noninformative priors for dispersion models summary the present paper provides a bayesian analysis of two parameter dispersion models under noninformative priors the focus is on first and second order probability matching priors other noninformative priors including jeffreys and reference priors are examined in the light of these criteria for certain models some unique second order probability matching priors are found which are different from either jeffreys or reference priors

bayesian and frequentist bartlett corrections for likelihood ratio and conditional likelihood ratio tests summary this paper characterizes priors under which the bayesian and frequentist bartlett corrections for the likelihood ratio and the conditional likelihood ratio clr statistics differ by o 1 it is seen that except for sample points with negligible probability the clr statistic has a posterior distribution for which a posterior bartlett correction exists this observation leads to an alternative proof of the existence of a frequentist bartlett correction for the clr statistic

f quantum spaces and their dynamics abstract f quantum space has been suggested by riecan as an alternative model for quantum mechanics in this paper we study the dynamics of f quantum spaces

frequentist validity of posterior quantiles in the presence of a nuisance parameter higher order asymptotics given a random sample from a distribution with density function that depends on an unknown parameter 1 2 we are concerned with frequentist validity up to o n 1 of posterior quantiles of 1 treating 2 as a nuisance parameter we propose to make the best choice of the prior on by matching as far as practicable the posterior and frequentist coverage probabilities up to o n 1

probability matching priors for non regular cases we study probability matching priors in non regular cases both one parameter and multi parameter cases are considered the resulting priors are shown to satisfy certain differential equations several examples are discussed it is observed that the reference prior in the sense of bernardo is in many cases also probability matching as a necessary tool for finding such priors asymptotic expansion of posterior distributions for multi parameter non regular cases is also obtained

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

on local entropy of fuzzy partitions in this paper we will introduce a new kind of fuzzy version of the local entropy of a continuous dynamical system on a compact metric space and will prove some of its properties then we will define an average entropy of fuzzy partitions by integrating the local fuzzy entropy we will also state the relationship between this entropy and the fuzzy entropy of dynamical systems based on the entropy of fuzzy partitions in the sense of dumitrescu

fuzzy dynamical systems inverse and direct spectra abstract the present paper is concerned with the study of fuzzy dynamical systems the notions of equivalence of f dynamical systems a factor of an f dynamical system and corresponding homomorphism inverse and direct spectra are introduced and a few propositions are proved

fuzzy p measure on the real line abstract the fuzzy measurable space on the real line say is defined by means of fuzzy relation less or equal 5 the main properties of are given these results are used for investigation of fuzzy p measure on the principal emphasis is laid on the connections between a fuzzy p measure and its cumulative distribution function a theorem extending a fuzzy p measure to is shown

on the invariance of noninformative priors various noninformative priors have been proposed in the literature this article explores the invariance or lack thereof of some of these noninformative priors including the reference prior of berger and bernardo the reverse reference prior of j k ghosh and the probabilitymatching prior of peers and stein under reparameterization berger and bernardo s m group ordered reference prior is shown to remain invariant under a special type of reparameterization the reverse reference prior of j k ghosh is shown not to remain invariant under reparameterization however the probability matching prior is shown to remain invariant under any reparameterization also for spherically symmetric distributions certain noninformative priors are derived using the principle of group invariance

i fuzzy equivalence relations and i fuzzy partitions a t fuzzy equivalence relation is a fuzzy binary relation on a set x which is reflexive symmetric and t transitive for a t norm t recently mesiar et al r mesiar b reusch h thiele fuzzy equivalence relations and fuzzy partitions j multi valued logic soft comput 12 2006 167 181 have generalised the t norm t to any general conjunctor c and investigated the minimal assumptions required on such operations called duality fitting conjunctors such that the fuzzification of the equivalence relation admits any value from the unit interval and also the one one correspondence between the fuzzy equivalence relations and fuzzy partitions is preserved in this work we conduct a similar study by employing a related form of c transitivity viz i transitivity where i is an implicator we show that although every i fuzzy equivalence relation can be shown to be a c fuzzy equivalence relation there exist c fuzzy equivalence relations that are not i fuzzy equivalence relations and hence these concepts are not equivalent most importantly we show that the class of duality fitting implicators i is much richer than the residuals of the duality fitting conjunctors in the study of mesiar et al we also show that the i fuzzy partitions have a constant wise structure

