comparison of fuzzy numbers based on the probability measure of fuzzy events abstract most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only and suffer from lack of discrimination and occasionally conflict with intuition it is true that fuzzy numbers are frequently partial order and cannot be compared however this does not alleviate the need for comparison in practical applications in this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to zadeh it considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions the approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number it is shown that several comparison indices in the literature can be obtained based on the probability present measure approach finally some typical examples are used to compare the various different approaches the different interpretations of the dispersion index under different physical situations are emphasized

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

on the maximum entropy parameterized interval approximation of fuzzy numbers this paper extends the interval valued weighted possibilistic mean of a fuzzy number of fuller and majlender to a general weighting function without the monotonic increasing assumption this weighting function determines a weighted average aggregation of the cuts of the fuzzy number according to the preference of a decision maker some properties of the weighting function are provided and a preference index that qualifies this aggregation and can serve as a parameter for the definition of interval approximation of a fuzzy number is proposed a special class of parameterized weighting functions satisfying the maximal entropy principle is proposed

reasonable properties for the ordering of fuzzy quantities ii as a continuation of the first part related to the first and second class of ordering approaches this paper deals with the fulfilment of reasonable properties in the third class of ordering approaches to do so we briefly introduce fuzzy relations on which the third class of approaches is based then we recall some transitivity related concepts and an ordering procedure based on a acyclic fuzzy relation acyclicity is a very weak restriction on a fuzzy relation we prove that many fuzzy relations used for the comparison of fuzzy quantities satisfy some conditions stronger than acyclicity so we give a widely applicable formulation to derive a total ranking order from a fuzzy relation with our formulation we examine all the ordering indices in the third class with respect to the proposed axioms in part i

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

statistical methods for eliciting probability distributions elicitation is a key task for subjectivist bayesians although skeptics hold that elicitation cannot or perhaps should not be done in practice it brings statisticians closer to their clients and subject matter expert colleagues this article reviews the state of the art reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively and how they respond to questions about that information in a discussion of the elicitation process the first issue to address is what it means for an elicitation to be successful that is what criteria should be used our answer is that a successful elicitation faithfully represents the opinion of the person being elicited it is not necessarily true in some objectivistic sense and cannot be judged in that way we see that elicitation as simply part of the process of statistical modeling indeed in a hierarchical model at which point the likelihood ends and the pr

on the centroids of fuzzy numbers in a paper by cheng a new approach for ranking fuzzy numbers by distance method fuzzy sets and systems 95 1998 307 317 a centroid based distance method was suggested for ranking fuzzy numbers both normal and non normal where the fuzzy numbers are compared and ranked in terms of their euclidean distances from their centroid points to the origin it is found that the centroid formulae provided by the above paper are incorrect and have led to some misapplications in this paper we present the correct centroid formulae for fuzzy numbers and justify them from the viewpoint of analytical geometry a numerical example demonstrates that cheng s formulae can significantly alter the result of the ranking procedure

a method for ranking fuzzy numbers and its application to decision making since fuzzy numbers represent uncertain numeric values it is difficult to rank them according to their magnitude in the paper a method for ranking fuzzy numbers is proposed the method considers the overall possibility distributions of fuzzy numbers in their evaluations for ranking and provides users with a method of changing viewpoints for evaluations users represent their viewpoints with fuzzy sets the method evaluates fuzzy numbers with a satisfaction function and the viewpoint given by users and then ranks the numbers according to their evaluation values the satisfaction function is a measure of comparisons between fuzzy numbers in order to illustrate the ranking method two numeric examples are shown and for the comparative study our method is compared with four existing ranking methods through eight examples as an example of potential applications the proposed method is applied to a decision making problem a two person game with fuzzy profit and loss the ranking method is used to analyze player choices

