shock models with dependence and asymmetric linkages abstract this paper introduces a new class of copulas and shows its relevance for applications in particular a stochastic interpretation in terms of a system of dependence components affected by a global shock is given as a main feature of the model the global shock has an opposite effect on the different components of the system copulas generated by this mechanism are characterized in the bivariate case and their main properties are illustrated connections with concepts like semilinear copulas and conic aggregation functions are also highlighted moreover a high dimensional extension is presented

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

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

convergence of the ruelle operator for a function satisfying bowen s condition we consider a positively expansive local homeomorphism t x x satisfying a weak specification property and study the ruelle operator l phi of a real valued continuous function phi satisfying a property we call bowen s condition we study convergence properties of the iterates l phi n and relate them to the theory of equilibrium states

final solution to the problem of relating a true copula to an imprecise copula abstract in this paper we solve in the negative the problem proposed in this journal montes et al 2015 13 whether an order interval defined by an imprecise copula contains a copula namely if c is a nonempty set of copulas then c inf c c c and c sup c c c are quasi copulas and the pair c c is an imprecise copula according to the definition introduced in the cited paper following the ideas of p boxes we show that there is an imprecise copula a b in this sense such that there is no copula c whatsoever satisfying a c b so it is questionable whether the proposed definition of the imprecise copula is in accordance with the intentions of the initiators our methods may be of independent interest we upgrade the ideas of dibala et al 2016 7 where possibly negative volumes of quasi copulas as defects from being copulas were studied

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

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

multivariate imprecise sklar type theorems abstract the omnipotent instrument for modeling multivariate dependence of random variables in standard probability theory has become copulas discovered by a sklar in 1959 only recently omladic and stopar prove that in the bivariate case an analogous role is played by exactly the same copulas for random variables coming from finitely additive probability spaces one of the main results of this paper is that this is true also in the general multivariate case the extension to n dimensions requires a better understanding of quasi copulas the lattice closure of copulas with respect to the pointwise order we need to develop a new equivalent definition of this notion that should be useful in other applications as well another tool we introduce and seems to be new even in the standard probability approach is multivariate quasi distributions we also expand the coherence theory for quasi copulas and quasi distributions to the multivariate situation finally our main result is a multivariate sklar type theorem in the imprecise setting

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

reflection invariant copulas abstract in the present paper we study the class of all those copulas that are invariant under a special class of transformations called reflections in particular we focus on the special role played by the independence copula within this class for this purpose we introduce a bijective transformation which turns every copula into a reflection invariant copula and enforces a strong geometric property the n fold composition of this transformation to a d dimensional copula coincides with the independence copula on the mesh 0 1 2 n 2 n 1 2 n 1 d it turns out that the independence copula is the unique fixed point of the introduced transformation

transitivity preserving fuzzification schemes for cardinality based similarity measures abstract a family of fuzzification schemes is proposed that can be used to transform cardinality based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe the family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets in particular the fuzzy set intersections are pointwisely generated by frank t norms the fuzzification schemes are applied to a variety of previously studied rational cardinality based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process

a hitchhiker s guide to quasi copulas abstract this paper presents a review of the concept of an n quasi copula starting from the characterization of functions that can be derived from operations on random variables we recall several other characterizations and properties that have been proven in the literature highlighting the differences between the bivariate case and the higher dimensional case additionally we recall several applications of n quasi copulas such as their role in the study of bounds on sets of n copulas we also recall various classes of n quasi copulas that have been studied in the literature finally we present some questions that have not yet been answered in the literature

williams s conjecture is false for reducible subshifts we show that for two subshifts of finite type having exactly two irreducible components strong shift equivalence is not the same as shift equiv alence this refutes the williams conjecture w in the reducible case the irreducible case remains an open problem mathematics research group alabama state university montgomery alabama 36101 this content downloaded from 207 46 13 180 on thu 08 sep 2016 04 22 09 utc all use subject to http about jstor org terms

bell type inequalities for quasi copulas we present all bell type inequalities regarding at most four random events of which not more than two are intersected at the same time reformulating these inequalities in the context of fuzzy probability calculus leads to related inequalities on commutative conjunctors we prove that some of these inequalities hold for quasi copulas or copulas additionally for the important parametric family of frank t norms which are also copulas we identify for each of the inequalities the parameter values for which it is fulfilled thereby completing the results of pykacz and d hooghe

infinite to one codes and markov measures we study the structure of infinite to one continuous codes between subshifts of finite type and the behaviour of markov measures under such codes we show that if an infinite to one code lifts one markov measure to a markov measure then it lifts each markov measure to uncountably many markov measures and the fibre over each markov measure is isomorphic to any other fibre calling such a code markovian we characterize markovian codes through pressure we show that a simple condition on periodic points necessary for the existence of a code between two subshifts of finite type is sufficient to construct a markovian code several classes of markovian codes are studied in the process of proving illustrating and providing contrast to the main results a number of examples and counterexamples are given in particular we give a continuous code between two bernoulli shifts such that the defining vector of the image is not a clustering of the defining vector of the domain