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

entropy of a fuzzy process abstract using an additive fuzzy measure 1 in 5 a general concept of entropy of a fuzzy partition has been considered this concept is used to define the entropy of a fuzzy process in this paper some properties of this entropy are summarized these results could be used to build a fuzzy ergodic theory in a further paper the entropy of a measure preserving transformation of a fuzzy measure space will be studied

probability of fuzzy events defined as denumerable additivity measure abstract in this paper the probability of fuzzy events is defined as a denumerable additivity measure this definition is based on a non conventional approach of separativity between fuzzy subsets the presented measure fulfils all properties analogous to the properties of classical probability in the crisp case further the notion of conditional probability of fuzzy events complete fuzzy repartition and independent fuzzy events are defined by means of the probability measure considered here connections between all the above notions are presented in this paper too finally the bayes formula is proved for the fuzzy case

on priors providing frequentist validity of bayesian inference for multiple parametric functions summary we characterise priors which match up to o n 1 the posterior joint cumulative distribution function of multiple parametric functions with the corresponding frequentist cumulative distribution function this work extends and unifies the work of ghosh mukerjee 1993 and datta ghosh 1995a on the topic of probability matching priors a set of necessary and sufficient conditions is obtained for the above characterisation some of these conditions depend only on the parametric functions and not on the prior examples are given where the joint probability matching is possible and where it is not possible

complex bi orthogonal decomposition of a chain of coupled wakes abstract this work is devoted to the experimental analysis of the flow created by a row of cylinders as each cylinder wake appears by the hopf bifurcation of a global oscillating mode this experiment is similar to a chain of coupled non linear oscillators and this dynamic system can be modelled using a ginzburg landau type equation a video analysis technique is performed on visualization pictures in order to obtain the spatio temporal evolution of the wakes this diagram is then analysed using the bi orthogonal decomposition extended to its complex form it is shown that only a few eigenmodes are excited giving a low dimensional dynamic system that enables the different parameters of the model to be estimated

bayesian prediction with approximate frequentist validity we characterize priors which asymptotically match the posterior coverage probability of a bayesian prediction region with the corresponding frequentist coverage probability this is done considering both posterior quantiles and highest predictive density regions with reference to a future observation the resulting priors are shown to be invariant under reparameterization the role of jeffreys prior in this regard is also investigated it is further shown that for any given prior it may be possible to choose an interval whose bayesian predictive and frequentist coverage probabilities are asymptotically matched

the lebesgue decomposition theorem for fuzzy quantum spaces abstract the present paper is devoted to signed measures of fuzzy quantum spaces the lebesque decomposition theorem is proved for the fuzzy case

spatially uniform traveling cellular patterns at a driven interface we report on a study of asymmetric traveling patterns which develop at a driven fluid air interface in the experimental system known as the printer s instability we find that the traveling pattern appears via a supercritical parity breaking transition at which the pattern loses its reflection symmetry and begins to drift with constant speed from measurements of the degree of asymmetry of the drifting pattern as a function of the experimental control parameter we find that the asymmetry increases with the square root of the control parameter and that the drift velocity is linear in the asymmetry this behavior is in accord with recent theoretical predictions our results do not agree however with the predictions of a model of the parity breaking transition involving the coupling of spatial modes with wave numbers q and 2q

localized breather like solution in a discrete klein gordon model and application to dna abstract non propagating localized oscillating solutions are studied in the case of a discrete one dimensional system with the 2 3 power onsite potential a multiple scale asymptotic perturbation expansion is not adequate for describing the large amplitude oscillations we consider starting from an exact pulse like solution in the continuum we derive an approximate oscillating solution our numerical simulations reveal that whereas the excitations are strongly damped in the strong intersite coupling case they are long lived in the discrete cases an additional modulation phenomenon of the oscillation seen in the simulation is explained by combination of the breather oscillations with the zero group velocity phonons modes then applying the green s functions formalism in analogy with a previous work s takeno et al prog theor phys suppl 94 1988 we derive a very accurate expression for the discrete breather with a quasi infinite lifetime lastly we demonstrate how such excitations can explain why the breathers make the dominant contributions in the dynamics of a simple model of dna

