modeling interaction phenomena using fuzzy measures on the notions of interaction and independence interaction phenomena among elements of a finite set can be modeled by a discrete fuzzy measure the notion of marginal interaction between two elements is at the root of the definition of interaction we first extend this notion by defining that of marginal interaction among pairwise disjoint subsets and we study some of its properties then we generalize the notion of interaction index to pairwise disjoint subsets finally we formalize the intuitive notion of independence and we propose the concept of measure of marginal amount of interaction in order to fill the gap between the notions of interaction and independence

a simplified expression of the shapley function for fuzzy game abstract in this paper a simplified expression of the shapley function for games with fuzzy coalition is proposed which can be regarded as the generalization of shapley functions defined in some particular games with fuzzy coalition the simplified expression of the shapley function is compared with two definitions established by butnariu tsurumi et al a conclusion is drawn that the simplified expression of the shapley function is equivalent to butnariu s definition when characteristic function is a game with proportional values and is equivalent to tsurumi s definition when characteristic function is a game with choquet integral forms furthermore from an angle of interaction between two participation levels the properties of the two games defined by butnariu and tsurumi are respectively studied

the binomial gini inequality indices and the binomial decomposition of welfare functions abstract in the context of social welfare and choquet integration we briefly review on the one hand the generalized gini welfare functions and inequality indices for populations of n 2 individuals and on the other hand the mobius representation framework for choquet integration particularly in the case of k additive symmetric capacities we recall the binomial decomposition of owa functions due to calvo and de baets and we examine it in the restricted context of generalized gini welfare functions with the addition of appropriate s concavity conditions we show that the original expression of the binomial decomposition can be formulated in terms of two equivalent functional bases the binomial gini welfare functions and the atkinson kolm sen aks associated binomial gini inequality indices according to blackorby and donaldson s correspondence formula the binomial gini pairs of welfare functions and inequality indices are described by a parameter j 1 n associated with the distributional judgements involved the j th generalized gini pair focuses on the n j 1 n poorest fraction of the population and is insensitive to income transfers within the complementary richest fraction of the population

on strong invariance principles under dependence assumptions on obtient des principes d invariance forts avec un ordre d approximation o t 1 2 k pour des suites de variables aleatoires dependantes

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

on the set of imputations induced by the k additive core an extension to the classical notion of core is the notion of k additive core that is the set of k additive games which dominate a given game where a k additive game has its mobius transform or harsanyi dividends vanishing for subsets of more than k elements therefore the 1 additive core coincides with the classical core the advantages of the k additive core is that it is never empty once k geq 2 and that it preserves the idea of coalitional rationality however it produces k imputations that is imputations on individuals and coalitions of at most k individuals instead of a classical imputation therefore one needs to derive a classical imputation from a k order imputation by a so called sharing rule the paper investigates what set of imputations the k additive core can produce from a given sharing rule

weighted banzhaf power and interaction indexes through weighted approximations of games the banzhaf power index was introduced in cooperative game theory to measure the real power of players in a game the banzhaf interaction index was then proposed to measure the interaction degree inside coalitions of players it was shown that the power and interaction indexes can be obtained as solutions of a standard least squares approximation problem for pseudo boolean functions considering certain weighted versions of this approximation problem we define a class of weighted interaction indexes that generalize the banzhaf interaction index we show that these indexes define a subclass of the family of probabilistic interaction indexes and study their most important properties finally we give an interpretation of the banzhaf and shapley interaction indexes as centers of mass of this subclass of interaction indexes

on path correlation and pert bias most studies of project time estimation assume that a activity times are mutually independent random variables many also assume that b path completion times are mutually independent in this paper we subject the impact of both these assumptions to close scrutiny using tools from multivariate analysis we make a theoretical study of the direction of the error in the classical pert method of estimating mean project completion time when correlation is ignored we also investigate the effect of activity dependence on the normality of path length via simulation

on the structure of some families of fuzzy measures the generation of fuzzy measures is an important question arising in the practical use of these operators in this paper we deal with the problem of developing a random generator of fuzzy measures more concretely we study some of the properties that any random generator should satisfy these properties lead to some theoretical problems concerning the group of isometries that we tackle in this paper for some subfamilies of fuzzy measures

determination of weights of interacting criteria from a reference set abstract in this paper we present a model allowing to determine the weights related to interacting criteria this is done on the basis of the knowledge of a partial ranking over a reference set of alternatives prototypes a partial ranking over the set of criteria and a partial ranking over the set of interactions between pairs of criteria