the intersection operation in light of joint observables and bell inequalities in operational probability theory operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs in this paper we first explain the need to extend the concept of the intersection operation in the light of the concept of joint observables then we tried to determine the basic features that characterize any possible definition of the intersection operation furthermore we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories these relations are used first to find a suitable suggestion to define the intersection operation second they are used besides the studies made on bell inequalities in fuzzy probability theory to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of bell inequalities in operational probability theory

additive decomposition of fuzzy pre orders fuzzy pre orders reflexive and min transitive fuzzy relations constitute an important class of fuzzy relations by means of an indifference generator a fuzzy pre order can be decomposed additively into two parts an indifference relation and a strict preference relation when using a frank t norm as indifference generator we fully characterize the transitivity of these parts only in case the minimum operator is used as generator both parts are min transitive the transitivity of the indifference relation is determined by the frank t norms while the transitivity of the strict preference relation is determined by transforms of the nilpotent minimum t norm

on the relationship between modular functions and copulas copulas are nothing else but supermodular functions with absorbing element 0 and neutral element 1 although a copula c cannot be modular on the unit square itself it is effectively so on every rectangle with zero c volume in this paper we show that an appropriate modular function on the unit square can be transformed into a copula by performing a simple truncation operation either from below or above to ensure the compatibility with the frechet hoeffding bounds modular functions on the unit square admit an additive representation in terms of two univariate functions we specifically focus on cases where these univariate functions are sections horizontal vertical diagonal of a given copula ample illustrations are provided

computing degree and class degree abstract let be a factor code from a one dimensional shift of finite type x onto an irreducible sofic shift y if is finite to one then the number of preimages of a typical point in y is an invariant called the degree of in this paper we present an algorithm to compute this invariant the generalized notion of the degree when is not limited to finite to one factor codes is called the class degree of the class degree of a code is defined to be the number of transition classes over a typical point of y and is invariant under topological conjugacy we show that the class degree is computable

the metric entropy of diffeomorphisms soit m une variete de riemann compacte c sans bord soit f un diffeomorphisme c 2 de m et soit m une mesure de probabilite de borel f invariante sur m soit h m f l entropie de f on donne des relations entre h m f et les proprietes geometriques de f et de m

the impact on the properties of the efgm copulas when extending this family abstract several extensions of the family of bivariate eyraud farlie gumbel morgenstern copulas efgm copulas are considered some of them are well known from the literature others have recently been suggested copulas based on quadratic constructions based on some forms of convexity and polynomial copulas for each of these extensions we analyze which properties of efgm copulas are preserved or even improved and which are partly lost such properties can be structural order theoretical or topological in nature or algebraic symmetry or being a polynomial or analytic absolute continuity other examples are forms of convexity quadrant dependence and symmetry with respect to copula transformations the last group of properties considered here is related to some dependence parameters

a full scale sklar s theorem in the imprecise setting abstract in this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal montes et al 2015 13 the main tools we develop in order to do so are 1 a theory on quasi distributions based on an idea presented in a paper by r nelsen with collaborators 2 starting from what is called bivariate p box in the above mentioned paper we propose some new techniques based on what we call restricted bivariate p box and 3 a substantial extension of a theory on coherent imprecise copulas developed by m omladic and n stopar in a previous paper in order to handle coherence of restricted bivariate p boxes a side result of ours of possibly even greater importance is the following every bivariate distribution whether obtained on a usual additive probability space or on an additive space can be obtained as a copula of its margins meaning that its possible extraordinariness depends solely on its margins this might indicate that copulas are a stronger probability concept than probability itself

biconic aggregation functions we introduce a new method to construct aggregation functions these aggregation functions are called biconic aggregation functions with a given diagonal resp opposite diagonal section and their construction is based on linear interpolation on segments connecting the diagonal resp opposite diagonal of the unit square to the points 0 1 and 1 0 resp 0 0 and 1 1 subclasses of biconic aggregation functions such as biconic semi copulas biconic quasi copulas and biconic copulas are studied in detail

class degree and relative maximal entropy given a factor code from a shift of finite type x onto an irreducible sofic shift y and a fully supported ergodic measure on y we give an explicit upper bound on the number of ergodic measures on x which project to and have maximal entropy among all measures in the fiber 1 this bound is invariant under conjugacy we relate this to an important construction for finite to one symbolic factor maps

piecewise linear aggregation functions based on triangulation we introduce a method to construct piecewise linear binary aggregation functions on the unit interval based on a triangulation of the unit square with one additional vertex we derive conditions under which such piecewise linear aggregation functions possess additional interesting properties such as idempotence symmetry lipschitz continuity and 2 monotonicity this construction method can also be used to approximate binary aggregation functions in this way copulas and quasi copulas are approximated by singular copulas

