a monte carlo based method for the estimation of lower and upper probabilities of events using infinite random sets of indexable type random set theory is a useful tool to quantify lower and upper bounds on the probability of the occurrence of events given uncertain information represented for example by possibility distributions probability boxes or dempster shafer structures among others in this paper it is shown that the belief and plausibility estimated by dempster shafer evidence theory are basically approximations by riemann stieltjes sums of the integrals of the lower and upper probability employed when using infinite random sets of indexable type in addition it is shown that the evaluation of the lower and upper probability is more efficient if it is done by pseudo monte carlo strategies this discourages the use of dempster shafer evidence theory and suggests the use of infinite random sets of indexable type specially in high dimensions not only because the initial discretization step of the basic variables is not required anymore but also because the evaluation of the lower and upper probability of events is much more efficient using the different techniques for multidimensional integration like monte carlo simulation

spectral variation bounds in hyperbolic geometry abstract we derive new estimates for distances between optimal matchings of eigenvalues of non normal matrices in terms of the norm of their difference we introduce and estimate a hyperbolic metric analogue of the classical spectral variation distance the result yields a qualitatively new and simple characterization of the localization of eigenvalues our bound improves on the best classical spectral variation bounds due to krause if the distance of matrices is sufficiently small and is sharp for asymptotically large matrices our approach is based on the theory of model operators which provides us with strong resolvent estimates the latter naturally lead to a chebyshev type interpolation problem with finite blaschke products which can be solved explicitly and gives stronger bounds than the classical chebyshev interpolation with polynomials as compared to the classical approach our method does not rely on hadamard s inequality and immediately generalizes to algebraic operators on hilbert space

threshold effect with stochastic fluctuation in bacteria colony like proliferation dynamics as analyzed through a comparative study of reaction diffusion equations and cellular automata we report a comparative study on pattern formation between the methods of cellular automata ca and reaction diffusion equations rd applying to a morphology of bacterial colony formation to do so we began the study with setting an extremely simple model which was designed to realize autocatalytic proliferation of bacteria denoted as x fed with nutrition n and their inactive state prespore state p1 due to starvation x n 2x and x p1 respectively it was found numerically that while the ca could successfully generate rich patterns ranging from the circular fat structure to the viscous finger like complicated one the naive rd reproduced only the circular pattern but failed to give a finger structure augmenting the rd equations by adding two physical factors i a threshold effect in the dynamics of x n 2x breaking the continuity limit of rd and ii internal noise with onset threshold breaking the inherent symmetry of rd we have found that the viscous finger like realistic patterns are indeed recovered by thus modified rd this highlights the important difference between ca and rd and at the same time clarifies the necessary factors for the complicated patterns to emerge in such a surprisingly simple model system

decompositions and range for additive fuzzy measures the aim of the present paper is to prove the existence of hahn and lebesgue decompositions for additive fuzzy measures in the sense of 3 it is shown that the radon nikodym theorem can be carried over from classical measures to additive fuzzy measures with their corresponding integrals these results are applied to obtain a generalization of liapounoff s convexity theorem 12 whose utility in the theory of fuzzy games is argued in the last section

spectral resolutions in dedekind σ complete l groups abstract using recent results on a generalized form of the loomis sikorski theorem a dvurecenskij loomis sikorski theorem for complete mv algebras and l groups j austral math soc ser a 68 2000 261 277 d mundici tensor product and the loomis sikorski theorem for mv algebras adv appl math 22 1999 227 248 it is shown that a unital dedekind complete l group is a compatible rickart comgroup in the sense of d j foulis d j foulis spectral resolutions in a rickart comgroup rep math phys 54 2004 229 250 in particular elements in unital dedekind complete l groups and consequently elements in mv algebras admit uniquely defined spectral resolutions similar to spectral resolutions of self adjoint operators a functional calculus and spectra of elements are considered in relation with the loomis sikorski representation by functions