k maxitive fuzzy measures a scalable approach to model interactions abstract fuzzy measures are powerful at modeling interactions between elements unfortunately they use a number of coefficients that exponentially grows with the number of elements beyond the computational complexity assigning a value to any coalition of a large set of elements does not make sense k order measures model interactions involving at most k elements the number of coefficients to identify is reduced and their modeling capacity is preserved in real problems where the number of interacting elements is limited in extreme situations of full redundancy or complementariness it is mathematically proven that the complete fuzzy measure is both k additive and k maxitive a learning algorithm to identify k maxitive measures from labeled data is designed on the basis of hlms heuristic least mean squares in a classification context the study of synthetic data with partial redundancy or complementariness supports the idea that the difference between full and partial interaction is a matter of degree not of kind dealing with two real world datasets a comparison of the complete fuzzy measure and a k maxitive one shows the number of interacting elements is limited and the k maxitive measures yield the same characterization of interactions and a comparable classification accuracy

strong invariance principles for dependent random variables we establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds applications to linear and some nonlinear processes are discussed strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions

the combination of evidence in the transferable belief model a description of the transferable belief model which is used to quantify degrees of belief based on belief functions is given the impact of open and closed world assumption on conditioning is discussed the nature of the frame of discernment on which a degree of belief will be established is discussed a set of axioms justifying dempster s rule for the combination of belief functions induced by two distinct evidences is presented

on the extension of pseudo boolean functions for the aggregation of interacting criteria abstract the paper presents an analysis on the use of integrals defined for non additive measures or capacities as the choquet and the sipos integral and the multilinear model all seen as extensions of pseudo boolean functions and used as a means to model interaction between criteria in a multicriteria decision making problem the emphasis is put on the use besides classical comparative information of information about difference of attractiveness between acts and on the existence for each point of view of a neutral level allowing to introduce the absolute notion of attractive or repulsive act it is shown that in this case the sipos integral is a suitable solution although not unique properties of the sipos integral as a new way of aggregating criteria are shown with emphasis on the interaction among criteria

central limit theorem for fourier transforms of stationary processes we consider asymptotic behavior of fourier transforms of stationary ergodic sequences with finite second moments we establish a central limit theorem clt for almost all frequencies and also an annealed clt the theorems hold for all regular sequences our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram and it provides a nice blend of harmonic analysis theory of stationary processes and theory of martingales

k intolerant capacities and choquet integrals we define an aggregation function to be at most k intolerant if it is bounded from above by its kth lowest input value applying this definition to the discrete choquet integral and its underlying capacity we introduce the concept of k intolerant capacities which when varying k from 1 to n cover all the possible capacities on n objects just as the concepts of k additive capacities and p symmetric capacities have been previously introduced essentially to overcome the problem of computational complexity of capacities k intolerant capacities are proposed here for the same purpose but also for dealing with intolerant or tolerant behaviors of aggregation we also introduce axiomatically indices to appraise the extent to which a given capacity is k intolerant and we apply them on a particular recruiting problem

conditional belief functions as lower envelopes of conditional probabilities in a finite setting the aim is to provide a characterization of full conditional measures on a finite boolean algebra obtained as lower envelope of the extensions of a full conditional probability defined on another finite boolean algebra such conditional measures are conditional belief functions defined by means of a generalized bayesian conditioning rule relying on a linearly ordered class of belief functions this notion of bayesian conditioning for belief functions is compared with other well known conditioning rules by looking for those conditional measures that can be seen as lower conditional probabilities

families of relations modelling preferences under incomplete information abstract let us consider a preferential information of type preference indifference incomparability p i j with additional information about differences in attractiveness between pairs of alternatives the present paper offers a theoretical framework for the study of the level of constraint of this kind of partial preferential information it suggests a number of structures as potential models being less demanding than the classical one in which differences in utilities can be used to represent the comparison of differences in attractiveness the models are characterized in the more general context of families of non complete preference structures according to two different perspectives called semantico numerical and matrix both perspectives open the door to further practical applications connected with elicitation of the preferences of a decision maker

parameter identifiability of nonlinear systems the role of initial conditions identifiability is a fundamental prerequisite for model identification it concerns uniqueness of the model parameters determined from the input output data under ideal conditions of noise free observations and error free model structure in the late 1980s concepts of differential algebra have been introduced in control and system theory recently differential algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations these methods all exploit the characteristic set of the differential ideal generated by the polynomials defining the system in this paper it will be shown that the identifiability test procedures based on differential algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions in particular when the system is not accessible from the given initial conditions the ideal i having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution in this case a new ideal that includes all differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated an identifiability test is proposed which works under certain technical hypothesis also for systems with specific initial conditions