ranking fuzzy numbers with an area method using radius of gyration ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems many methods have been proposed to deal with ranking fuzzy numbers chu pointed out some shortcomings of the existing distance method and proposed to rank the fuzzy numbers with the area between the centroid point and original point however drawbacks are also found in the area method for example it cannot rank fuzzy numbers when some fuzzy numbers have the same centroid point in this paper we propose a modified area method to rank fuzzy numbers the modified method can effectively rank various fuzzy numbers and their images we also used some comparative examples to illustrate the advantage of the proposed method

limits and degenerations of unitary conformal field theories in the present paper degeneration phenomena in conformal field theories are studied for this purpose a notion of convergent sequences of cfts is introduced properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of cfts which as familiar from large volume limits of non linear sigma models can be regarded as commutative degenerations of the corresponding quantum geometries as an application the large level limit of the a series of unitary virasoro minimal models is investigated in detail in particular its geometric interpretation is determined

geometric structures gromov norm and kodaira dimensions abstract we define the kodaira dimension for 3 dimensional manifolds through thurston s eight geometries along with a classification in terms of this kodaira dimension we show this is compatible with other existing kodaira dimensions and the partial order defined by non zero degree maps for higher dimensions we explore the relations of geometric structures and mapping orders with various kodaira dimensions and other invariants especially we show that a closed geometric 4 manifold has nonvanishing gromov norm if and only if it has geometry h 2 h 2 h 2 c or h 4

lusternik schnirelmann category and systolic category of low dimensional manifolds we show that the geometry of a riemannian manifold m is sensitive to the apparently purely homotopy theoretic invariant of m known as the lusternik schnirelmann category denoted catls m here we introduce a riemannian analogue of catls m called the systolic category of m it is denoted catsys m and defined in terms of the existence of systolic inequalities satisfied by every metric as initiated by c loewner and later developed by m gromov we compare the two categories in all our examples the inequality catsysm catlsm is satisfied which typically turns out to be an equality e g in dimension 3 we show that a number of existing systolic inequalities can be reinterpreted as special cases of such equality and that both categories are sensitive to massey products the comparison with the value of catls m leads us to prove or conjecture new systolic inequalities on m 2006 wiley periodicals inc

collapsing manifolds obtained by kummer type constructions we construct f structures on a bott manifold and on some other manifolds obtained by kummer type constructions we also prove that if m e x where e is a fiber bundle with structure group g and a fiber admitting a g invariant metric of non negative sectional curvature and x admits an f structure with one trivial covering then one can construct on m a sequence of metrics with sectional curvature uniformly bounded from below and volume tending to zero i e vol k m 0 as a corollary we prove that all the elements in the spin cobordism ring can be represented by manifolds m with vol k m 0

a new approach for ranking fuzzy numbers by distance method abstract many ranking methods have been proposed so far however there is yet no method that can always give a satisfactory solution to every situation some are counterintuitive not discriminating some use only the local information of fuzzy values some produce different rankings for the same situation for overcoming the above problems we propose a new method for ranking fuzzy numbers by distance method our method is based on calculating the centroid point where the distance means from original point to the centroid point x 0 y 0 and the x 0 index is the same as murakami et al s x 0 however the y 0 index is integrated from the inverse functions of an lr type fuzzy number thus we use ranking function r a x 2 y 2 distance index as the order quantities in a vague environment our method can rank more than two fuzzy numbers simultaneously and the fuzzy numbers need not be normal furthermore we also propose the coefficient of variation cv index to improve lee and li s method comput math appl 15 1988 887 896 lee and li rank fuzzy numbers based on two different criteria namely the fuzzy mean and the fuzzy spread of the fuzzy numbers and they pointed out that human intuition would favor a fuzzy number with the following characteristics higher mean value and at the same time lower spread however when higher mean value and at the same time higher spread or lower mean value and at the same time lower spread exists it is not easy to compare its orderings clearly our cv index is defined as cv standard error mean which can overcome lee and li s problem efficiently in this way our proposed method can also be easily calculated by the mathematica package to solve problems of ranking fuzzy numbers at last we present three numerical examples to illustrate our proposed method and compare with other ranking methods

