuzzified versions of the simple matching coefficient and the jaccard coefficient or equivalently the triangle inequality of the corresponding dissimilarity measures

distributivity inequalities of monotonic operations the aim of this work is to complement recent results about distributive binary operations our investigation was motivated by non distributive logical connectives and their generalizations in fuzzy set theory in spite of the title we neither solve the concerned functional inequalities nor look for characterization of the solutions of such inequalities we only lay bare conditions for their fulfilment for monotonic operations with neutral or zero element we present the sufficient conditions to obtain the subdistributivity or superdistributivity in the case of the lack of distributivity for the considered pairs of operations in particular we describe families of increasing binary operations subdistributive or superdistributive with respect to idempotent uninorms and nullnorms

w1 p estimates for elliptic problems with neumann boundary conditions in lipschitz domains abstract we study w 1 p estimates in lipschitz domains for second order elliptic equations and systems of divergence form with real valued bounded measurable coefficients for any fixed p 2 we prove that a weak reverse holder inequality implies the w 1 p estimates for solutions with neumann boundary conditions as a result we are able to show that if the coefficient matrix of elliptic equation is symmetric and in vmo r n the w 1 p estimate holds for 3 2 e p 3 e if n 3 and for 4 3 e p 4 e if n 2 and for elliptic systems the w 1 p estimate is true for 2 n n 1 e p 2 n n 1 e

on the roughness induced effective boundary conditions for an incompressible viscous flow abstract we consider the laminar viscous channel flow with the lateral surface of the channel containing surface irregularities it is supposed that a uniform pressure gradient is maintained in the longitudinal direction of the channel after studying the corresponding boundary layers we obtain rigorously the navier friction condition it is valid when the size and amplitude of the imperfections tend to zero furthermore the coefficient in the law is determined through an auxiliary boundary layer type problem and the tangential drag force and the effective mass flow are determined up to order o e3 2 the value of the effective coefficient is shown to be independent with respect to the position of the mean surface in the range of o e

quasi copulas with a given sub diagonal section abstract as is well known the frechet hoeffding bounds are the best possible for both copulas and quasi copulas for every quasi copula q max x y 1 0 q x y min x y for all x y 0 1 sharper bounds hold when the quasi copulas take prescribed values e g along their diagonal or horizontal resp vertical sections here we pursue two goals first we investigate construction methods for quasi copulas with a given sub diagonal section i e with prescribed values along the straight line segment joining the points x 0 0 and 1 1 x 0 for x 0 0 1 then we determine the best possible bounds for sets of quasi copulas with a given sub diagonal section

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 distributivity property of increasing binary operations abstract this paper is mainly devoted to solving the functional equations of distributivity and conditional distributivity of increasing binary operations with the unit our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory in particular some assumptions namely associativity and commutativity and results about conditional distributivity of uninorms and triangular norms and triangular conorms were simplified moreover some other properties e g componentwise convexity concavity for special operations from the class of quasi copulas is considered

metrics and t equalities abstract the relationship between metrics and t equalities is investigated the latter are a special case of t equivalences a natural generalization of the classical concept of an equivalence relation it is shown that in the construction of metrics from t equalities triangular norms with an additive generator play a key role conversely in the construction of t equalities from metrics this role is played by triangular norms with a continuous additive generator or equivalently by continuous archimedean triangular norms these results are then applied to the biresidual operator e t of a triangular norm t it is shown that e t is a t equality on 0 1 if and only if t is left continuous furthermore it is shown that to any left continuous triangular norm t there correspond two particular t equalities on f x the class of fuzzy sets in a given universe x one of these t equalities is obtained from the biresidual operator e t t by means of a natural extension procedure these t equalities then give rise to interesting metrics on f x

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

parametric classes of generalized conjunction and disjunction operations for fuzzy modeling it is argued that inference procedures of fuzzy models do not always require commutativity and associativity of the operations used this raises the possibility of considering nonassociative and noncommutative conjunction and disjunction operations such operations are investigated in this paper and different methods for their generation are proposed a number of new types of conjunction operations that are simpler than the known parametric classes of t norms are given and as an application example the approximation of a function by a fuzzy inference system is considered

triangular norms position paper i basic analytical and algebraic properties we present the basic analytical and algebraic properties of triangular norms we discuss continuity as well as the important classes of archimedean strict and nilpotent t norms triangular conorms and de morgan triples are also mentioned finally a brief historical survey on triangular norms is given