second order probability matching priors for a parametric function with application to bayesian tolerance limits summary conditions are obtained for the approximate frequentist validity of the posterior quantiles of any smooth parametric function an application to bayesian tolerance limits is indicated

entropy of fuzzy dynamical systems abstract entropy of a finite fuzzy partition had been defined dumitrescu 1983 1993 using an additive fuzzy measure butnariu 1983 in this paper we define the independence of fuzzy partitions with respect to a fuzzy measure some properties concerning the entropy of independent fuzzy partitions are proved this concept of independence is also relevant for the study of the entropy of a fuzzy process dumitrescu 1993 we prove some new results concerning the entropy of a fuzzy process the fuzzy measure preserving transformations dumitrescu 1993 may be related with the fuzzy ergodic theory the main problem in ergodic theory is to build the isomorphism invariants kolmogorov s 1958 transformation entropy is such an invariant in this paper we define the entropy of a fuzzy dynamical system we prove that this entropy is an isomorphism invariant

spatio temporal intermittency in a 1d convective pattern theoretical model and experiments abstract we describe the occurence of spatio temporal intermittency in a one dimensional convective system that first shows time dependent patterns we recall experimental results and propose a model based on the normal form description of a secondary hopf bifurcation of a stationary periodic structure numerical simulations of this model show spatio temporal intermittent behaviors which we characterize briefly and compare to those given by the experiment

on fuzzily measurable random variables abstract a fuzzy random variable is given as a measurable function transforming the sets of elementary events into the real line where is a fuzzy algebra and is a soft fuzzy algebra defined by means of the fuzzy relation less or equal 8 the main properties of a fuzzy random variable are proved the connections between a fuzzy random variable its distribution and its cumulative distribution are investigated too

on a possible generalization of the bayes method of inference abstract the main purpose of this paper is investigation of the bayes formula problem for klement s fuzzy probability measure this measure is defined here on a family of fuzzy subsets which is among other things closed under complement given as an involution satisfying zadeh s extension principle due to ovchinnikov s result 6 we express this complement as a variable pointwise involution next we prove that the bayes formula holds for fuzzy probability measure iff it is a fuzzy p measure more generally defined here moreover we show that there exists an automorphism between fuzzy probability space with the usual zadeh operator of complement and fuzzy probability space with ovchinnikov s operator of complement so using the bayes method of inference we can always replace the generalized operator of complement by zadeh s one

on a property of probability matching priors matching the alternative coverage probabilities summary in frequentist inference based on confidence sets both the true coverage and the probability for a confidence set to include an alternative value of the parameter of interest are important thus if probability matching priors also match such alternative coverage probabilites there is perhaps a stronger justification for calling them noninformative considering contiguous alternatives we obtain the relevant necessary and sufficient conditions in particular with n denoting the sample size it is seen that probability matching priors up to o n 2 also match the alternative coverage probabilities up to that order while this is not necessarily the case with probability matching priors up to o n

one to one correspondences between ɛ partitions 1 ɛ equivalences and ɛ pseudometrics the generalization of the concept of a classical or crisp partition to that of a fuzzy partition requires in our researches the choice of a family of fuzzy subsets which preserves the conditions characterizing crisp partitions however the usual constraints for the union and intersection of subsets are very limiting and seem to be far from the fuzzy spirit so that the union of subsets in the partitions is forced to be close to the universe of discourse and the intersection of any two subsets in the partition is forced to be close to the empty set furthermore since the classical definition of partition is very related to the union and intersection the generalization of this concept has to be applicable for any extension of these operations for fuzzy sets apart from this we need to redefine the concept of fuzzy partition to establish a one to one correspondence between fuzzy partitions and some kind of fuzzy equivalence relations the different definitions that we found in the literature did not exactly verify these requirements although some of them were more appropriate than others finally we have given a definition of fuzzy partition of any fuzzy subset of the universe which is a generalization of crisp partitions and of most of the different definitions of fuzzy partitions which preserves the classical ideas of covering and disjointness and such that it is appropriate in our researches classification problems fuzzy questionnaires fuzzy information theory once our fuzzy partitions epartitions are defined it is necessary to find the fuzzy binary relation which generates and characterizes the fuzzy partitions this fuzzy relation has to be by analogy with the crisp case a fuzzy equivalence relation two points in the same fuzzy subset of the partition will be related and two points in different subsets will not in relation with this equivalence relation it is also possible to obtain a way to measure the distance between two points by means of the degree of relation that there exists between them and therefore by means of the membership degree to a same subset in the fuzzy partition the definitions of these concepts and the relationships between them are the purpose of this paper