assessing non additive utility for multicriteria decision aid abstract in the framework of multi attribute utility theory maut several methods have been proposed to build a decision maker s dm utility function representing his her preferences among such methods the uta method infers an additive utility function from a set of exemplary decisions using linear programming however the uta method does not guarantee to find a utility function which is coherent with the available information this drawback is due to the underlying utility model of uta viz the additive one which does not allow to include additional information such as an interaction among criteria in this paper we present a methodology for building a non additive utility function in the framework of the so called fuzzy integrals which permits to model preference structures with interaction between criteria like in the uta method we aim at searching a utility function representing the dm s preferences but unlike uta the functional form is a specific fuzzy integral choquet integral as a result we obtain weights which can be interpreted as the importance of coalitions of criteria exploiting the potential interaction between criteria as already proposed by other authors however within the same framework we obtain also the marginal utility functions relative to each one of the considered criteria that are evaluated on a common scale as a consequence of the implemented methodology finally we illustrate our approach with an example

central limit theorem for stationary linear processes we establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in mcleish ann probab 5 1977 616 621 and motivated by gordin soviet math dokl 10 1969 1174 1176 in doing so we shall preserve the generality of the coefficients including the long range dependence case and we shall express the variance of partial sums in a form easy to apply ergodicity is not required

practical identifiability analysis of large environmental simulation models large environmental simulation models are usually overparameterized with respect to given sets of observations this results in poorly identifiable or nonidentifiable model parameters for small models plots of sensitivity functions have proven to be useful for the analysis of parameter identifiability for models with many parameters however near linear dependence of sensitivity functions can no longer be assessed graphically in this paper a systematic approach for tackling the parameter identifiability problem of large models based on local sensitivity analysis is presented the calculation of two identifiability measures that are easy to handle and interpret is suggested the first accounts for the sensitivity of model results to single parameters and the second accounts for the degree of near linear dependence of sensitivity functions of parameter subsets it is shown how these measures provide identifiability diagnosis for parameter subsets how they are able to guide the selection of identifiable parameter subsets for parameter estimation and how they facilitate the interpretation of the correlation matrix of the parameter estimate with respect to parameter identifiability in addition we show how potential bias of the parameter estimates due to a priori fixing of some of the parameters can be analyzed finally two case studies are presented in order to illustrate the suggested approach

identifiability of homogeneous systems using the state isomorphism approach new results are presented concerning the state isomorphism approach to global identifiability analysis of parameterized classes of nonlinear state space systems with specified initial states in particular we study the class of homogeneous systems for which under certain conditions the local state isomorphism for a pair of indistinguishable parameter vectors is shown to be homogeneous of degree one for homogeneous polynomial systems conditions are given under which the local state isomorphism becomes linear here the issue of whether or not the observability rank condition holds at the origin is shown to be of key importance the scope of the results which extend to the multivariable case is discussed and illustrated by a number of worked examples this demonstrates how the developed theory can be put to use to investigate the global identifiability properties of parameterized model classes

random generation of k interactive capacities abstract the theory of capacities provides powerful formal methodology to account for criteria dependencies in multiple criteria decision problems the discrete choquet and sugeno integrals aggregate criteria valuations accounting for criteria synergies and redundancies we address an important problem of randomly generating capacities of special classes for simulation studies and for capacity learning through evolutionary algorithms we discuss two efficient methods suitable for k interactive capacities the results are supported by the extensive numerical evidence and provide a useful tool for large scale simulations

uniformly root n consistent density estimators for weakly dependent invertible linear processes convergence rates of kernel density estimators for stationary time series are well studied for invertible linear processes we construct a new density estimator that converges in the supremum norm at the better parametric rate n 1 2 our estimator is a convolution of two different residual based kernel estimators we obtain in particular convergence rates for such residual based kernel estimators these results are of independent interest