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

combining probability distributions from dependent information sources inferences or decisions in the face of uncertainty should be based on all available information thus when probability distributions for an uncertain quantity are obtained from experts models or

simplifying the search for effective ranking of fuzzy numbers we prove that a ranking index which generates an order on some subset of fuzzy numbers can be reduced to a ranking index with a simpler form and which generates an equivalent order this way the finding of ranking indices generating orders with desirable properties can be essentially simplified such that we need to search only from additive or scale invariant ranking indices we determine exactly making an abstraction of equivalent orders the class of ranking indices on trapezoidal fuzzy numbers which generate orders satisfying all the basic requirements finally ranking indices used to rank trapezoidal fuzzy numbers are extended to ranking indices used to rank arbitrary fuzzy numbers so that the desired properties are preserved

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

ranking fuzzy numbers with preference weighting function expectations based on the recent research developments of fuzzy number ranking the paper extends the centroid expectation approach and proposes a preference weighting function expectation method to rank fuzzy numbers the weighting function gives different emphasis on the possible values of the fuzzy number which can be used to represent the decision maker s pessimistic neutral or optimistic attitude an optimistic measure to represent this preference information is proposed some properties of the weighting function and optimistic measure are systematically analyzed then the paper proposes a special class weighting function with maximum entropy principle and analyzes some of its properties with this parameterized maximum entropy weighting function we can get preference expectation of any fuzzy number with given optimistic level next the weighting function is extended to represent the confidential attitude of the decision maker by giving different emphasis on the cut level set of the fuzzy number some results about confidential attitude that parallel to the valuation attitude are attained we especially extended the badd basic defuzzification distribution approach with preference expectation of fuzzy numbers and another confidential measure with badd operator is proposed finally the expected valuations of fuzzy numbers are used to ranking the fuzzy numbers compared with other fuzzy number ranking methods the method of this paper is easily interpreted robust flexible and invariant with translating and scaling for real numbers

entropy and collapsing of compact complex surfaces we study the problem of existence of mathcal f structures in the sense of cheeger and gromov but not necessarily polarized on compact complex surfaces we give a complete classification of compact complex surfaces of kahler type admitting mathcal f structures in the non kahler case we give a complete classification modulo the gap in the classification of surfaces of class vii we then use these results to study the minimal entropy problem for compact complex surfaces we prove that modulo the gap in the classification of surfaces of class vii all compact complex surfaces of kodaira dimension less than or equal to 1 have minimal entropy zero and such a surface admits a smooth metric g with zero topological entropy if and only if it is mathbb c p 2 a ruled surface of genus 0 or 1 a hopf surface a complex torus a kodaira surface a hyperelliptic surface or a kodaira surface modulo a finite group the key result we use to prove this is a new topological obstruction to the existence of metrics with vanishing topological entropy finally we show that these results fit perfectly into wall s study of geometric structures on compact complex surfaces for instance we show that the minimal entropy problem can be solved for a minimal compact kahler surface s of kodaira dimension infty 0 or 1 if and only if s admits a geometric structure modelled on mathbb c p 2 s 2 times s 2 s 2 times mathbb e 2 or mathbb e 4

a bayesian approach to compatibility improvement and pooling of quantum states in approaches to quantum theory in which the quantum state is regarded as a representation of knowledge information or belief two agents can assign different states to the same quantum system this raises two questions when are such state assignments compatible and how should the state assignments of different agents be reconciled in this paper we address these questions from the perspective of the recently developed conditional states formalism for quantum theory leifer m s and spekkens r w 2013 phys rev a 88 052310 specifically we derive a compatibility criterion proposed by brun finkelstein and mermin from the requirement that upon acquiring data agents should update their states using a quantum generalization of bayesian conditioning we provide two alternative arguments for this criterion based on the objective and subjective bayesian interpretations of probability theory we then apply the same methodology to the problem of quantum state improvement i e how to update your state when you learn someone else s state assignment and to quantum state pooling i e how to combine the state assignments of several agents into a single assignment that accurately represents the views of the group in particular we derive a pooling rule previously proposed by spekkens and wiseman under much weaker assumptions than those made in the original derivation all of our results apply to a much broader class of experimental scenarios than have been considered previously in this context

