capturing complexity classes by fragments of second order logic abstract we investigate the expressive power of certain fragments of second order logic on finite structures the fragments are second order horn logic second order krom logic as well as a symmetric and a deterministic version of the latter it is shown that all these logics collapse to their existential fragments in the presence of successor relation they provide characterizations of polynomial time deterministic and nondeterministic logspace and of the complement of symmetric logspace without successor relation these logics still can express certain problems that are complete in the corresponding complexity classes but on the other hand they are strictly weaker than previously known logics for these classes and fail to express some very simple properties

multilinear calderon zygmund theory abstract a systematic treatment of multilinear calderon zygmund operators is presented the theory developed includes strong type and endpoint weak type estimates interpolation a multilinear t 1 theorem and a variety of results regarding multilinear multiplier operators

existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

compactness for nonlinear continuity equations abstract we prove compactness and hence existence for solutions to a class of nonlinear transport equations the corresponding models combine the features of linear transport equations and scalar conservation laws we introduce a new method which gives quantitative compactness estimates compatible with both frameworks

on interpolation of bilinear operators abstract in this paper we study interpolation of bilinear operators between products of banach spaces generated by abstract methods of interpolation in the sense of aronszajn and gagliardo a variant of bilinear interpolation theorem is proved for bilinear operators from corresponding weighted c 0 spaces into banach spaces of non trivial the periodic fourier cotype this result is then extended to the spaces generated by the well known minimal and maximal methods of interpolation determined by quasi concave functions in the case when a maximal construction is generated by hilbert spaces we obtain a general variant of bilinear interpolation theorem combining this result with the abstract grothendieck theorem of pisier yields further results the results are applied in deriving a bilinear interpolation theorem for calderon lozanovsky for orlicz spaces and an embedding interpolation formula for e p summing operators

on a trilinear form related to the carleson theorem abstract demeter and thiele introduced the two dimensional bilinear hilbert transform in demeter and thiele 2010 3 and showed that the carleson operator can be identified in particular instances of the corresponding trilinear form demeter considered the walsh model of one such form in demeter 2012 2 in relation to the discussion of the walsh carleson theorem we prove boundedness of this trilinear form for a single triple of exponents at the boundary of the previously established range for this purpose we adapt the multilinear bellman function technique from kovac 2011 5 to the one and a half dimensional time frequency space

criteria for evaluating fuzzy ranking methods abstract in this paper four criteria for evaluating fuzzy ranking methods are investigated fuzzy preference representation rationality of fuzzy ordering distinguishability and robustness based on these criteria two existing ranking methods baas and kwakernaak s and nakamura s are evaluated and a new improved ranking method is suggested

reconstruction of singularities from full scattering data by new estimates of bilinear fourier multipliers we prove that the singularities of a complex valued potential q in the schrodinger hamiltonian q can be reconstructed from the linear born approximation for full scattering data by averaging in the extra variables we prove that with this procedure the accuracy in the reconstruction improves the previously known accuracy obtained from fixed angle or backscattering data in particular for q in w alpha 2 for 0 in 2d we recover the main singularity of q with an accuracy of one derivative in 3d the accuracy is epsilon 1 2 increasing with this gives a mathematical basis for diffraction tomography the proof is based on some new estimates for multidimensional bilinear fourier multipliers of independent interest

multiple weighted estimates for commutators of multilinear singular integrals with non smooth kernels abstract multilinear commutators and iterated commutators generated by the multilinear singular integrals with non smooth kernels and bmo functions are studied by the weighted estimates of a class of new variant maximal operators and the sharp maximal functions the multiple weighted norm inequalities for such operators are obtained in particular some previous results in anh and duong 2010 1 lerner et al 2009 4 perez et al 2011 5 are improved or extended significantly