simple modifications for signed roots of likelihood ratio statistics summary in the context of inference about a scalar parameter in the presence of nuisance parameters some simple modifications for the signed root of the log likelihood ratio statistic r are developed that reduce the order of error in the standard normal approximation to the distribution of r from o n 1 2 to o n 1 barndorff nielsen has introduced a variable u such that the error in the standard normal approximation to the distribution of r r r log u r is of order o n 3 2 but calculation of urequires the specification of an exact or approximate ancillary statistic a this paper proposes an alternative variable to u denoted by t that is available without knowledge of a and satisfies t u op n 1 in general thus the standard normal approximation to the distribution of r r log t r has error of order o n 1 and it can be used to construct approximate confidence limits having coverage error of order o n 1 in certain cases however tand uare identical the derivation of tinvolves the bayesian approach to constructing confidence limits considered by welch and peers and peers similar modifications for the signed root of the conditional likelihood ratio statistic are also developed and these modifications are seen to be useful when a large number of nuisance parameters are present several examples are presented including inference for natural parameters in exponential models and inference about location scale models with type ii censoring in each case the relationship between tand u is discussed numerical examples are also given including inference for regression models inference about the means of log normal distributions and inference for exponential lifetime models with type i censoring where barndorff nielsen s variable u is not available

boolean representations of fuzzy quantum spaces abstract let f be a fuzzy quantum space by a boolean representation of f we mean a boolean algebra f with a mapping h f onto f such that for each state s and for each observable y on f there is a state probability measure s and an observable y on f such that the following diagram commutes r is the real line and b r is the borel algebra we prove that 1 a boolean representation always exists 2 there is a minimal and a maximal boolean representation 3 a minimal boolean representation possesses the uniqueness property for observables further all states resp observables on f correspond to states resp observables on f this makes it possible to transfer many results from boolean algebras to fuzzy quantum spaces we argue that the noncompatibility encountered in fuzzy quantum spaces originates rather from the ambiguous representation of events by fuzzy sets than from the systems they describe

noninformative priors for one parameter of many summary we consider the problem of constructing a prior that is noninformative for a single parameter in the presence of nuisance parameters our approach is to require that the resulting marginal posterior intervals have accurate frequentist coverage stein 1985 derived nonrigorously a sufficient condition for such a prior through the use of orthogonal parameters we give a general form for the class of priors satisfying stein s condition the priors are proportional to the square root of the information element for the parameter of interest times an arbitrary function of the nuisance parameters this is in contrast to jeffreys 1946 invariant prior for the overall parameter which is proportional to the square root of the determinant of the information matrix several examples are given and comparisons are made to the reference priors of bernardo 1979

the radon nikody m theorem for fuzzy probability spaces abstract in the present paper we prove the radon nikod m theorem for fuzzy probability spaces its proof depends on general methods for handling observables which enable us to formulate and to prove many interesting results of probability theory as for example the completeness of l p spaces the conditional mean value etc