infinite dimensional features of matrices and pseudospectra abstract given a hilbert space operator t the level sets of function t z t z 1 1 determine the so called pseudospectra of t we set t to be zero on the spectrum of t after giving some elementary properties of t which as it seems were not noticed before we apply them to the study of the approximation we prove that for any operator t there is a sequence t n of finite matrices such that t n z tends to t z uniformly on c in this proof quasitriangular operators play a special role this is merely an existence result we do not give a concrete construction of this sequence of matrices one of our main points is to show how to use infinite dimensional operator models in order to produce examples and counterexamples in the set of finite matrices of large size in particular we get a result which means in a sense that the pseudospectrum of a nilpotent matrix can be anything one can imagine we also study the norms of the multipliers in the context of cowen douglas class operators we use these results to show that to the opposite to the function s the function s z for certain finite matrices s may oscillate arbitrarily fast even far away from the spectrum

bounds for the variation of the roots of a polynomial and the eigenvalues of a matrix we derive some new bounds for the distance between the roots of two polynomials in terms of their coefficients and for the distance between the eigenvalues of two matrices in terms of the norm of their difference

on generalized versions of central limit theorems for if events if sets were introduced by atanassov to model imprecision which can be often met in real world applications if sets were also used for definition of if events for which probability theories were considered including if probability theory and m probability theory within these theories if observables and m observables were introduced and their properties have been studied in this paper we consider limit behavior of the row sums of triangular arrays of independent if observables and m observables we prove generalized versions of the central limit theorem clt for short for both types of observables i e the lindeberg clt and the lyapounov clt furthermore we prove the feller theorem for null arrays of if observables and m observables finally we illustrate our theoretical results by examples

discreteness induced stochastic steady state in reaction diffusion systems self consistent analysis and stochastic simulations abstract a self consistent equation to derive a discreteness induced stochastic steady state is presented for reaction diffusion systems for this formalism we use the so called kuramoto length a typical distance over which a molecule diffuses in its lifetime as was originally introduced to determine if local fluctuations influence globally the whole system we show that this kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not if the number of molecules of a certain species within the kuramoto length is small and discrete localization of some other chemicals is brought about which can accelerate certain reactions when this acceleration influences the concentration of the original molecule species it is shown that a novel stochastic steady state is induced that does not appear in the continuum limit a theory to obtain and characterize this state is introduced based on the self consistent equation for chemical concentrations this stochastic steady state is confirmed by numerical simulations on a certain reaction model which agrees well with the theoretical estimation formation and coexistence of domains with different stochastic states are also reported which is maintained by the discreteness relevance of our result to intracellular reactions is briefly discussed

a connection between a system of random walks and rumor transmission abstract we establish a relationship between the phenomenon of rumor transmission on a population and a probabilistic model of interacting particles on the complete graph more precisely we consider variations of the maki thompson epidemic model and the frog model of random walks which were introduced in the scientific literature independently and in different contexts we analyze the markov chains which describe these models and show a coupling between them our connection shows how the propagation of a rumor in a closed homogeneously mixing population can be described by a system of random walks on the complete graph additionally we discuss further applications of the random walk model which are relevant to the modeling of different biological dynamics

on condition numbers of polynomial eigenvalue problems in this paper we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients generalizing classical results of matrix perturbation theory we provide a relation between the condition numbers of eigenvalues and the pseudospectral growth rate we obtain that if a simple eigenvalue of a matrix polynomial is ill conditioned in some respects then it is close to be multiple and we construct an upper bound for this distance measured in the euclidean norm we also derive a new expression for the condition number of a simple eigenvalue which does not involve eigenvectors moreover an elsner like perturbation bound for matrix polynomials is presented

resolvent bounds and spectral variation abstract a new spectral variation bound is given for linear operators acting on normed linear spaces this bound is derived using the cayley hamilton theorem and chebychev polynomials

fuzzy probability measures abstract in 4 hohle has defined fuzzy measures on g fuzzy sets 2 where g stands for a regular boolean algebra consequently since the unit interval is not complemented fuzzy sets in the sense of zadeh 8 do not fit in this framework in a straightforward manner it is the purpose of this paper to continue the work started in 5 which deals with 0 1 fuzzy sets and to give a natural definition of a fuzzy probability measure on a fuzzy measurable space 5 we give necessary and sufficient conditions for such a measure to be a classical integral as in 9 in the case the space is generated a counterexample in the general case is also presented finally it is shown that a fuzzy probability measure is always an integral if the space is generated if we replace the operations and by the t norm to and its dual s0 see 6