use of abstract hardy spaces real interpolation and applications to bilinear operators this paper can be considered as the sequel of bernicot and zhao j func anal 255 1761 1796 2008 where the authors have proposed an abstract construction of hardy spaces h1 they shew an interpolation result for these hardy spaces with the lebesgue spaces here we describe a more precise result using the real interpolation theory and we clarify the use of hardy spaces then with the help of the bilinear interpolation theory we then give applications to study bilinear operators on lebesgue spaces these ideas permit us to study singular operators with singularities similar to those of bilinear calderon zygmund operators in a far more abstract framework as in the euclidean case

on multilinear oscillatory integrals nonsingular and singular basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered l p norm inequalities are established for multilinear integral operators of calderon zygmund type which incorporate oscillatory factors e ip where p is a real valued polynomial

regular languages defined with generalized quantifiers we study an extension of first order logic obtained by adjoining quantifiers that count with respect to an integer modulus it is shown that the languages definable in this framework are precisely the regular languages whose syntactic monoids contain only solvable groups we obtain an analogous result for regular languages and establish some connections with complexity theory for fixed depth families of circuits

combining predictions in pairwise classification an optimal adaptive voting strategy and its relation to weighted voting weighted voting is the commonly used strategy for combining predictions in pairwise classification even though it shows good classification performance in practice it is often criticized for lacking a sound theoretical justification in this paper we study the problem of combining predictions within a formal framework of label ranking and under some model assumptions derive a generalized voting strategy in which predictions are properly adapted according to the strengths of the corresponding base classifiers we call this strategy adaptive voting and show that it is optimal in the sense of yielding a map prediction of the class label of a test instance moreover we offer a theoretical justification for weighted voting by showing that it yields a good approximation of the optimal adaptive voting prediction this result is further corroborated by empirical evidence from experiments with real and synthetic data sets showing that even though adaptive voting is sometimes able to achieve consistent improvements weighted voting is in general quite competitive all the more in cases where the aforementioned model assumptions underlying adaptive voting are not met in this sense weighted voting appears to be a more robust aggregation strategy

on calderon s conjecture with constants cfi p1 p2 depending only on fi p1 p2 and p p1p2 p1 p2 hold the flrst result of this type is proved in 4 and the purpose of the current paper is to extend the range of exponents p1 and p2 for which 2 is known in particular the case p1 2 p2 1 is solved to the a rmative this was

uniform estimates for bilinear hilbert transforms and bilinear maximal functions associated to polynomials we study the bilinear hilbert transforms and bilinear maximal functions associated to non flat polynomial curves and obtain uniform l r estimates for r d 1 over d where d is the degree of the polynomial in addition the lower bound of r is sharp up to the end point

managing non homogeneous information in group decision making within the frame of decision aid literature decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines in decision situations with multiple individuals each one has his own knowledge on the alternatives of the decision problem the use of information assessed in different domains is not a seldom situation this non homogeneous information can be represented as values belonging to domains with different nature as linguistic numerical and interval valued or can be values assessed in label sets with different granularity multi granular linguistic information decision processes for solving these problems are composed by two phases aggregation and exploitation the main problem to deal with non homogeneous contexts is how to aggregate the information assessed in these contexts in this paper taking as base the 2 tuple fuzzy linguistic representation model we shall develop an aggregation process for dealing with non homogeneous contexts in first place we shall develop an aggregation process for combining numerical interval valued and linguistic information afterwards we shall propose different extensions of this process to deal with contexts in which can appear other type of information as intuitionistic fuzzy sets or multi granular linguistic information

closure properties of locally finite ω languages locally finite omega languages were introduced by ressayre in journal of symbolic logic volume 53 no 4 p 1009 1026 they generalize omega languages accepted by finite automata or defined by monadic second order sentences we study here closure properties of the family loc omega of locally finite omega languages in particular we show that the class loc omega is neither closed under intersection nor under complementation giving an answer to a question of ressayre

