monotonic convergent iterative learning controller design based on interval model conversion this note presents a robust iterative learning controller design method for plants subject to interval model uncertainty in the a matrix of their state space description first order perturbation theory is used to find bounds on the eigenvalues and eigenvectors of the powers of a when a is an interval matrix these bounds are then used for calculation of the interval uncertainty of the markov matrix the bounds on the markov matrix are then used to design an iterative learning controller that ensures monotonic convergence for all systems in the interval plant

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

on lattices with a smallest set of aggregation functions given a bounded lattice l with bounds 0 and 1 it is well known that the set pol 0 1 l of all 0 1 preserving polynomials of l forms a natural subclass of the set c l of aggregation functions on l the main aim of this paper is to characterize all finite lattices l for which these two classes coincide i e when the set c l is as small as possible these lattices are shown to be completely determined by their tolerances also several sufficient purely lattice theoretical conditions are presented in particular all simple relatively complemented lattices or simple lattices for which the join meet of atoms coatoms is 1 0 are of this kind

uninorms on bounded lattices we study uninorms on bounded lattices we show the existence of uninorms with the neutral element which is different from the top element and the bottom element using the fact that the t norms and t conorms on arbitrary lattice l always exist as a by product we give a method of constructing uninorms using this method we obtain also the smallest uninorm and the greatest uninorm with a given neutral element e

aggregation on boolean multi polar space three types of aggregation operators defined on a boolean multi polar space 0 1 m are compared three different monotonicity conditions that yield different types of aggregation operators are discussed and the structure of these aggregation operators on 0 1 m with additional properties of associativity and commutativity is studied for any m n the commutative associative boolean multi polar aggregation operators are shown to coincide with boolean multi polar uninorms the structure of commutative associative sl aggregation operators is shown to be dependent on the structure of the class of abelian idempotent semigroups based on m 1 elements with an annihilator we show that each commutative associative sl aggregation operator with annihilator 0 corresponds to a lower semi lattice with bottom element 0 for m 2 the class of commutative associative c aggregation operators is proved to be equal to the intersection of the class of commutative associative boolean multi polar aggregation operators and the class of commutative associative sl aggregation operators examples of the three types of commutative associative aggregation operators are shown and discussed for m 1 2 3

technical communique pi control of discrete linear repetitive processes abstract repetitive processes are a distinct class of 2d systems i e information propagation in two independent directions of both systems theoretic and applications interest they cannot be controlled by direct extension of existing techniques from either standard termed 1d here or 2d systems theory in this paper we exploit their unique physical structure to show how two term i e proportional plus integral or pi action can be used to control these processes to produce desired behavior as opposed to just stability

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

the notion of weak contradiction definition and measures in this paper we present a way to represent contradiction between fuzzy sets this representation is given in terms of the notion of f weak contradiction unlike other approaches we do not define contradiction just by using one of the relations of f weak contradiction but by considering the whole set of relations this consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets as a result we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties symmetry antitonicity if the intersection is empty then the measure is one and if there is an element in the intersection with degree of membership hbox 1 then the measure is zero

prioritized measure guided aggregation operators this paper mainly investigates a particular type of multicriteria aggregation imperative called prioritized aggregations in order to handle a class of multicriteria decision making problems in which there are prioritizations among criteria in such problems the satisfaction degrees of higher prioritized criteria cannot be compensated by the lower prioritized criteria to describe the prioritizations among criteria quantitatively yager has introduced a prioritized measure from the viewpoint of fuzzy measure which is validated as an effective method except for some little imperfectness on the basis of detailed analysis with respect to yager s prioritized measure we elaborate the properties of prioritized measures and then propose a generalized form of prioritized measure moreover by using the generalized prioritized measure to convey the prioritized imperative we develop a generalized prioritized measure guided aggregation operator that is based on the choquet integral additionally the prioritized weight aggregation operator introduced by yager is verified to be a special case of the generalized prioritized measure guided aggregation operator at length we develop a concrete prioritized measure and the corresponding prioritized measure guided aggregation operator under the framework of the generalized prioritized measure guided aggregation operator and illustrate their feasibility and effectiveness through several numerical examples