construction of fuzzy σ algebras using triangular norms abstract generalizing the definitions given by the author fuzzy sets and systems4 1980 83 93 we introduce and study t fuzzy algebras t being any triangular norm the main result is that for a large class of triangular norms each t fuzzy algebra is generated i e consists of all functions x 0 1 being measurable with respect to some algebra on x

characterization of fuzzy measures constructed by means of triangular norms abstract following the ideas presented by the author e p klement j math anal appl 85 1982 543 565 finite t fuzzy measures are introduced t being a measurable triangular norm we show that a t fuzzy measure is always a fuzzy measure as considered earlier e p klement j math anal appl 25 1980 330 339 then we study the relation to the integral with respect to some classical measure finally for some special triangular norms t we give precise characterizations of the corresponding classes of t fuzzy measures

on triangular norm based propositional fuzzy logics abstract fuzzy logics based on triangular norms and their corresponding conorms are investigated an affirmative answer to the question whether in such logics a specific level of satisfiability of a set of formulas can be characterized by the same level of satisfiability of its finite subsets is given tautologies contradictions and contigencies with respect to such fuzzy logics are studied in particular for the important cases of min max and ukasiewicz logics finally fundamental t norm based fuzzy logics are shown to provide a gradual transition between min max and ukasiewicz logics

correspondence between fuzzy measures and classical measures abstract in this paper we study the question whether given a fuzzy measure as defined in 3 and 4 there exists a classical measure such that the fuzzy measure of a measurable fuzzy set equals the classical measure of the area below the membership function of the results are that in the case of finite additivity there is a one to one correspondence between classical measures and fuzzy measures whereas in the case of countable additivity this result only holds for generated fuzzy algebras finally some connections of that problem with the existence of an extension of a fuzzy measure defined on an arbitrary fuzzy algebra to the generated fuzzy algebra are discussed

the entropy of fuzzy dynamical systems general scheme and generators in this paper some fuzzy modifications of the kolmogorov sinaj entropy are studied we introduce the general scheme which includes the mentioned entropies finally the kolmogorov sinaj theorem on generators is proved for special cases

geometrical methods in wajsberg hoops abstract the aim of this paper is to show that certain geometric methods originally developed for investigating ukasiewicz many valued logics may be profitably applied to the study of classes of partially ordered residuated monoids we substantiate this claim by characterizing all free wajsberg hoops in terms of mcnaughton functions over the n cube and by giving complete axiomatizations for all varieties of wajsberg hoops

on a problem of radko mesiar general form of if probabilities recently axiomatic definition has been given of probability on the family of all if events any if event consists of two fuzzy events and the probability of the event is a compact interval on the real line hence if probability is a mapping from the family of if events to the family of all compact intervals prof mesiar asked to construct such a probability measure which is nondivisible into two components in this paper we describe the form of all if probability measures as a consequence we obtain an existence of a nondivisible probability hence the positive answer to the mesiar question

pseudofundamental triangular norms and g t tribes abstract we generalize the theory of t tribes of butnariu and klement this generalization may serve as a basis of a common theory of t measures and decomposable measures of fuzzy events

synchronization of coupled systems with spatiotemporal chaos we argue that the synchronization transition of stochastically coupled cellular automata discovered recently by l g morelli it et al phys rev bf 58 e r8 1998 is generically in the directed percolation universality class in particular this holds numerically for the specific example studied by these authors in contrast to their claim for real valued systems with spatiotemporal chaos such as coupled map lattices we claim that the synchronization transition is generically in the universality class of the kardar parisi zhang equation with a nonlinear growth limiting term

on the variation of the spectra of matrix pencils several distances between the spectra of two regular matrix pencils are discussed and compared the relations obtained enable us to estimate upper bounds on one distance via known upper bounds on others we also give some perturbation bounds and then show how to apply the relations obtained in this note