fr3 a fuzzy rule learner for inducing reliable classifiers this paper introduces a fuzzy rule based classification method called fuzzy round robin repeated incremental pruning to produce error reduction ripper fr3 as the name suggests fr3 builds upon the ripper algorithm a state of the art rule learner more specifically in the context of polychotomous classification it uses a fuzzy extension of ripper as a base learner within a round robin scheme and thus can be seen as a fuzzy variant of the r3 learner that has recently been introduced in the literature a key feature of fr3 in comparison with its nonfuzzy counterpart is its ability to represent different facets of uncertainty involved in a classification decision in a more faithful way fr3 thus provides the basis for implementing ldquoreliable classifiersrdquo that may abstain from a decision when not being sure enough or at least indicate that a classification is not fully supported by the empirical evidence at hand besides our experimental results show that fr3 outperforms r3 in terms of classification accuracy and therefore suggest that it produces predictions that are not only more reliable but also more accurate the superb classification performance of fr3 is furthermore confirmed by comparing it to other state of the art fuzzy rule learners

learning valued preference structures for solving classification problems this paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling more specifically our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems one for each ordered pair of classes the corresponding classifiers are trained on the relevant subsets of the transformed original training data in the classification phase a new query is submitted to every binary learner the output of each classifier is interpreted as a fuzzy degree of preference for the first in comparison with the second class by combining the outputs of all classifiers one thus obtains a fuzzy preference relation which is taken as a point of departure for the final classification decision this way the problem of classification is effectively reduced to a problem of decision making based on a fuzzy preference relation corresponding techniques which have been investigated quite intensively in the field of fuzzy set theory hence become amenable to the task of classification in particular by decomposing a preference relation into a strict preference an indifference and an incomparability relation this approach allows one to quantify different types of uncertainty in classification and thereby supports sophisticated classification and postprocessing strategies

applications of finite interval valued hesitant fuzzy preference relations in group decision making the main purpose of this paper is to present the twofold group decision making problem which is a new point of view of the group decision making problem where several experts and criteria can be considered at the same time this problem is based on the study of finitely generated sets and finite interval valued hesitant fuzzy preference relations furthermore the extended weighted voting method which is used in the exploitation phase of a classical group decision making problem is generalized to the twofold case

existential second order logic over strings existential second order logic eso and monadic second order logic mso have attracted much interest in logic and computer science eso is a much expressive logic over successor structures than mso however little was known about the relationship between msoand syntatic fragments of eso we shed light on this issue by completely characterizing this relationship for the prefix classes of eso over strings i e finite successor structures moreover we determine the complexity of model checking over strings for all eso prefix classes let eso q denote the prefix class containing all sentences of the shape r q 4 where r is a list of predicate variables q is a first order predicate qualifier from the prefix set q and 4 is quantifier free we show that eso and eso are the maximal standard eso prefix classes contained in mso thus expressing only regular languages we further prove the following dichotomy theorem an eso prefix class either expresses only regular languages and is thus in mso or it expresses some np complete languages we also give a precise characterization of those eso prefix classes that are equivalent to mso over strings and of the eso prefix classes which are closed under complementation on strings

a class of bilinear multipliers given by littlewood paley decomposition abstract in this paper we study a particular class of bilinear multipliers which are given by littlewood paley decompositions in the first part of the paper we show that if is a bilinear multiplier for p q r 1 p q satisfying the holder s condition 1 p 1 q 1 r and have support inside 0 1 then its periodization j z j is also a bilinear multiplier for the same triplet p q r further we show that for a given triplet p q r of exponents outside the local l 2 range there exists sequence j j z of uniformly bounded bilinear multipliers so that the function j z j is not a bilinear multiplier for the triplet p q r in the second part we describe several results for bilinear multipliers of the type m which are similar to the first part in nature in particular we point out that the results described by p honzik 2014 13 can be generalized to a more general setting

polynomial growth estimates for multilinear singular integral operators on demontre un theoreme pour des mesures de carleson et on l applique a l operateur de kato en dimension 1 on demontre un critere de limitation general on donne une application aux commutateurs de coolderon on etudie les d commutateurs