solitary dilation waves in a circular array of liquid columns abstract solitary dilation waves and self sustained oscillations optical mode are observed in a one dimensional pattern of liquid columns produced in the pouring of a liquid film from a solid ceiling a new experiment carried out on a circular fountain allows us to achieve periodic boundary conditions and thus to observe free propagation of the dilation waves in an infinite medium measurements of the drift and group velocities of the dilation waves and of the optical pulsation are presented as functions of the flow rate in addition starting from qualitative observations and order of magnitude estimates we build a discrete model of non linear dynamics in this system in which dissipation is compensated by an external energy supply transient drop formation this model allows us to recover the appearance of the optical mode induced by a wavelength increase and predicts the focusing of this mode into a localized kink traveling at a constant speed along the column array the kink structure is reminiscent of the dilation waves observed experimentally both the model and experiment support a relationship between the wave velocity and the oscillation frequency similar to that observed by michalland and rabaud in the printer s instability

on a representation of observables in fuzzy measurable spaces abstract we give a representation of observables in fuzzy measurable spaces by random variables and vice versa and we prove a loomis sikorski theorem analogue moreover some applications are presented

entropy of fuzzy partitions a general model abstract the entropy of fuzzy partitions with regard to a fuzzy measure is analyzed a general model based on pseudo arithmetical operations and g functions will be created the entropy of fuzzy partitions introduced by ruspini inform and control 15 1969 22 and dumitrescu j math anal appl 176 1993 359 is shown to be reasonable only up to an isomorphism

probabilities and fuzzy events an operational approach abstract this paper tries to give a redesign of a well established research area of traditional fuzzy set theory the notion of a probability of a fuzzy event as well as related results are reexamined and new definitions for them are given which are based on the operational viewpoint of f set theory and on some concepts of operational statistics a critical survey of existing concepts will show some advantages of the operational approach

the selection of prior distributions by formal rules abstract subjectivism has become the dominant philosophical foundation for bayesian inference yet in practice most bayesian analyses are performed with so called noninformative priors that is priors constructed by some formal rule we review the plethora of techniques for constructing such priors and discuss some of the practical and philosophical issues that arise when they are used we give special emphasis to jeffreys s rules and discuss the evolution of his viewpoint about the interpretation of priors away from unique representation of ignorance toward the notion that they should be chosen by convention we conclude that the problems raised by the research on priors chosen by formal rules are serious and may not be dismissed lightly when sample sizes are small relative to the number of parameters being estimated it is dangerous to put faith in any default solution but when asymptotics take over jeffreys s rules and their variants remain reasonable choices we also provide an annotated b

the entropy of fuzzy dynamical systems and generators abstract in this paper the entropy and conditional entropy of stochastical complete repartitions are defined the represented measure satisfies all properties analogous to the properties of entropy of measurable repartitions in the crisp case further the notion of entropy of fuzzy dynamical systems is defined the above notion generalizes the notion of entropy of dynamical systems from the classical probability theory finally the kolmogorov sinaj theorem on generators is proved for the fuzzy case

on the implementation of local probability matching priors for interest parameters probability matching priors are priors for which the posterior probabilities of certain specified sets are exactly or approximately equal to their coverage probabilities these priors arise as solutions of partial differential equations that may be difficult to solve either analytically or numerically recently levine casella 2003 presented an algorithm for the implementation of probability matching priors for an interest parameter in the presence of a single nuisance parameter in this paper we develop a local implementation that is very much more easily computed a local probability matching prior is a data dependent approximation to a probability matching prior and is such that the asymptotic order of approximation of the frequentist coverage probability is not degraded we illustrate the theory with a number of examples including three discussed in levine casella 2003

on limit theorems in fuzzy quantum spaces two kinds of fuzzy connectives are used for constructing two models of quantum mechanics in the framework some versions of the weak law of large numbers and the central limit theorem are presented

a decomposition for the likelihood ratio statistic and the bartlett correction a bayesian argument let l n 1 log p x be the log likelihood of an n dimensional x under a p dimensional let j be the mle under h j 1 1 0 j j 0 and 0 be the unrestricted mle define t j as 2n l j 1 1 2 sgn j j 1 j 0 let t t 1 t p then under regularity conditions the following theorem is proved under 0 t is asymptotically n n 1 2 a 0 n 1 a j n 1 o n 3 2 where j is the identity matrix the result is proved by first establishing an analogous result when is random and then making the prior converge to a degenerate distribution the existence of the bartlett correction to order n 3 2 follows from the theorem we show that an edgeworth expansion with error o n 2 for t involves only polynomials of degree less than or equal to 3 and hence verify rigorously lawley s 1956 result giving the order of the error in the bartlett correction as o n 2