application of weighting functions to the ranking of fuzzy numbers this paper proposes a new ranking method for fuzzy numbers which uses a defuzzification of fuzzy numbers and a weighting function following saeidifar and pasha 2008 first we define a weighted distance measure on fuzzy numbers and then by minimizing this distance the weighted interval and point approximations of fuzzy numbers are obtained these indices are applied to rank the fuzzy numbers this method is new and interesting for ranking fuzzy numbers and it can be applied for solving and optimizing engineering and economics problems in a fuzzy environment

modeling expert judgments for bayesian updating this paper examines how a bayesian decision maker would update his her probability p for the occurrence of an event a in the light of a number of expert opinions expressed as probabilities q 1 cdots q n of a it is seen among other things that the linear opinion pool lambda 0p sum n i 1 lambda iq i corresponds to an application of bayes theorem when the decision maker has specified only the mean of the marginal distribution for q 1 cdots q n and requires his her formula for the posterior probability of a to satisfy a certain consistency condition a product formula similar to that of bordley 1982 is also derived in the case where the experts are deemed to be conditionally independent given a and given its complement

inconsistent property of lee and li fuzzy ranking method abstract this paper analyzes the lee and li fuzzy ranking method for the normalized trapezoidal fuzzy numbers ntfns every ntfn has associated with it another ntfn which posseses an inconsistent property an inconsistent property is that the results of comparison of these two ntfns are conflicting when two different comparison indices are used based on this property lee and li fuzzy ranking method suffers from lack of discrimination and occasionally conflicts with intuition

maximum entropy aggregation of expert predictions this paper presents a maximum entropy framework for the aggregation of expert opinions where the expert opinions concern the prediction of the outcome of an uncertain event the event to be predicted and individual predictions rendered are assumed to be discrete random variables a measure of expert competence is defined using a distance metric between the actual outcome of the event and each expert s predicted outcome following levy and delic levy w b h delic 1994 maximum entropy aggregation of individual opinions ieee trans sys man cybernetics 24 606 613 we use shannon s information measure shannon shannon c e 1948 a mathematical theory of communication bell syst tech j 27 379 423 jaynes jaynes e t 1957 information theory and statistical mechanics phys rev 106 part i 620 630 108 part ii 171 190 to derive aggregation rules for combining two or more expert predictions into a single aggregated prediction that appropriately calibrates different degrees of expert c

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

nearest interval approximation of a fuzzy number the problem of the interval approximation of fuzzy numbers is discussed a new interval approximation operator which is the best one with respect to a certain measure of distance between fuzzy numbers is suggested

classification and characterization of rationally elliptic manifolds in low dimensions we give a characterization of closed simply connected rationally elliptic 6 manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings we classify rational real and complex homotopy types of closed simply connected rationally elliptic 7 manifolds we give partial results in dimensions 8 and 9

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

metrics and orders in space of fuzzy numbers abstract two classes of metrics p q and p where 1 p 0 q 1 in space of fuzzy numbers are introduced then a method of ranking fuzzy numbers based on these metrics is proposed and investigated not only fuzzy numbers but also the left sided and right sided fuzzy numbers are considered applications in making decisions and statistics are suggested

ranking of fuzzy numbers by sign distance several different strategies have been proposed for ranking of fuzzy numbers these include methods based on the coefficient of variation cv index distance between fuzzy sets centroid point and original point and weighted mean value each of these techniques has been shown to produce non intuitive results in certain cases in this paper we propose a modification of the distance based approach called the sign distance which is both efficient to evaluate and able to overcome the shortcomings of the previous techniques the calculation of the proposed method is far simpler than the other approaches