multilinear interpolation between adjoint operators abstract multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak type estimates a typical situation occurs when one knows that a multilinear operator satisfies a weak l q estimate for a single index q which may be less than one and that all the adjoints of the multilinear operator are of similar nature and thus they also satisfy the same weak l q estimate under this assumption in this note we give a general multilinear interpolation theorem which allows one to obtain strong type boundedness for the operator and all of its adjoints for a large set of exponents the key point in the applications we discuss is that the interpolation theorem can handle the case q 1 when q 1 weak l q has a predual and such strong type boundedness can be easily obtained by duality and multilinear interpolation cf interpolation spaces an introduction springer new york 1976 math ann 319 2001 151 in function spaces and applications lund 1986 lecture notes in mathematics vol 1302 springer berlin new york 1988 j amer math soc 15 2002 469 proc amer math soc 21 1969 441

the bilinear hilbert transform in umd spaces we prove l p bounds for the bilinear hilbert transform acting on functions valued in intermediate umd spaces such bounds were previously unknown for umd spaces that are not banach lattices our proof relies on bounds on embeddings from bochner spaces l p mathbb r x into outer lebesgue spaces on the time frequency scale space mathbb r 3

preference relations on a set of fuzzy utilities as a basis for decision making abstract in fuzzy decision problems we often encounter situations of choosing among alternatives which are assigned fuzzy utilities these problems have been approached using fuzzy implications or direct comparisons among fuzzy utilities in the literature however there are few attempts to investigate the issues addressing reasonable choice or reasonable ordering using fuzzy sets theory this paper first introduces some fundamental properties of fuzzy binary relations and certain conditions of reasonable orderings of fuzzy utilities then a method for constructing a fuzzy preference relation on a given set of fuzzy utilities is proposed for the sake of rational decision making this procedure employs the concepts of the extended minimum and the hamming distance between the greatest upper sets or the greatest lower sets of fuzzy utilities finally it is shown that the proposed fuzzy preference relations have reasonable properties as fuzzy orderings for decision making

some computational aspects of circumscription the effects of circumscribing first order formulas are explored from a computational standpoint first extending work of v lifschitz it is shown that the circumscription of any existential first order formula is equivalent to a first order formula after this it is established that a set of universal horn clauses has a first order circumscription if and only if it is bounded when considered as a logic program thus it is undecidable to tell whether such formulas have first order circumscription finally it is shown that there arefirst order formulas whode circumscription has a conp complete model checking problem

uniform bounds for the bilinear hilbert transforms i it is shown that the bilinear hilbert transforms h f g x p v r f x t g x t dt t map l p1 r l p2 r l p r uniformly in the real parameters when 2 p 1 p 2 oo and 1 p p 1 p 2 p 1 p 2 2 combining this result with the main result in 9 we deduce that the operators h 1 map l 2 r x l r l 2 r uniformly in the real parameter 0 1 this completes a program initiated by a calderon

quantitative estimates and extrapolation for multilinear weight classes in this paper we prove a quantitative multilinear limited range extrapolation theorem which allows us to extrapolate from weighted estimates that include the cases where some of the exponents are infinite this extends the recent extrapolation result of li martell and ombrosi we also obtain vector valued estimates including ell infty spaces and in particular we are able to reprove all the vector valued bounds for the bilinear hilbert transform obtained through the helicoidal method of benea and muscalu moreover our result is quantitative and in particular allows us to extend quantitative estimates obtained from sparse domination in the banach space setting to the quasi banach space setting our proof does not rely on any off diagonal extrapolation results and we develop a multilinear version of the rubio de francia algorithm adapted to the multisublinear hardy littlewood maximal operator as a corollary we obtain multilinear extrapolation results for some upper and lower endpoints estimates in weak type and mathrm bmo spaces

quantifiers and approximation we investigate the relationship between logical expressibility of np optimization problems and their approximation properties first such attempt was made by papadimitrou and yannakakis 1988 who defined the class of npo problems max np we show that many important optimization problems do not belong to max np and that in fact there are problems in p which are not in max np the problems that we consider fit naturally in a new complexity class that we call max 1 we prove that several natural optimization problems are complete for max 1 under approximation preserving reductions all these complete problems are not approximable unless p np this motivates the definition of subclasses of max 1 that only contain problems which are presumably eaiser with respect to approximation in particular the class that we call rmax 2 contains approximable problems and problems like max clique that are not known to be nonapproximable we prove the max clique and several other optimization problems are complete for rmax 2 all the complete problems in rmax 2 share the interesting property that they either are nonapproximable or are approximable to any degree of accuracy