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

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

weighted lq estimates for stationary stokes system with partially bmo coefficients abstract we prove the unique solvability of solutions in sobolev spaces to the stationary stokes system on a bounded reifenberg flat domain when the coefficients are partially bmo functions i e locally they are merely measurable in one direction and have small mean oscillations in the other directions using this result we establish the unique solvability in muckenhoupt type weighted sobolev spaces for the system with partially bmo coefficients on a reifenberg flat domain we also present weighted a priori l q estimates for the system when the domain is the whole euclidean space or a half space

the dominance relation in some families of continuous archimedean t norms and copulas the dominance relation in several families of continuous archimedean t norms and copulas is investigated on the one hand the contribution provides a comprehensive overview on recent conditions and properties of dominance as well as known results for particular cases of families on the other hand it contains new results clarifying the dominance relationship in five additional families of continuous archimedean t norms and copulas

one problem of the navier type for the stokes system in planar domains we study the problem u f u f u g u g in u gu g h h on for a bounded simply connected lipschitz domain in the plane for f 0f 0 g 0g 0 g lp g lp h lq h lq we study a solution in the sense of a nontangential limit for f ws 1 q r2 f ws 1 q r2 g ws q g ws q g wt 1 p p g wt 1 p p h ws 1 q q h ws 1 q q with t s 1t s 1 we prove the existence of a unique solution u wt p r2 ws q u wt p r2 ws q for f bs 1q r r2 g bsq r g bt 1 pp h bs 1 qq r with t s 1t s 1 we prove the existence of a unique solution u btp r2 bsq r for f ck 1 r2 g ck h ck h ck g ck 1 g ck 1 we prove the existence of a unique solution u ck 1 r2 ck

the convergence of dg fuzzy integrals abstract the definition of another kind of generalized fuzzy integrals is introduced by means of the so called generalized triangular conorm it is said to be dual generalized fuzzy integrals and is denoted by dg fuzzy integrals in this paper several equivalent forms of dg fuzzy integrals are given particularly the convergence theorem in fuzzy measure and the monotone convergence theorems are obtained

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

slip with friction and penetration with resistance boundary conditions for the navier stokes equations numerical tests and aspects of the implementation we consider slip with friction and penetration with resistance boundary conditions in the steady state navier stokes equations this paper describes some aspects of the implementation of these boundary conditions for finite element discretizations numerical tests on two and three dimensional channel flows across a step using the slip with friction boundary condition study the influence of the friction parameter on the position of the reattachment point and the reattachment line of the recirculating vortex respectively

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

viscous boundary layers for the navier stokes equations with the navier slip conditions we tackle the issue of the inviscid limit of the incompressible navier stokes equations when the navier slip with friction conditions are prescribed on impermeable boundaries we justify an asymptotic expansion which involves a weak amplitude boundary layer with the same thickness as in prandtl s theory and a linear behavior this analysis holds for general regular domains in both dimensions two and three

dominance on strict triangular norms and mulholland inequality abstract this paper is devoted to the question of transitivity of the dominance relation defined on the set of strict triangular norms and to the connection between dominance and mulholland inequality a summary of the results reached in this field is given and a new result for the strict triangular norms of family 19 is shown further some parametric classes of solutions of mulholland inequality that do not comply with the mulholland s condition are presented and finally it is shown that the dominance relation is in general not transitive on the set of strict triangular norms

properties of the aggregation operators related with fuzzy relations abstract the problem of information generalization in multicriteria decision making is considered in this paper the information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations which they aggregate are proved the sensitivity of the operators with respect to variations in their arguments is investigated the numerical example deciding the problem of alternatives ranking is given as well