characterization of continuous t norms compatible with zadeh s probability of fuzzy events in this work we study the concept of p z compatibility which holds for those t norms for which zadeh s probability of fuzzy events fulfills kolmogorov s axioms whether a probability satisfies kolmogorov s axioms or not depends almost exclusively on the t norm and dual t conorm used to define intersection and union respectively of fuzzy sets in order to better understand fuzzy probability theory we provide a complete characterization of the p z compatible continuous t norms

compatibility of t norms with the concept of e partition in this paper we study the behaviour of a kind of partitions formed by fuzzy sets the e partitions with respect to three important operations refinement union and product of partitions in the crisp set theory the previous operations lead to new partitions every refinement of a partition is also a partition the union of partitions of disjoint sets is a partition of the union set the product of two partitions of two sets is a partition of the intersection of the partitioned sets it has been proven that e partitions extend the three previous properties when the intersection of fuzzy sets is defined by the minimum t norm and the union by the maximum t conorm in this paper we consider any t norm defining the intersection of fuzzy sets and we characterize those t norms for which refinements unions and products of e partitions are e partitions we pay special attention to these characterizations in the case of continuous t norms

m equivalence entropy and f dynamical systems the present paper deals with the theory of entropy of f dynamical systems using the concept of atoms in a fuzzy algebra having introduced the notions of m equivalence and m refinement it is proved that entropy of an f dynamical system with respect to each m equivalence class is an m isomorphism invariant results proved in this paper include the corresponding classical results as particular cases

fuzzy δ ɛ partitions in this paper the concept of a fuzzy e partitions of any fuzzy subset of the universe is introduced as a generalization of that of a classical partition the approach is based on four observations the first one is that for any two members of a classical partition their intersection is the empty set if they are not equal the second one is that the union of all members of a classical partition is equal to the partitioned set the third one is that this definition has to be applicable for any extension of the union and intersection for fuzzy subsets and the fourth one is that this definition has to allow us to establish a one to one correspondence between fuzzy partitions and some kind of fuzzy equivalence relations once this new concept is introduced by considering that the constrains for union and intersection are too limiting and that they have to be slightly modified some equivalence definitions of e partitions are proposed in particular two very important cases are studied they are the case when is equal to e because this is very useful in practical applications and the case when is equal to 1 e that is when the degree of fuzziness for the union and the intersection are equal this case is very useful in theoretical applications and it will be related to the concept of e equal fuzzy subsets apart from the fact that they are a generalization of that of a classical partition the new concept of e partition is also a generalization of that of the best known definitions of fuzzy partitions proposed in the literature

second order probability matching priors summary the paper considers priors obtained by ensuring approximate frequentist validity of a posterior quantiles and of b the posterior distribution function it is seen that at the second order of approximation the two approaches do not necessarily lead to identical conclusions examples are given to illustrate this the role of invariance in the context of probability matching is also discussed

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

fuzzy a algebras and conditional entropy the purpose of the present paper is to introduce and study the concept of conditional entropy of fuzzy sub algebras having finitely many atoms

localized phenomena during spatio temporal intermittency in directional viscous fingering in the directional viscous fingering instability the interface can evolve from a basic steady state to chaos by spatio temporal intermittency one essential feature of such a transition is that the chaotic domains appear by a contamination process of the steady phase this mechanism is investigated here and it is shown that contamination occurs by two localized structures dilatation waves and pairs of static asymmetric cells these two structures suggest an elastic behaviour of the pattern