some remarks on multilinear maps and interpolation a multilinear version of the boyd interpolation theorem is proved in the context of quasi normed rearrangement invariant spaces a multilinear marcinkiewicz interpolation theorem is obtained as a corollary several applications are given including estimates for bilinear fractional integrals

generalizations of the carleson hunt theorem i the classical singularity case in this article we prove l p estimates for a general maximal operator which extend both the classical coifman meyer and carleson hunt theorems in harmonic analysis

quasi banach valued inequalities via the helicoidal method abstract we extend the helicoidal method from 1 to the quasi banach context proving in this way multiple banach and quasi banach vector valued inequalities for paraproducts and for the bilinear hilbert transform bht as an immediate application we obtain mixed norm estimates for in the whole range of lebesgue exponents one of the novelties in the quasi banach framework that is when 0 r 1 which we expect to be useful in other contexts as well is the linearization of the operator k t f k g k r 1 r achieved by dualizing its weak l p quasinorms through l r see proposition 8 another important role is played by the sharp evaluation of the operatorial norm t i 0 f 1 f g 1 g 1 h r which is obtained by dualizing the weak l p quasinorms through l with r in the banach case the linearization of the operator and the sharp estimates for the localized operatorial norm can be both achieved through the classical generalized restricted type l 1 dualization

integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations abstract the purpose of this paper is to study a fuzzy multipurpose decision making problem where the information about the alternatives provided by the experts can be of a diverse nature the information can be represented by means of preference orderings utility functions and fuzzy preference relations and our objective is to establish a general model which cover all possible representations firstly we must make the information uniform using fuzzy preference relations as uniform preference context secondly we present some selection processes for multiple preference relations based on the concept of fuzzy majority fuzzy majority is represented by a fuzzy quantifier and applied in the aggregation by means of an owa operator whose weights are calculated by the fuzzy quantifier we use two quantifier guided choice degrees of alternatives a dominance degree used to quantify the dominance that one alternative has over all the others in a fuzzy majority sense and a non dominance degree that generalises orlovski s non dominated alternative concept the application of the two above choice degrees can be carried out according to two different selection processes a sequential selection process and a conjunction selection process

a quadratic programming approach in estimating similarity relations the problem of estimating how similar n objects are when they are compared with each other is investigated using comparative judgments of all possible pairs of the n objects as data the pairwise comparisons focus on the similarity relations instead of the relative importance of each object a quadratic programming model is also proposed it processes the similarity based pairwise comparisons and determines the similarity relations among the n objects the model has linear constraints therefore it can be solved easily by transferring it into a system of linear equations

on commutators of vector bmo functions and multilinear singular integrals with non smooth kernels abstract let t be a bounded multilinear operator on some product of l q r n spaces assume that t has a non smooth associated kernel which satisfies certain weak regularity conditions but not regular enough to fall under the scope of the standard multilinear calderon zygmund theory the main aim of this paper is to establish a sufficient condition on the kernel of t so that the commutator of a vector bmo function b and t is bounded on certain product l p r n spaces we obtain boundedness of the commutator of b and t by first proving certain pointwise estimates on the fefferman stein sharp maximal operator an important example of multilinear operators which satisfy our kernel conditions is the maximal m th order calderon commutator

variational estimates for the bilinear iterated fourier integral abstract we prove pointwise variational l p bounds for a bilinear fourier integral operator in a large but not necessarily sharp range of exponents this result is a joint strengthening of the corresponding bounds for the classical carleson operator the bilinear hilbert transform the variation norm carleson operator and the bi carleson operator terry lyon s rough path theory allows for extension of our result to multilinear estimates we consider our result a proof of concept for a wider array of similar estimates with possible applications to ordinary differential equations