an analysis of the rayleigh ritz method for approximating eigenspaces this paper concerns the rayleigh ritz method for computing an approximation to an eigenspace x of a general matrix a from a subspace w that contains an approximation to x the method produces a pair n x that purports to approximate a pair l x where x is a basis for x and ax xl in this paper we consider the convergence of n x as the sine e of the angle between x and w approaches zero it is shown that under a natural hypothesis called the uniform separation condition the ritz pairs n x converge to the eigenpair l x when one is concerned with eigenvalues and eigenvectors one can compute certain refined ritz vectors whose convergence is guaranteed even when the uniform separation condition is not satisfied an attractive feature of the analysis is that it does not assume that a has distinct eigenvalues or is diagonalizable

estimates for the spectrum near algebraic elements abstract we extend a result of s friedland linear algebra appl 12 1982 81 98 on the variation of eigenvalues of matrices to show that if a b are elements of a banach algebra both algebraic of degree at most n then the hausdorff distance between their spectra satisfies a b n c n 2m n 1 a b where m max a b and c n 23n 13 the same technique also re proves a local form of this result obtained earlier by b aupetit and j zemanek linear algebra appl 52 53 1983 39 44 but with improved bounds on the constants we further investigate the sharpness of these bounds

computation of eigenpair partial derivatives by rayleigh ritz procedure based on rayleigh ritz procedure a new method is proposed for a few eigenpair partial derivatives of large matrices this method simultaneously computes the approximate eigenpairs and their partial derivatives the linear systems of equations that are solved for eigenvector partial derivatives are greatly reduced from the original matrix size and the left eigenvectors are not required moreover errors of the computed eigenpairs and their partial derivatives are investigated hausdorff distance and containment gap are used to measure the accuracy of approximate eigenpair partial derivatives error bounds on the computed eigenpairs and their partial derivatives are derived finally numerical experiments are reported to show the efficiency of the proposed method

t evaluators and s evaluators the scalar evaluation of the aggregation of elements from a complete lattice via the operation meet join is compared with the aggregation of scalar evaluations of these elements via a t norm t conorm based on this comparison the notion of a t evaluator s evaluator is introduced and its basic properties are studied the relationship between t s evaluators fuzzy measures and generalized filters is investigated an application of t evaluators in fuzzy preference modelling is presented

principles of inclusion and exclusion for interval valued fuzzy sets and if sets abstract the principle of inclusion and exclusion is one of basic tools of classical set theory many previous papers have presented its generalizations to fuzzy sets or if sets atanassov s intuitionistic fuzzy sets with godel or product operations in our previous work we clarified these questions for fuzzy sets with intersections and unions based on continuous triangular norms and conorms here we extend these results to interval valued fuzzy sets and if sets

studies of bacterial branching growth using reaction diffusion models for colonial development abstract various bacterial strains exhibit colonial branching patterns during growth on poor substrates these patterns reflect bacterial cooperative self organization and cybernetic processes of communication regulation and control employed during colonial development one method of modeling is the continuous or coupled reaction diffusion approach in which continuous time evolution equations describe the bacterial density and the concentration of the relevant chemical fields in the context of branching growth this idea has been pursued by a number of groups we present an additional model which includes a lubrication fluid excreted by the bacteria we also add fields of chemotactic agents to the other models we then present a critique of this whole enterprise with focus on the models potential for revealing new biological features

principles of inclusion and exclusion for fuzzy sets abstract many previous papers have presented generalizations of the principle of inclusion and exclusion to fuzzy sets or if sets atanassov s intuitionistic fuzzy sets with godel or product operations we clarify for which fuzzy intersections and unions based on continuous triangular norms and conorms the principle of inclusion and exclusion holds

explicit upper bounds for the spectral distance of two trace class operators abstract given two trace class operators a and b on a separable hilbert space we provide an upper bound for the hausdorff distance of their spectra involving only the distance of a and b in operator norm and the singular values of a and b by specifying particular asymptotics of the singular values our bound reproduces or improves existing bounds for the spectral distance the proof is based on lower and upper bounds for determinants of trace class operators of independent interest