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

learning k maxitive fuzzy measures from data by mixed integer programming abstract fuzzy measures model interactions between the inputs in aggregation problems their complexity grows exponentially with the dimensionality of the problem and elicitation of fuzzy measure coefficients either from domain experts or from empirical data poses a significant challenge the notions of k additivity and k maxitivity simplify the fuzzy measures by limiting interactions to subsets of up to k elements learning fuzzy measures from data is an important elicitation technique which relies on solving an optimisation problem a heuristic learning algorithm to identify k maxitive fuzzy measures from the data on the basis of hlms heuristic least mean squares was recently presented in murillo et al 2017 11 we present an alternative formulation of the fitting problem which delivers a globally optimal solution through the solution of a mixed integer programming mip problem to deal with high computational cost of mip in moderate to large dimensions we also propose a simple mip relaxation technique which involves solving two related linear programming problems we also provide a linear programming formulation for fitting k tolerant fuzzy measures we discuss implementations of the fitting methods and present the results of numerical experiments

k balanced games and capacities in this paper we present a generalization of the concept of balanced game for finite games balanced games are those having a nonempty core and this core is usually considered as the solution of the game based on the concept of k additivity we define the so called k balanced games and the corresponding generalization of core the k additive core whose elements are not directly imputations but k additive games we show that any game is k balanced for a suitable choice of k so that the corresponding k additive core is not empty for the games in the k additive core we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion moreover we look for necessary and sufficient conditions for a game to be k balanced for the general case it is shown that any game is either balanced or 2 balanced finally we treat the special case of capacities

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

necessary and sufficient conditions for the conditional central limit theorem following lindeberg s approach we obtain a new condition for a stationary sequence of square integrable and real valued random variables to satisfy the central limit theorem in the adapted case this condition is weaker than any projective criterion derived from gordin s theorem dokl akad nauk sssr 188 1969 739 741 about approximating martingales moreover our criterion is equivalent to the conditional central limit theorem which implies stable convergence in the sense of renyi to a mixture of normal distributions we also establish functional and triangular versions of this theorem from these general results we derive sufficient conditions which are easier to verify and may be compared to other results in the literature to be complete we present an application to kernel density estimators for some classes of discrete time processes

clt in functional linear regression models we propose in this work to derive a clt in the functional linear regression model the main difficulty is due to the fact that estimation of the functional parameter leads to a kind of ill posed inverse problem we consider estimators that belong to a large class of regularizing methods and we first show that contrary to the multivariate case it is not possible to state a clt in the topology of the considered functional space however we show that we can get a clt for the weak topology under mild hypotheses and in particular without assuming any strong assumptions on the decay of the eigenvalues of the covariance operator rates of convergence depend on the smoothness of the functional coefficient and on the point in which the prediction is made

k additivity and c decomposability of bi capacities and its integral k additivity is a convenient way to have less complex bi capacities this paper gives a new characterization of k additivity introduced by grabisch and labreuche of bi capacities and contrasts between the existing characterization and the new one that differs from the one of saminger and mesiar besides in the same way for capacities a concept of c decomposability distinct from the proposal of saminger and mesiar but closely linked to k additivity is introduced for bi capacities moreover the concept of c decomposability applies to the choquet integral with respect to bi capacities

on policy capturing with fuzzy measures policy capturing methods generally apply linear regression analysis to model human judgment in this paper we examine the application of fuzzy set and fuzzy measure theories to obtain subjective descriptions of cue importance for policy capturing at the heart of the approach is a method of learning fuzzy measures the shapley values associated with the fuzzy measures provide a basis for comparison with the results of linear regression however the fuzzy measure theoretical approach provides additional insight into interaction effects corresponding to the nonlinear noncompensatory nature of the underlying decision model to illustrate the methodology we estimated the importance of factors and the interactions among them that influence decisions related to strategic investments in telecommunications infrastructure and compared the results from the fuzzy approach to those obtained from traditional statistical methods

limit theory for panel data models with cross sectional dependence and sequential exogeneity abstract the paper derives a general central limit theorem clt and asymptotic distributions for sample moments related to panel data models with large n the results allow for the data to be cross sectionally dependent while at the same time allowing the regressors to be only sequentially rather than strictly exogenous the setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and or from the presence of common factors the latter leads to the need for random norming the limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied we prove such a central limit theorem by first extending results for stable convergence in hall and heyde 1980 to non nested martingale arrays relevant for our applications we illustrate our result by establishing a generalized estimation theory for gmm estimators of a fixed effect panel model without imposing i i d or strict exogeneity conditions we also discuss a class of maximum likelihood ml estimators that can be analyzed using our clt