weak and strong type weighted estimates for multilinear calderon zygmund operators abstract in this paper we study the weighted estimates for multilinear calderon zygmund operators from l p 1 w 1 l p m w m to l p v w where 1 p p 1 p m with 1 p 1 1 p m 1 p and w w 1 w m is a multiple a p weight we give weak and strong type weighted estimates of mixed a p a type moreover the strong type weighted estimate is sharp whenever max i p i p m p 1

lipschitz estimates for the commutators of multilinear singular integrals with non smooth kernels this paper is concerned with certain commutators generated by the lipschitz functions and multilinear singular integrals with non smooth kernels some mapping properties for these operators on the lipschitz spaces and triebel lizorkin spaces are obtained

l p estimates for the biest ii the fourier case we prove l p estimates theorem 1 2 for the biest a trilinear multiplier operator with singular symbol the methods used are based on the treatment of the walsh analogue of the biest in the prequel 13 of this paper but with additional technicalities due to the fact that in the fourier model one cannot obtain perfect localization in both space and frequency

the hormander multiplier theorem for multilinear operators in this paper we provide a version of the mikhlin hormander multiplier theorem for multilinear operators in the case where the target space is l p for pe 1 this extends a recent result of tomita 15 who proved an analogous result for p 1

multilinear operators with non smooth kernels and commutators of singular integrals we obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the standard calder6n zygmund kernels as a consequence we deduce endpoint l 1 x l 1 to weak l 1 m estimates for the mth order commutator of calderon our results reproduce known estimates for m 1 2 but are new for m 3 we also explore connections between the 2nd order higher dimensional commutator and the bilinear hilbert transform and deduce some new off diagonal estimates for the former

multilinear calderon zygmund operators with kernels of dini s type and applications abstract the main purpose of this paper is to establish a number of results concerning boundedness of multi linear calderon zygmund operators with kernels of mild regularity let t be a multilinear calderon zygmund operator of type t with being nondecreasing and dini 1 but without assuming to be concave we obtain the end point weak type estimates for multilinear operator t the multiple weighted norm inequalities for multilinear operator t and multilinear commutators of t with b m o functions are also established as applications multiple weighted norm estimates for para products and bilinear pseudo differential operators with mild regularity and their commutators are obtained moreover some boundedness properties of the multilinear operators are also established on variable exponent lebesgue spaces our results improve most of the earlier ones in the literature by removing the assumption of concavity of t and weakening the assumption of dini 1 2 to dini 1

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

relational queries computable in polynomial time we characterize the polynomial time computable queries as those expressible in relational calculus plus a least fixed point operator and a total ordering on the universe we also show that even without the ordering one application of fixed point suffices to express any query expressible with several alternations of fixed point and negation this proves that the fixed point query hierarchy suggested by chandra and harel collapses at the first fixed point level it is also a general result showing that in finite model theory one application of fixed point suffices

multiple weighted norm inequalities for maximal multi linear singular integrals with non smooth kernels we obtain weighted norm inequalities for maximal truncated operators of multi linear singular integrals with non smooth kernels in the sense of duong et al this class of operators extends the class of multi linear calderon zygmund operators introduced by coifman and meyer and includes the higher order commutators of calderon the weighted norm inequalities obtained in this work are with respect to the new class of multiple weights of lerner et al the key ingredient in the proof is the introduction of a new multi sublinear maximal operator that plays the role of the hardy littlewood maximal function in a version of cotlar s inequality as applications of these results new weighted estimates for the m th order calderon commutators and their maximal counterparts are deduced

multi factorial risk assessment the main purpose of this paper is to develop a new method to aggregate the information given by several experts or criteria about different alternatives in order to obtain the preferred alternative or alternatives this method has to take into account the interaction of the different alternatives and a parameter modelling the flexibility of this method has to be introduced more precisely this method uses fuzzy preference relations aggregated by means of weighted ordered weighted averaging aggregation operators wowa for the exploitation phase the extended weighted voting algorithm is introduced and studied in detail finally the goodness of this approach is analyzed using it to combine different points of view people environment assets and reputation impact for the company in the assessment of risk associated with human reliability