description of sup and inf preserving aggregation functions via families of clusters in data tables abstract connection between the theory of aggregation functions and formal concept analysis is discussed and studied thus filling a gap in the literature by building a bridge between these two theories one of them living in the world of data fusion the second one in the area of data mining we show how galois connections can be used to describe an important class of aggregation functions preserving suprema and by duality to describe aggregation functions preserving infima our discovered method gives an elegant and complete description of these classes also possible applications of our results within certain biclustering fuzzy fca based methods are discussed

invariant functionals on completely distributive lattices in this paper we are interested in functionals defined on completely distributive lattices and which are invariant under mappings preserving arbitrary joins and meets we prove that the class of nondecreasing invariant functionals coincides with the class of sugeno integrals associated with 0 1 valued capacities the so called term functionals thus extending previous results both to the infinitary case as well as to the realm of completely distributive lattices furthermore we show that in the case of functionals over complete chains the nondecreasing condition is redundant characterizations of the class of sugeno integrals as well as its superclass comprising all polynomial functionals are provided by showing that the axiomatizations given in terms of homogeneity of their restriction to finitary functionals still hold over completely distributive lattices we also present canonical normal form representations of polynomial functionals on completely distributive lattices which appear as the natural extensions to their finitary counterparts and as a by product we obtain an axiomatization of complete distributivity in the case of bounded lattices

on additive generators of overlap functions in this paper we introduce the notion of additive generator pair for overlap functions we also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair in particular given a continuous and positive t norm t we analyze the overlap functions which are obtained by the distortion of t by a pseudo automorphism showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo automorphism and the additive generator of t finally we also consider the influence of the migrativity homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

unobserved heterogeneity and endogeneity in nonparametric frontier estimation in production theory and eciency analysis rm eciencies are measured by their distances to a production frontier which is the geometrical locus of optimal combinations of inputs and outputs it is today recognized that in the presence of heterogenous conditions like environmental factors that influence the shape and the position of the frontier traditional measures of efficiency obtained in the space of inputs outputs have no sensible economic meaning this is because the benchmark frontier may not be attainable for a firm facing different heterogenous conditions using a nonparametric approach this can be corrected by using conditional frontiers and conditional efficiency scores developed in the literature in this paper we extend these concepts in the case where the heterogeneity is not observed we propose and analyze a model where the heterogeneity variable is linked to a particular input or output it is defined as the part of the input or the output independent from some instrumental variable through a nonseparable nonparametric model we discuss endogeneity issues involved in this model under certain regularity assumptions we show that the model is identified we propose nonparametric estimators of the conditional frontier and the conditional efficiency score and analyze their asymptotic properties when using fdh estimators we prove the asymptotic convergence to a weibull distribution whereas when using the robust order m estimators we obtain the asymptotic normality of the estimators the method is illustrated with some simulated and real data examples a monte carlo experiment shows how the procedure works for finite samples

congruences and the discrete sugeno integrals on bounded distributive lattices we study compatible aggregation functions on a general bounded distributive lattice l where the compatibility is related to the congruences on l as a by product a new proof of an earlier result of g gratzer is obtained moreover our results yield a new characterization of discrete sugeno integrals on bounded distributive lattices

transfer stable means on finite chains abstract according to 5 the arithmetic mean is a function characterized by four features it is non decreasing idempotent symmetric and additive the first three of them can be naturally converted to the theory of posets but the last one generally can not due to this problem we will replace it with another suitable property which is called transfer stability however we do not get the exact arithmetic mean but some approximation these functions will be called transfer stable means the first aim of the paper is to show that transfer stable means on a finite chain form a lattice which is isomorphic to the direct power of a finite chain the second goal is to create a generating set of transfer stable means i e means that can generate all other transfer stable means of the same arity by classical composition of functions the last goal deals with question of how to generate all transfer stable means of any arity by binary transfer stable means only for this problem we define special transfer stable means composition

bimigrativity of binary aggregation functions we introduce the notions of bimigrativity and total bimigrativity of an aggregation function w r t another aggregation function as a natural generalization of the notions of migrativity and bisymmetry we investigate the role of the presence of neutral or absorbing elements we also pay attention to the class of weighted quasi arithmetic means a well known class of bisymmetric aggregation functions