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

graded dominance and related graded properties of fuzzy connectives graded properties of binary and unary fuzzy connectives valued in mtl algebras are studied including graded monotony a generalized lipschitz property commutativity associativity unit and null elements and the dominance relation between fuzzy connectives the apparatus of fuzzy class theory or higher order fuzzy logic is employed as a tool for easy derivation of graded theorems on the connectives

strict preference relations based on weak t norms abstract in this paper we introduce and investigate weak t norms and related concepts in order to give a general representation of valued strict preference relations associated with a given valued preference relation all the well known forms of valued strict preference relations are particular cases of our results moreover when some types of rationality assumptions are made our unified approach seems to be the only possible one

lp theory for stokes and navier stokes equations with navier boundary condition abstract this work was intended as an attempt at studying stationary stokes and navier stokes problem with navier boundary conditions 1 3 we wish to investigate some results of existence uniqueness and regularity of solutions in hilbert case and in l p theory

representation and construction of self dual aggregation operators abstract two different characterizations of self dual aggregation operators are available in the literature one based on c x y x x 1 y and one based on the arithmetic mean both approaches construct a self dual aggregation operator by combining an aggregation operator with its dual in this paper we fit these approaches into a more general framework and characterize n invariant aggregation operators with n an involutive negator various binary aggregation operators fulfilling some kind of symmetry w r t n and with a sufficiently large range can be used to combine an aggregation operator and its dual into an n invariant aggregation operator moreover using aggregation operators to construct n invariant aggregation operators seems rather restrictive it suffices to consider n ary operators fulfilling some weaker conditions special attention is drawn to the equivalence classes that arise as several of these n ary operators can yield the same n invariant aggregation operator

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

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

preservation of fuzzy relation properties based on fuzzy conjunctions and disjunctions during aggregation process in this contribution necessary and sufficient conditions for n argument functions to preserve properties of fuzzy relations during aggregation process are presented the proposed properties depend on binary operations including t norms and t conorms and more generally fuzzy conjunctions and disjunctions generalizations of the following properties are studied antisymmetry asymmetry connectedness transitivity negative transitivity semitransitivity and ferrers property

uniform regularity for the navier stokes equation with navier boundary condition we prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the navier stokes equation with the navier boundary condition has a strong solution this solution is uniformly bounded in a conormal sobolev space and has only one normal derivative bounded in l this allows us to obtain the vanishing viscosity limit to the incompressible euler system from a strong compactness argument

representations and constructions of similarity based fuzzy orderings this contribution advocates the dissemination of similarity based fuzzy orderings a generalized concept of fuzzy orderings which appears to be unavoidable as soon as the classical correspondences between preorderings equivalence relations and orderings are taken into account in contrast to earlier papers on the topic this paper is focused on representation and construction results which once more demonstrate the feasibility of the proposed concept

archimedean overlap functions the ordinal sum and the cancellation idempotency and limiting properties abstract overlap functions are a particular type of aggregation functions given by increasing continuous commutative bivariate functions defined over the unit square satisfying appropriate boundary conditions overlap functions are applied mainly in classification problems image processing and in some problems of decision making based on some kind of fuzzy preference relations in which the associativity property is not strongly required moreover the class of overlap functions is reacher than the class of t norms concerning some properties like idempotency homogeneity and mainly the self closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap functions this flexibility of overlap functions increases their applicability the aim of this papers is to introduce the concept of archimedean overlap functions presenting a study about the cancellation idempotency and limiting properties and providing a characterization of such class of functions the concept of ordinal sum of overlap functions is also introduced providing constructing representing methods of certain classes of overlap functions related to idempotency cancellation limiting and archimedean properties

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

aggregation operators and commuting commuting is an important property in any two step information merging procedure where the results should not depend on the order in which the single steps are performed we investigate the property of commuting for aggregation operators in connection with their relationship to bisymmetry in case of bisymmetric aggregation operators we show a sufficient condition ensuring that two operators commute while for bisymmetric aggregation operators with neutral element we even provide a full characterization of commuting n ary operators by means of unary distributive functions the case of associative operations especially uninorms is considered in detail

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

semi copulas capacities and families of level sets we point out how capacities non additive measures can be used to provide explanations about the concept of bivariate ageing function the latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi copula

subdistributivity and superdistributivity of binary operations recently the property of distributivity of binary operations on 0 1 is of great interest both for practical as well as fundamental reasons in this paper we summarize some facts connected with distributivity and non distributivity of binary operations on 0 1 motivated by non distributive logical connectives in fuzzy set theory we show some new results concerning the above property a new direction of investigations mainly concerns the distributivity inequalities for triangular norms and conorms and their diverse generalizations in particular we look for examples of binary operations fulfilling the distributivity inequalities