variation of grassman powers and spectra the operator norm of the derivative of the map which takes a finite dimensional linear operator to its kth grassman power the kth compound is evaluated this leads to a bound for the distance between the grassman powers of two operators as an important application a bound for the distance between the eigenvalues of two operators is obtained

optimal bounds for the spectral variation of two regular matrix pairs for the generalized eigenvalue problem we establish upper bounds for the spectral variation of two regular matrix pairs some of which are optimal we describe the set of regular matrix pairs for which the bounds are attained

bounds for the variation of matrix eigenvalues and polynomial roots abstract for two given complex matrices a b upper bounds are derived for the optimal matching distance between the spectra a and b in terms of a b2 where 2 is the spectral norm the case of arbitrary matrix norms is treated a similar result estimates the optimal matching distance between the roots of two polynomials these bounds replace a factor of 4 in earlier results by the value 16 3 3 3 08

improving spectral variation bounds with chebyshev polynomials a new spectral variation bound is established for linear operators a and b on finite dimensional vector spaces this bound is v a b c a b 1n a b n 1 n with c 8 this result affirmatively answers a conjecture of friedland

on the variation of the spectra of matrices abstract several distances between the spectra of two matrices are discussed and compared optimal bounds are given which enable us to reduce certain bounds on the eigenvalue variation of matrices by a factor of about two the results of bhatia and mukherjea and of bhatia and friedland on the eigenvalue variation are derived in an elementary way using results of henrici on the spectral variation

additive fuzzy measures and integrals iii abstract a point of view concerning fuzzy measures is explained to this end a new concept of disjointness for fuzzy is introduced and studied also a concept of an additive class of fuzzy sets is defined to be a class of fuzzy sets closed under some additive operations the fuzzy measures are defined to be sum preserving real functions over such additive classes some basic properties of the fuzzy measures are derived in contrast with other homonymous concepts studied in literature our fuzzy measures lead to an additive fuzzy integral see the part ii of the paper

sharp and unsharp observables on σ mv algebras a comparison with the hilbert space approach we prove that any observable with a standard value space on a probability mv algebra m can be extended from a mapping defined on measurable subsets with values in m to a mapping defined on bounded real valued measurable functions with values in the set of sharp observables associated with m our method of proof is quite different from the method of the proof of analogous result for pov observables on a hilbert space we show that for pov observables with commuting range both approaches give the same results

the inclusion exclusion principle for l states and if events the principle of inclusion and exclusion for classical sets belongs to the very well known theorems of combinatorics and probability theory with the appearance of fuzzy sets and their generalizations it is natural to ask if this principle holds for them as well it turns out that this is true e g for if events which include fuzzy sets as a special case as it was shown in 8 in contrast to the mentioned paper we work with l states and with a wider set of probabilities as a consequence of this approach we obtain another method for proving the inclusion exclusion principle for if sets

counterexample to a conjecture of elsner on the spectral variation of matrices abstract in 1985 elsner proved that the hausdorff distance between the spectra of two n n matrices a and b satisfies a b n a b n 1 a b where denotes the operator norm with respect to the euclidean norm on c n he further conjectured that the same inequality holds for all operator norms we disprove this conjecture and also the weaker conjecture where a b is replaced by 2max a b