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

binary generating set of the clone of idempotent aggregation functions on bounded lattices abstract in a recent paper botur et al 2018 we have presented a generating set of the clone of idempotent aggregation functions on bounded lattices as the main result we have shown that this clone is generated by certain ternary idempotent functions from which all idempotent aggregation functions of l can be obtained by usual term composition the aim of this paper is to present an essential improvement of the result above by presenting a new generating set of this clone a bit artificial ternary functions are substituted here by natural binary lattice a medians and certain binary characteristic functions consequently the clone is generated by its binary part and the result strengthens the essential role of medians within all idempotent aggregation functions moreover we will show that for an n element lattice l the upper bound of binary generators is 2 n 1

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

on the decomposability of aggregation functions on direct products of posets abstract based on results concerning equivalences on direct products of sets a representation of aggregation functions acting on products of ordered structures by means of aggregation functions acting component wise is obtained and discussed in particular t norms and t conorms on direct products of bounded lattices are considered generalizing some earlier results of de baets and mesiar

comparison meaningful operators and ordinal invariant preferences this work has been partially supported by the research projects eco2012 34828 mtm2012 37894 c02 02 and tin2013 40765 p spain

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

on generating sets of the clone of aggregation functions on finite lattices abstract in a recent paper 12 we have shown that aggregation functions on a bounded lattice l form a clone i e the set of functions closed under projections and composition of functions moreover for any finite lattice l we gave a finite set of unary and binary aggregation functions on l from which the aggregation clone is generated in this paper a general method for constructing generating sets of the aggregation clone on l is presented our approach is based on extending of l valued capacities leading to so called full systems of aggregation functions several full systems on l are presented including singleton ones and their arities are discussed

on the estimation of technical inefficiency in the stochastic frontier production function model abstract the error term in the stochastic frontier model is of the form v u where v is a normal error term representing pure randomness and u is a non negative error term representing technical inefficiency the entire v u is easily estimated for each observation but a previously unsolved problem is how to separate it into its two components v and u this paper suggests a solution to this problem by considering the expected value of u conditional on v u an explicit formula is given for the half normal and exponential cases

on generating of idempotent aggregation functions on finite lattices abstract in a recent paper 9 we proposed the study of aggregation functions on lattices via clone theory approach observing that aggregation functions on lattices just correspond to 0 1 monotone clones as the main result of 9 we have shown that all aggregation functions on a finite lattice l can be obtained as usual composition of lattice operations and certain unary and binary aggregation functions the aim of this paper is to present a generating set for the class of intermediate or equivalently idempotent aggregation functions this set consists of lattice operations and certain ternary idempotent aggregation functions

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

further studies on relaxed stabilization conditions for discrete time two dimension takagi sugeno fuzzy systems this paper investigates the stabilization problem of discrete time two dimension 2 d takagi sugeno t s fuzzy systems based on a novel non parallel distributed compensation non pdc control scheme combined with a new non quadratic lyapunov function less conservative stabilization conditions are developed the proposed non quadratic lyapunov function is homogeneous polynomially parameter dependent on membership functions as the degree of the lyapunov function increases the conservatism of the obtained stabilization conditions is gradually reduced by exploiting the algebraic property of membership functions the stabilization conditions approach to exactness in the sense of convergence compared with the existing methods no slack variables are introduced in control synthesis and hence the same or less conservative results can be obtained with a lower computational cost a numerical example is given to illustrate the effectiveness of the proposed method

environmental factors in frontier estimation a monte carlo analysis we compare three recently developed frontier estimators namely the conditional dea daraio and simar 2005 2007b the latent class sfa greene 2005 orea and kumbhakar 2004 and the stonezd approach johnson and kuosmanen 2011 by means of monte carlo simulation we focus on their ability to identify production frontiers and efficiency rankings in the presence of environmental factors our simulations match features of real life datasets and cover a wide range of scenarios with variations in sample size distribution of noise and inefficiency as well as in distributions intensity and number of environmental variables our results provide insight in the finite sample properties of the estimators while also identifying estimator specific characteristics overall the latent class approach is found to perform best although in many cases stonezd shows a similar performance performance of cdea is most often inferior