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

learning choquet integral based metrics for semisupervised clustering we consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering we investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete choquet integral suitable for defining a metric as a byproduct we can obtain the analogous conditions for the ordered weighted averaging owa operators which constitute a special case we then generalize these results for power based choquet and owa operators we show that this metric learning problem can be formulated as a linear programming problem and specify the required sets of linear constraints we present the results of numerical experiments on artificial and real world datasets which illustrate the potential usefulness and limitations of this construction

combinatorial structure of the polytope of 2 additive measures in this article we study the polytope of 2 additive measures an important subpolytope of the polytope of fuzzy measures for this polytope we obtain its combinatorial structure namely the adjacency structure and the structure of two dimensional faces three dimensional faces and so on based on this information we build a triangulation of this polytope satisfying that all simplices in the triangulation have the same volume as a consequence this allows a very simple and appealing way to generate points in a random way in this polytope an interesting problem arising in the practical identification of 2 additive measures finally we also derive the volume and the centroid of this polytope

an axiomatic approach of the discrete choquet integral as a tool to aggregate interacting criteria the most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean however in many problems the criteria considered interact and a substitute to the weighted arithmetic mean has to be adopted we show that under rather natural conditions the discrete choquet integral is an adequate aggregation operator that extends the weighted arithmetic mean by taking into consideration of the interaction among criteria the axiomatic that supports the choquet integral is presented and an intuitive approach is proposed as well

non additive robust ordinal regression a multiple criteria decision model based on the choquet integral abstract within the multicriteria aggregation disaggregation framework ordinal regression aims at inducing the parameters of a decision model for example those of a utility function which have to represent some holistic preference comparisons of a decision maker dm usually among the many utility functions representing the dm s preference information only one utility function is selected since such a choice is arbitrary to some extent recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the dm s preference information until now robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence in this paper we propose a non additive robust ordinal regression on a set of alternatives a whose utility is evaluated in terms of the choquet integral which permits to represent the interaction among criteria modelled by the fuzzy measures parameterizing our approach in our methodology besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives a a the dm is also requested to express the intensity of preference on pairs of alternatives from a and to supply pairwise comparisons on the importance of criteria and the sign and intensity of interaction among pairs of criteria the output of our approach defines a set of fuzzy measures capacities such that the corresponding choquet integral is compatible with the dm s preference information moreover using linear programming our decision model establishes two preference relations for any a b a the necessary weak preference relation if for all compatible fuzzy measures the utility of a is not smaller than the utility of b and the possible weak preference relation if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b

the choquet integral for the aggregation of interval scales in multicriteria decision making this paper addresses the question of which models fit with information concerning the preferences of the decision maker over each attribute and his preferences about aggregation of criteria interacting criteria we show that the conditions induced by these information plus some intuitive conditions lead to a unique possible aggregation operator the choquet integral

robust optimization of the choquet integral we study the problem of the choquet integral maximization for the case when preferences of the decision maker do not define a unique capacity but rather some convex set we introduce a robust version of the problem based on the minimax regret criterion and construct a global optimization algorithm it is shown that the decision rule based on regret minimization over a set of capacities is equivalent to maximization of the choquet integral with respect to a certain capacity belonging to this set we compare our method to various capacity identification approaches developed in the literature and provide a semantic interpretation in terms of information value

on the polytope of non additive measures in this paper we deal with the problem of studying the structure of the polytope of non additive measures for finite referential sets we give a necessary and sufficient condition for two extreme points of this polytope to be adjacent we also show that it is possible to find out in polynomial time whether two vertices are adjacent these results can be extended to the polytope given by the convex hull of monotone boolean functions we also give some results about the facets and edges of the polytope of non additive measures we prove that the diameter of the polytope is 3 for referentials of three elements or more finally we show that the polytope is combinatorial and study the corresponding properties more concretely we show that the graph of non additive measures is hamilton connected if the cardinality of the referential set is not 2

limits of variance based sensitivity analysis for non identifiability testing in high dimensional dynamic models in systems biology a common approach to model biological processes is to use large systems of nonlinear differential equations the associated parameter estimation problem then requires a prior handling of the global identifiability question in a realistic experimental framework the lack of a method able to solve this issue has indirectly encouraged the use of global sensitivity analysis to select the subset of parameters to estimate nevertheless the links between these two global analyses are not yet fully explored the present work reveals new bridges between sensitivity analyses and global non identifiability through the use of functions derived from the sobol high dimensional representation of the model output we particularly specify limits of variance based sensitivity tools to completely conclude on global non identifiability of parameters in a given experimental context