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

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

frank s family of bivariate distributions summary this paper examines the properties of a new class of bivariate distributions whose members are stochastically ordered and likelihood ratio dependent the proposed class can be used to construct bivariate families of distributions whose marginals are arbitrary and which include the frechet bounds as well as the distribution corresponding to independent variables three nonparametric estimators of the association parameter are suggested and monte carlo experiments are used to compare their small sample behaviour to that of the maximum likelihood estimate

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

dominance in the family of sugeno weber t norms the dominance relationship between two members of the family of sugeno weber t norms is proven by using a quantifier elimination algorithm further it is shown that dominance is a transitive and therefore also an order relation on this family of t norms

a generalization of the mulholland inequality for continuous archimedean t norms it is well known that dominance between strict t norms is closely related to the mulholland inequality which can be seen as a generalization of the minkowski inequality however strict t norms constitute only one part of the class of continuous archimedean t norms the basic elements from which all continuous t norms are composed in this paper dominance between continuous archimedean t norms is shown to be related to a generalization of the mulholland inequality we provide sufficient and necessary conditions for its fulfillment

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

orthogonal grid constructions of copulas we establish a general framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with nonoverlapping rectangles as patches we derive a family of construction methods that require the choice of a single background copula when this background copula is the greatest copula we retrieve the well known ordinal sum construction while in the case of the smallest copula we obtain a construction method that is dual to the ordinal sum construction also nonsingular background copulas lead to suitable construction methods

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

stationary stokes oseen and navier stokes equations with singular data the concept of very weak solution introduced by giga math z 178 287 329 1981 for the stokes equations has hardly been studied in recent years for either the navier stokes equations or the navier stokes type equations we treat the stationary stokes oseen and navier stokes systems in the case of a bounded open set connected of class mathcal c 1 1 of mathbb r 3 taking up once again the duality method introduced by lions and magenes problemes aus limites non homogenes et applications vols 1 2 dunod paris 1968 and giga math z 178 287 329 1981 for open sets of class mathcal c infty see also chapter 4 of necas les methodes directes en theorie des equations elliptiques french masson et cie ed paris academia editeurs prague 1967 which considers the hilbertian case p 2 for general elliptic operators we give a simpler proof of the existence of a very weak solution for stationary oseen and navier stokes equations when data are not regular enough based on density arguments and a functional framework adequate for defining more rigourously the traces of non regular vector fields in the stationary navier stokes case the results will be valid for external forces not necessarily small which lets us extend the uniqueness class of solutions for these equations considering more regular data regularity results in fractional sobolev spaces will also be discussed for the three systems all these results can be extended to other dimensions

a novel approach to scatterers localization problem a new approach to find the number and locations of electromagnetic scatterers sources from one view one frequency field data is presented the case of scatterers sources with dimensions comparable to the wavelength is considered first in order to devise an effective technique a new relevant property of the electromagnetic field the point source spectral content is introduced and its relationship with both the sliding windowed fourier transform of the field and the local bandwidth function is discussed to enlighten its usefulness it is also shown that a footprint of the scattering system encoding information on its geometry can be easily extracted from the scattered field by exploiting this new property on this basis the new localization technique is introduced in order to restrict the search region the minimum circular envelope enclosing the scatterers is found by purposely introducing a new technique exploiting the effective bandwidth of the radiated field then the number and locations of scatterers is retrieved by using the field local quantitative feature previously introduced without the complexities of the full inverse problem as it is usually done by the traditional approaches in this way not only a simplified technique is obtained but also the ill posedness of the problem and the noise effects are significantly mitigated the effectiveness of the proposed technique and its overall performance with respect to a singular value decomposition based approach are proved by means of a numerical analysis

the stability of local properties of fuzzy relations under ordinal equivalence abstract we consider a notion of equivalence relation between fuzzy relations and its properties the relation is called ordinal equivalence since it partitions the family of fuzzy relations into equivalence classes by means of the order defined on elements of each relation we compare fuzzy relations by their membership values and as a consequence we propose two types of local properties of fuzzy relations new properties of fuzzy relations are more compatible with the ordinal equivalence relation namely they are stable in the equivalence classes moreover we study dependencies between these new properties of fuzzy relations finally notes on applications of the presented local properties and the ordinal equivalence relation are provided