multiple model evaluation absent the gold standard through model combination we describe a method for evaluating an ensemble of predictive models given a sample of observations comprising the model predictions and the outcome event measured with error our formulation allows us to simultaneously estimate measurement error parameters true outcome the gold standard and a relative weighting of the predictive scores we describe conditions necessary to estimate the gold standard and to calibrate these estimates and detail how our approach is related to but distinct from standard model combination techniques we apply our approach to data from a study to evaluate a collection of brca1 brca2 gene mutation prediction scores in this example genotype is measured with error by one or more genetic assays we estimate true genotype for each individual in the data set operating characteristics of the commonly used genotyping procedures and a relative weighting of the scores finally we compare the scores against the gold standard genotype and find that mendelian scores are on averag

modelling agent forecast distributions problems in the analysis and interpretation of uncertain inferences obtained from individuals or agents are considered in the context of forecasting a scalar random quantity based on new theoretical results presented by west and crosse bayesian updating is developed for cases in which agents opinions are proveded in terms of full forecast distributions discrete or continuous or parital summaries such as forecast means and variances a particular focus is on problems in which partial agent information is communicated in terms of a few sumary probabilities or alternatively quantiles of the agent s distribution example models highlight the key features of the theory and illustrate applications

combining probability forecasts summary linear pooling is by far the most popular method for combining probability forecasts however any non trivial weighted average of two or more distinct calibrated probability forecasts is necessarily uncalibrated and lacks sharpness in view of this linear pooling requires recalibration even in the ideal case in which the individual forecasts are calibrated towards this end we propose a beta transformed linear opinion pool for the aggregation of probability forecasts from distinct calibrated or uncalibrated sources the method fits an optimal non linearly recalibrated forecast combination by compositing a beta transform and the traditional linear opinion pool the technique is illustrated in a simulation example and in a case study on statistical and national weather service probability of precipitation forecasts

what bayesians expect of each other abstract our goal is to study general properties of one bayesian s subjective beliefs about the behavior of another bayesian s subjective beliefs we consider two bayesians a and b who have different subjective distributions for a parameter and study bayesian a s expectation of bayesian b s posterior distribution for given some data y we show that when can take only two values bayesian a always expects bayesian b s posterior distribution to lie between the prior distributions of a and b conditions are given under which a similar result holds for an arbitrary real valued parameter for a vector parameter we present useful expressions for the mean vector and covariance matrix of a s expectation of b s posterior distribution examples are given illustrating the relevance of the conditions under which the results are derived

modelling probabilistic agent opinion summary a single agent an individual expert or model provides a decision maker with probabilistic information partially or completely describing the agent s opinion about a collection of uncertain quantities or events this paper discusses ways in which the decision maker may model the agent s opinion to provide rules for updating his own probability for a related event or random quantity of particular interest concepts discussed include the relevance of the agent s information and experience the accord between the agent and decision maker in terms of common or conflicting information and calibration of probability assessments new theory develops and extends that of genest and schervish requiring only a partial specification of the decision maker s prior over the agent s opinion several illustrative examples are developed

characterization of externally bayesian pooling operators on donne une caracterisation de toutes les formules de groupement externes bayesiennes et on donne des conditions sous lesquelles l opinion d un groupe sera proportionnelle a la moyenne geometrique des densites individuelles

continuity properties of entropy on donne une borne superieure sur le defaut en semicontinuite superieure des entropies topologiques et metriques d une auto application c r d une variete c r r 1

rationality of geometric signatures of complete 4 manifolds according to cg4 and cfg the complete manifolds with bounded sectional curvature and finite volume admit positive rank f structures near infinity in this paper we show that in dimension four if the manifolds also have bounded covering geometry near infinity then there exist f structures with special topological properties f structures with these properties cannot be constructed solely by means of the general methods in cg4 and cfg using these special properties we prove a conjecture of cheeger gromov on the rationality of the geometric signatures in the four dimensional case

a multiplicative formula for aggregating probability assessments this paper presents an axiomatic approach to the problem of aggregating expert assessments of an event s probability into some group probability assessment a multiplicative formula is derived