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

p measures on soft fuzzy σ algebras abstract we study p measures on soft fuzzy algebras as defined by piasecki 46 and further investigated in 2 5 etc we prove as main result that the space of p measures of a soft fuzzy algebra is faithfully isomorphic to the space of probability measures of a boolean algebra this result we believe may allow to employ the well developed boolean technique in certain fuzzy investigations especially in the stochastic ones but on the other hand it lowers to some extent the chance for the soft fuzzy algebras to be applied in quantum theories see also 9 and 8 it should be noted that our result gives as a by product a negative answer to the problem posed in 3

prior distributions from pseudo likelihoods in the presence of nuisance parameters consider a model parameterized by where is the parameter of interest the problem of eliminating the nuisance parameter can be tackled by resorting to a pseudo likelihood function l for namely a function of only and the data y with properties similar to those of a likelihood function if one treats l as a true likelihood the posterior distribution y l for can be considered where is a prior distribution on the goal of this article is to construct probability matching priors for a scalar parameter of interest only i e priors for which bayesian and frequentist inference agree to some order of approximation to be used in y when l is a marginal a conditional or a modification of the profile likelihood we show that is simply proportional to the square root of the inverse of the asymptotic variance of the pseudo maximum likelihood estimator the proposed priors are compared with the reference or jeffreys priors in four

fuzzy measures and the entropy of fuzzy partitions abstract using an additive fuzzy measure a notion of the entropy of a finite fuzzy partition has been defined d dumitrescu on fuzzy partitions in itinerant seminar on functional equations approximation and convexity cluj napoca 1983 pp 57 60 d dumitrescu and m barbu fuzzy entropy and processes in itinerant seminar on functional equations approximation and convexity cluj napoca 1985 pp 71 74 this notion contains as a particular case a well known concept of entropy m a gil et al fuzzy sets and systems15 1985 65 78 h tanaka et al kybernetes5 1976 25 30 i j taneja bivariate entropies of finite partitions of fuzzy sets in preprints of second ifsa congress tokyo 1987 vol 2 pp 696 699 the aim of this paper is to review some basic properties of the considered entropy

the conjugation of fuzzy probability spaces to the unit interval abstract in this paper we give a fuzzy generalization of the halmos neumann theorem on the conjugation of probability spaces to the unit interval

bayesian intervals with good frequentist behaviour in the presence of nuisance parameters given a random sample from a distribution with density function that depends on an unknown parameter 1 p we are concerned with the problem of setting confidence intervals for a particular component of it say 1 treating the remaining components as a nuisance parameter adopting an objective bayesian approach we show that the bayes intervals with a certain conditional prior density on the parameter of interest 1 are confidence intervals as well having nearly the correct frequency of coverage the frequentist performance of the proposed intervals is tested in a simulation study for gamma mean and shape parameters

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

an algebraic generalization of the notion of tribe tribes became a successful basis of measure theory on fuzzy sets during their investigation new requirements arose we discuss possible modifications of the original definition of a tribe we suggest a more general structure which admits to apply different triangular norms in different parts emphasis is put on point free notions

a note to the kolmogorov sinaj entropy of fuzzy dynamical systems abstract in this note the kolmogorov sinaj entropy h m of fuzzy dynamical systems is studied it is showed that h m coincides on isomorphic objects finally we improve the formulation of kolmogorov sinaj s theorem on generators for the fuzzy case

on joint distribution of observables for f quantum spaces abstract in an f quantum space model for measurements of quantum mechanical observables based on fuzzy sets ideas we solve a problem of existence of a joint distribution for a given system of observables in a given f state of an f quantum space

fuzzy probability space defined by means of the fuzzy relation less than abstract in this paper a fuzzy relation less than and fuzzy probability spaces on the real line are defined fuzzy algebras of events are introduced in an analogous way to the classical theory of probability by means of the above relation furthermore specific properties of the fuzzy probability measures presented here are given

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

on priors providing frequentist validity for bayesian inference summary we derive the differential equation that a prior must satisfy if the posterior probability of a one sided credibility interval for a parametric function and its frequentist probability agree up to o n 1 this equation turns out to be identical with stein s equation for a slightly different problem for which also our method provides a rigorous justification our method is different in details from stein s but similar in spirit to dawid 1991 and bickel ghosh 1990 some examples are provided

a fuzzy measure algebra as a metric space in this paper we extend to fuzzy subset setting the results from classical measure theory that i a measure algebra a with its canonical metric is a complete metric space for which the mappings a a a b a b a b a b are uniformly continuous and ii a is a convex metric space iff a is nonatomic the classical results are particular cases of the extensions