the effects of exogenous variables in efficiency measurement a monte carlo study abstract a monte carlo study is conducted to compare the stochastic frontier method and the data envelopment analysis dea method in measuring efficiency in situations where firms are subject to the effects of factors which are beyond managerial control in making efficiency measurements and comparisons one must separate the effects of the environment the exogenous factors and the effects of the productive efficiency there are two basic approaches to account for the effects of exogenous variables 1 an one step procedure which includes the exogenous variables directly in estimating the efficiency measures and 2 a two step procedure which first estimates the relative gross efficiencies using inputs and outputs then analyzes the effects of the exogenous variables on the gross efficiency the results show that the magnitude of exogenous variables does not appear to have any significant effect on the performance of the one step stochastic frontier method as long as the exogenous variables are correctly identified and accounted for however the effects of exogenous variables are significant for the two step approach especially for the dea methods

generators of aggregation functions and fuzzy connectives we show that the class of all aggregation functions on 0 1 can be generated as a composition of infinitary sup operation bigvee acting on sets with cardinality not exceeding mathfrak c b medians mathsf med b b in 0 1 and unary aggregation functions 1 0 1 and 1 a 1 a in 0 1 moreover we show that we cannot relax the cardinality of argument sets for suprema to be countable thus showing a kind of minimality of the introduced generating set as a by product generating sets for fuzzy connectives such as fuzzy unions fuzzy intersections and fuzzy implications are obtained too

optimal bandwidth selection for conditional efficiency measures a data driven approach in productivity analysis an important issue is to detect how external environmental factors exogenous to the production process and not under the control of the producer might in uence the production process and the resulting efficiency of the rms most of the traditional approaches proposed in the literature have serious drawbacks an alternative approach is to describe the production process as being conditioned by a given value of the environmental variables cazals florens and simar 2002 daraio and simar 2005 this de nes conditional efficiency measures where the production set in the input output space may depend on the value of the external variables the statistical properties of nonparametric estimators of these conditional measures are now established jeong park and simar 2008 these involve the estimation of a nonstandard conditional distribution function which requires the speci cation of a smoothing parameter a bandwidth so far only the asymptotic optimal order of this bandwidth has been established this is of little interest for the practitioner in this paper we ll this gap and we propose a data driven technique for selecting this parameter in practice the approach based on a least squares cross validation procedure lscv provides an optimal bandwidth that minimizes an appropriate weighted integrated squared error ise the method is carefully described and exempli ed with some simulated data with univariate and multivariate environmental factors an application on real data performances of mutual funds illustrates how this new optimal method of bandwidth selection works in practice

generators of copulas and aggregation the most applied class of copulas for fitting purposes is undoubtedly the class of archimedean copulas due to their representation by means of single functions of one variable i e by means of additive generators or the corresponding pseudo inverses in this paper we characterize aggregation functions preserving additive generators pseudo inverses of additive generators of archimedean copulas as a by product we obtain an efficient method to construct new additive generators from some given ones

characterization of invariant aggregation operators abstract following the ideas of bartlomiejczyk and drewniak minimal invariant subsets of 0 1 n are investigated an equivalence relation on these subsets is introduced consequently invariant aggregation operators are characterized by means of choquet integral based representation there are exactly 68 binary invariant aggregation operators 4 among them are also continuous further there are 6 self dual invariant binary aggregation operators a recurrent method of constructing invariant aggregation operators for n 2 is proposed restriction of invariant aggregation operators to finite scales is also discussed

a new way to extend t norms t conorms and negations this work presents a method of extending t norms t conorms and fuzzy negations to a lattice valued setting by preserving the largest possible number of properties of these fuzzy connectives which are invariants under homomorphisms further we also apply this method to extend de morgan triples automorphisms and n dimensional t norms

on the clone of aggregation functions on bounded lattices the main aim of this paper is to study aggregation functions on lattices via clone theory approach observing that the aggregation functions on lattices just correspond to 0 1 monotone clones as the main result we show that for any finite n element lattice l there is a set of at most 2 n 2 aggregation functions on l from which the respective clone is generated namely the set of generating aggregation functions consists only of at most n unary functions at most n binary functions and lattice operations and all aggregation functions of l are composed of them by usual term composition moreover our approach works also for infinite lattices such as mostly considered bounded real intervals a b where in contrast to finite case infinite suprema or equivalently a kind of limit process have to be considered

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

on linear approximations of sugeno integrals on bounded distributive lattices this paper aims at extending the study of sugeno integrals on bounded distributive lattices also including several linguistic scales we introduce study and discuss linear approximations of such sugeno integrals the best linear approximations keeping as much information as possible are also characterized our approach significantly reduces the computational complexity which is illustrated by an example too