applying young diagrams to 2 symmetric fuzzy measures with an application to general fuzzy measures abstract in this paper we apply young diagrams a well known object appearing in combinatorics and group representation theory to study some properties of the polytope of 2 symmetric fuzzy measures with respect to a given partition a subpolytope of the set of fuzzy measures the main result in the paper allows to build a simple and fast algorithm for generating points on this polytope in a random fashion besides we also study some other properties of this polytope as for example its volume in the last section we give an application of this result to the problem of identification of general fuzzy measures

a characterization of the 2 additive choquet integral through cardinal information in the context of multiple criteria decision analysis we present the necessary and sufficient conditions to represent a cardinal preferential information by the choquet integral w r t a 2 additive capacity these conditions are based on some complex cycles called cyclones

inconsistency and non additive capacities the analytic hierarchy process in the framework of choquet integration we examine the ahp in the framework of choquet integration and we propose an extension of the standard ahp aggregation scheme on the basis of the shapley values associated with the criteria in our model a measure of dominance inconsistency between criteria is defined in terms of the totally inconsistent matrix associated with the main pairwise comparison matrix of the ahp the measure of dominance inconsistency is then used to construct a non additive capacity whose associated shapley values reduce to the standard ahp priority weights in the consistency case in the general inconsistency case however the extended aggregation scheme based on the shapley weighted mean tends to attenuate resp emphasize the priority weights of the criteria with higher resp lower average dominance inconsistency with respect to the other criteria

extreme points of some families of non additive measures non additive measures are a valuable tool to model many different problems arising in real situations however two important difficulties appear in their practical use the complexity of the measures and their identification from sample data for the first problem additional conditions are imposed leading to different subfamilies of non additive measures related to the second point in this paper we study the set of vertices of some families of non additive measures namely k additive measures and p symmetric measures these extreme points are necessary in order to properly apply a new method of identification of non additive measures based on genetic algorithms whose cross over operator is the convex combination we solve the problem through techniques of linear programming

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

a noncommutative extended de finetti theorem abstract the extended de finetti theorem characterizes exchangeable infinite sequences of random variables as conditionally i i d and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability our main result is a noncommutative version of this theorem in contrast to the classical result of ryll nardzewski exchangeability turns out to be stronger than spreadability for infinite sequences of noncommutative random variables out of our investigations emerges noncommutative conditional independence in terms of a von neumann algebraic structure closely related to popa s notion of commuting squares and kummerer s generalized bernoulli shifts our main result is applicable to classical probability quantum probability in particular free probability braid group representations and jones subfactors

k maxitive aggregation functions abstract inspired by the idea of k maxitive measures we introduce and study k maxitive aggregation functions in particular 1 maxitive aggregation functions are shown to be just maxitive aggregation functions i e maxima of distorted inputs we introduce among others a representation of symmetric k maxitive aggregation functions moreover we show that for any k maxitive capacity and the smallest universal integral based on an arbitrary fixed semicopula including the sugeno and shilkret integrals the resulting aggregation function is k maxitive

complex structured decision making model a hierarchical frame work for complex structured data we introduce a hierarchical framework we call complex structured decision making model for complexly structured knowledge representation in intelligent decision making we show that our model extends non hierarchical flat decision making models to hierarchical decision making models that are similar to comprehensible human decision making processes further we make an argument that hierarchial representation of knowledge in a complex structured decision making model simplifies the approximation of aggregation functions to easily adapt to the underline relation of the system additionally using a real world complex structured data set we show that hierarchically organized fuzzy integrals e g choquet integral and sugeno integral and fuzzy signatures outperform these non hierarchical fuzzy integrals

determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective abstract we consider multiple criteria decision aiding mcda in the case of interactions between criteria in dealing with interactions between criteria fuzzy measures and integrals have demonstrated great advantages nevertheless the determination of fuzzy measures has proven difficult because the capacities of not only single criterion but also all subsets of criteria need to be identified due to the value judgment essence of mcda the attitudes of the decision maker dm are typically modeled to identify fuzzy measures in this paper the tolerance attitudes of the dm which implies a direct requirement instead of partial preference are modeled with regard to the determination of fuzzy measures for the first time with two scales developed in this paper the dm can directly express the tolerance attitudes to certain criteria other than providing partial preference through pairwise comparison as a result it requires less prior knowledge and is more efficient to some extent further the inherent interacting mechanism of criteria under different tolerance attitudes is explored at last the tolerance attitudes are applied to the process of multiple criteria analysis using a choquet integral a classic student evaluation problem is given as an example the evaluation results are compared with additive models this paper not only provides a new inspiration to the determination of fuzzy measures but also improves the descriptive capacity of fuzzy measures to the real world