traveling excitable waves successively generated in a nonlinear proliferation system we study the dynamics of spatiotemporal pattern formation in a nonlinear proliferation system e g cell division supported on a field of nutrition in which the mechanism of activation and its self suppression is simultaneously implemented this dynamical model has been numerically realized with coupled cellular automata ca and various long standing spatiotemporal patterns have been observed among others a successive generation of traveling waves by implanting a spot of cells onto the field consisting of nutrition and activator is particularly interesting this takes place despite the fact that the present reaction network has a stable fixed point and therefore autonomous temporal oscillatory does not exist in the mean field indeed the reaction diffusion equation method rd applied to this network reproduces only a single excitable wave and soon falls into a steady state a fixed point without the following propagating waves this system having a stable fixed point is an excitable system of different kind from the fitzhugh nagumo model in that it can generate a pulse propagating outwards by adding only a single cell onto it from outside the system the present excitation upon dropping a cell is amplified to macroscopic level by a hidden dynamics of oscillation between the activation and its self suppression a pulse thus generated is propagated in space time with the help of diffusion through a precise comparison between ca and rd it is found that a very small amount of residue of the cells and activators which are left unburned in the stochastic treatment of reactions by the ca becomes a seed to excite the system and generate the next pulse wave this newly born wave can leave another seed of reaction in the field after its propagation based on this analysis we account for the appearance of other patterns observed a possible control of these patterns by varying the spatial distribution of initial concentration of the relevant agents such as the activator is also discussed

an elsner like perturbation theorem for generalized eigenvalues in 1985 elsner established a general bound on the distance between an eigenvalue of a matrix and the closest eigenvalue of a perturbation of that matrix in this note we show that a similar result holds for the generalized eigenvalue problem

conditional probability on σ mv algebras using the loomis sikorski representation of s mv algebras and dedekind s complete groups a conditional probability and expectation on these structures are defined as a natural generalization of the usual kolmogorovian conditioning

ludwig elsner and his contributions to core applied and numerical linear algebra ludwig elsner was bona on 17 january 1939 in grog strehlitz upper silesia in germany he studied mathematics physics and astronomy at the universities of hamburg and freiburg and received his diploma in mathematics in 1963 at the university of hamburg as a member of the lively and inspiring group of lothar collatz in hamburg he worked on his ph d while holding a position at the computing center of the university of hamburg he received his ph d in 1965 and became an assistant professor at collatz institute of applied mathematics at the university of hamburg for six years during this period he spent one year 1968 1969 as senior officer at the csir in pretoria south africa in 1971 ludwig eisner became associate professor at the university of erlangen where he worked at the institute for applied mathematics until 1976 since 1976 he has been a full professor at the university of bielefeld where he has built up the numerical analysis group among many other activities in bielefeld he has twice been chairman of the department of mathematics and has planned and formed the numerical analysis group of the sonderforschungsbereich diskrete strukturen in der mathematik which since 1989 has attracted many specialists in linear algebra and numerical linear algebra to work with eisner in bielefeld numerous publications prove the success of these collaborative efforts

representation theorem for probabilities on ifs events riecan gave in riecan 2004 9 an axiomatic characterization of a probability on ifs events and proved in riecan 2006 10 a representation theorem for it in rencova 9 rencova introduced the notions of additive f probability and strongly additive f probability and gave a representation theorem for strongly additive f probabilities in this paper we give a generalization of the axiomatic characterization given by riecan in riecan 2006 10 from this the representation theorem for strongly additive f probabilities will follow

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

characterization of measures based on strict triangular norms as a natural generalization of a measure space butnariu and klement 4 introduced t tribes of fuzzy sets with t measures they gave a complete characterization of t measures for a frank triangular norm t here we characterize t measures with respect to non frank strict triangular norms we show the specific roles of frank triangular norms and a newly introduced family nearly frank triangular norms

an optimal bound for the spectral variation of two matrices abstract we establish a bound for the spectral variation of two complex n n matrices a b in terms of a b and a b here denotes the spectral norm it is always better than a bound previously given by bhatia and friedland and it is optimal we describe the set of pairs a b for which the bound is attained

non atomic fuzzy measures and games in this paper liapounoff s theorem for fuzzy measures is proved and it is applied to extend a theorem of aumann and shapley 2 concerning the existence of the value for non atomic games precisely it is proved that the range of any non atomic n vector fuzzy measure in the sense of 6 is convex and compact and it is shown that this result allows to extend theorem b from 2 p 23 from games with unambiguous coalitions to games with fuzzy coalitions called fuzzy games defined on s algebras of fuzzy sets which are not necessarily s algebras of ideal sets