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

comparison of fuzzy numbers using a fuzzy distance measure a new approach for ranking fuzzy numbers based on a distance measure is introduced a new class of distance measures for interval numbers that takes into account all the points in both intervals is developed first and then it is used to formulate the distance measure for fuzzy numbers the approach is illustrated by numerical examples showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of several existing fuzzy ranking approaches

ranking fuzzy numbers with an area between the centroid point and original point abstract to improve the ranking method of lee and li 1 cheng 2 proposed the coefficient of variation cv index shortcomings are also found in the cv index cheng 2 also proposed the distance method to improve the ranking method of murakami et al however the distance method is not sound either moreover the cv index contradicts the distance method in ranking some fuzzy numbers therefore to overcome the above shortcomings we propose ranking fuzzy numbers with the area between the centroid point and original point

modeling expert opinion arising as a partial probabilistic specification abstract expert opinion is often sought with regard to unknowns in a decision making setting for a univariate unknown our presumption is that such opinion is elicited as a partial probabilistic specification in the form of either probability assignments regarding the chance of falling in a fixed set of disjoint exhaustive intervals or selected quantiles for treating such specification as data our focus is on the development of suitable probability densities for these data given the true in particular we advocate a rich class of densities created by transformation of random mixtures of beta distributions these densities become likelihoods when viewed as a function of given the data we presume that a decision maker here a so called supra bayesian presides over the opinion collection offering his or her assessment as well all of this opinion is synthesized using bayes s theorem resulting in the posterior distribution as the pooling mechanism the models are applied to opinion collec

ranking fuzzy numbers with maximizing set and minimizing set abstract up to now these are five methods of ranking n fuzzy numbers in order but these methods contain some confusions and occasionally conflict with intuition this paper introduces the concept of maximizing set and minimizing set to decide the ordering value of each fuzzy number and uses these values to determine the order of the n fuzzy numbers in addition we give a method for calculating the ordering value of each fuzzy number with triangular trapezoidal and two sided drum like shaped membership functions

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

ricci curvature minimal volumes and seiberg witten theory we derive new sharp lower bounds for certain curvature functionals on the space of riemannian metrics of a smooth compact 4 manifold with non trivial seiberg witten invariants these allow one for example to exactly compute the infimum of the l 2 norm of ricci curvature for any complex surface of general type we are also able to show that the standard metric on any complex hyperbolic 4 manifold minimizes volume among all metrics satisfying a point wise lower bound on sectional curvature plus suitable multiples of the scalar curvature these estimates also imply new non existence results for einstein metrics

copula models for aggregating expert opinions this paper discusses the use of multivariate distributions that are functions of their marginals for aggregating information from various sources the function that links the marginals is called a copula the information to be aggregated can be point estimates of an unknown quantity i or with suitable modeling assumptions probability distributions for i this approach allows the bayesian decision maker performing the aggregation to separate two difficult aspects of the model construction procedure qualities of the individual sources such as bias and precision are incorporated into the marginal distributions dependence among sources is encoded into the copula which serves as a dependence function and joins the marginal distributions into a single multivariate distribution the procedure is designed to be suitable for situations in which the decision maker must use subjective judgments as a basis for constructing the aggregation model we review properties of copulas pertinent to the information aggregation problem a subjectively assessable measure of dependence is developed that allows the decision maker to choose from a one parameter family of copulas a specific member that is appropriate for the level of dependence among the information sources the discussion then focuses on the class of archimedean copulas and frank s family of copulas in particular showing the specific relationship between the family and our measure of dependence a realistic example demonstrates the approach