flipping and cyclic shifting of binary aggregation functions we introduce two types of transformations of random variables called flipping and cyclic shifting as these transformations preserve monotonicity at the level of univariate cumulative distribution functions they can be used to develop corresponding coordinate wise transformations of binary aggregation functions we lay bare the admissibility of these transformations i e the necessary and sufficient conditions under which they result in a binary aggregation function we investigate which additional properties such as the 1 lipschitz property and 2 increasingness entail these admissibility conditions moreover we point out which of these properties are preserved under flipping and or cyclic shifting interestingly quasi copulas remain quasi copulas under flipping while copulas remain copulas under flipping as well as under cyclic shifting

quasi copulas and signed measures we study the relationship between multivariate quasi copulas and measures that they may or may not induce on 0 1 n we first study the mass distribution of the pointwise best possible lower bound for the set of n quasi copulas for n 3 as a consequence we show that not every n quasi copula induces a signed measure on 0 1 n

new families of symmetric asymmetric copulas abstract in 2004 rodriguez lallena and ubeda flores have introduced a class of bivariate copulas which generalizes some known families such as the farlie gumbel morgenstern distributions in 2006 dolati and ubeda flores presented multivariate generalizations of this class also they investigated symmetry dependence concepts and measuring the dependence among the components of each classes in this paper a new method of constructing binary copulas is introduced extending the original study of rodriguez lallena and ubeda flores to new families of symmetric asymmetric copulas several properties and parameters of newly introduced copulas are included among others relationship of our construction method with several kinds of ordinal sums of copulas is clarified

flipping of multivariate aggregation functions abstract we consider flipping transformations of multivariate aggregation functions and we investigate the closure of these transformations with respect to the class of aggregation functions with annihilator element equal to 0 moreover the consecutive application of flipping transformations is also discussed the results present interesting connections both with quasi copulas and with suitable modifications of the n increasing property of a multivariate probability distribution function

on the construction of radially symmetric copulas in higher dimensions abstract we prove a representation theorem for copulas that are simultaneously symmetric and radially symmetric we use this representation theorem to propose a method to construct an n ary symmetric function that is radially symmetric starting from an n 1 dimensional copula and an n ary auxiliary function we study the necessary and sufficient conditions on this auxiliary function that guarantee our construction method to result in a symmetric and radially symmetric n dimensional copula we examine several options for defining the auxiliary function in the trivariate case inspired by the nesting of copulas the lifting of copulas and product like extensions for each choice of auxiliary function we provide several examples for different families of copulas

binary survival aggregation functions we introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas a well studied class of binary aggregation functions with a profound probabilistic interpretation to their associated survival copulas the new transformation called double flipping is the composition of two elementary flipping transformations introduced earlier each operating on one of the arguments of the aggregation function we lay bare the relationships between these elementary flipping operations and double flipping we study invariants under these transformations furthermore we characterize the transformations that preserve flippability most importantly we characterize different subclasses of flippable aggregation functions in particular aggregation functions that have an absorbing element or that have a neutral element in this investigation the key role played by quasi copulas and their dual operations is highlighted these findings support the introduction of the term survival aggregation function

relative pressure relative equilibrium states compensation functions and many to one codes between subshifts soit s x x t y y des applications continues d espaces metrisables compacts et soit x y une surjection continue avec t o s t o on etudie la notion de pression relative et on etudie certaines fonctions de pression relative maximales qui s associent aux etats d equilibres relatifs on relie ces idees a la notion de fonction de compensation et on montre qu une fonction de compensation existe toujours quand s et t sont des sous decalages

dependence measures for perturbations of copulas abstract in this paper which is a substantially extended version of a conference paper from agop 2015 we investigate the effects of specific class of perturbations of bivariate copulas on several measures of dependence spearman s rho blomqvist s beta gini s gamma kendall s tau and tail dependence along both diagonal sections it is demonstrated that the influence of the perturbation parameter on the values of the first three of the above coefficients of dependence is linear while on the last one it is quadratic interesting numerical analyses for several important classes of archimedean copulas are presented it is also demonstrated that the considered perturbations do not change the coefficients of tail dependencies along the main diagonal but linearly reduce their values along the second diagonal an interesting possible application for analyzing dependencies along the second diagonal of copulas represent insurance data where censoring introduces a negative dependence between the investigated components of the claims as a by product we present a new class of perturbations of copulas that linearly reduce the more popular coefficients of tail dependencies along the main diagonal while preserving their values along the second diagonal subsequently using suitable elements of both above classes of perturbations any original copula can be transformed to a resulting one having coefficients of tail dependencies along both diagonals linearly reduced with any couple of preselected linear proportions from 0 1

quasimodular forms and jacobi like forms we study various properties of quasimodular forms by using their connections with jacobi like forms such connections are made by identifying quasimodular forms for a discrete subgroup gamma of sl 2 mathbb r with certain polynomials over the ring of holomorphic functions of the poincare upper half plane that are gamma invariant we consider a surjective map from jacobi like forms to quasimodular forms and prove that it has a right inverse which may be regarded as a lifting from quasimodular forms to jacobi like forms