a characterization of the ordering of continuous t norms abstract given two t norms t 1 and t 2 it is quite often difficult or even impossible to check directly whether t 1 t 2 in schweizer and sklar 1983 a necessary and sufficient condition is given for continuous archimedean t norms to be comparable we simplify this result proving a sufficient condition which involves only one argument of a one place function rather than two arguments this result is applied to show the monotonicity of some well known classes of t norms next we generalize the result of schweizer and sklar to the case of all continuous t norms and present also a sufficient condition which is again easier to check

markov kernels and tribes abstract we define an ordering on the set of bounded markov kernels associated with a tribe of fuzzy sets we show that under this order the set of bounded markov kernels is a dedekind complete lattice in addition we define a sum of bounded markov kernels such that the set of bounded markov kernels is a lattice ordered semigroup if we concentrate only to sharp bounded markov kernels then this set is even a dedekind complete l group with strong unit we show that our methods work also for bounded markov kernels associated with t s tribes of fuzzy sets where t s is any frank t norm and s 0

uncertainty measures problems concerning additivity additivity of an uncertainty measure on an mv algebra has a clear meaning if the divisibility is dropped we come up to a so called girard algebra there we discuss strong resp weak additivity based on so called divisible disjoint unions resp on additivity for all sub mv algebras we obtain a description of those extensions from additive measures on an mv algebra to the canonical girard algebra extension of pairs which are strongly additive and valuation measures finally we prove the non existence of strongly additive measure extensions if the underlying mv algebra is a finite chain with more than two non trivial elements

on hudetz entropy localization abstract in rahimi and riazi 2014 22 a type of entropy of continuous maps on compact metric spaces is defined via integrating a local entropy map this average entropy is represented in terms of the entropy in the sense of dumitrescu but the equality of these two types of entropy is left as an open problem in 22 in this paper we modify the problem stated in 22 by replacing the dumitrescu entropy by the hudetz entropy since in our case the two previous types of entropy take an infinite value and the problem stated in 22 reduces to a trivial equality then we conclude the paper by proving the equality of the modified average entropy and the hudetz entropy the key tool is a version of jaccob s theorem for the hudetz entropy

a note on a generalized frank functional equation abstract we study a generalized frank functional equation in the broader framework of associative aggregation functions and show that up to the two projections we obtain exactly the same set of solutions as in the original paper by m j frank aequationes mathematicae 19 1979

triangular norm based measures and their markov kernel representation abstract we approach the problem whether left continuous triangular norm based valuations called t measures or t probability measures defined on triangular normbased tribes of the unit cube can be disintegrated by markov kernels we prove that each t measure based on a fundamental triangular norm these triangular norms t together with their corresponding triangular conorms s satisfy the functional equation t x y s x y x y can be uniquely represented as a sum of a disintegrable t measure and a hard core which is either identically zero or which is monotonically irreducible i e cannot be disintegrated

subsystem interconnection and near optimum control of discrete balanced systems the relationship between subsystem interconnection of discrete balanced systems and the hankel singular values is explored upper bounds on the spectral norm of the submatrices of the discrete balanced representation are derived by approximating the matrix riccati equation by its power series expansion with respect to two scalar parameters related to the hankel singular values for diagonalizable symmetric discrete time systems the relation between the eigenvalues of the subsystems and the eigenvalues of the overall system is explored it is shown that an upper bound on the distance between corresponding eigenvalues in these two sets is related to the ratio of the hankel singular values

fuzzy measurability and integrability developpement d une nouvelle theorie relative au probleme de la mesure des objets flous continuite des fonctions sigma additives sur une classe sigma additive d ensembles flous extension de la notion d integrale floue methode de calcul des integrales floues problemes ouverts

synchronization of stochastically coupled cellular automata we analyze the dynamics of two coupled elementary cellular automata with complex spatiotemporal dynamics the coupling mechanism characterized by a probability p is stochastic from numerical simulations we find that a sharp transition to full synchronization of the two cellular automata occurs at a critical value of p this transition admits an approximate semianalytical description in terms of the evolution of the difference automaton and is found both for symmetric and asymmetric coupling it is argued that the behavior of cellular automata under coupling may inspire a classification of their individual dynamics s1063 651x 98 51407 9