the cutoff profile for the simple exclusion process on the circle in this paper we give a very accurate description of the way the simple exclusion process relaxes to equilibrium let ptpt denote the semi group associated the exclusion on the circle with 2n2n sites and nn particles for any initial condition and for any t 4n29 2lognt 4n29 2log n we show that the probability density pt pt is given by an exponential tilt of the equilibrium measure by the main eigenfunction of the particle system as 4n29 2logn4n29 2log n is smaller than the mixing time which is n22 2lognn22 2log n this allows to give a sharp description of the cutoff profile if dn t dn t denote the total variation distance starting from the worse initial condition we have limn dn n22 2logn n2 2s erf 2 e s limn dn n22 2log n n2 2s erf 2 e s where erferf is the gauss error function

fuzzy number valued fuzzy measure and fuzzy number valued fuzzy integral on the fuzzy set abstract in this paper some new concepts the fuzzy number valued fuzzy measure autocontinuity and null additivity of fuzzy number valued fuzzy measures on the fuzzy algebra and the fuzzy number valued fuzzy integral on the fuzzy set are introduced some properties of fuzzy number valued fuzzy integrals and some convergence theorems for sequences of fuzzy number valued fuzzy integrals on a fuzzy set are discussed

a linguistic approach to decision making problems abstract different decision making and information analysis models in fuzzy environment are described which can be considered as the extension of well known methods of decision making theory for the cases when fuzzy information must be updated

numerical solutions to statistical moment equations of groundwater flow in nonstationary bounded heterogeneous media in this paper we investigate the combined effect of nonstationarity in log hydraulic conductivity and the presence of boundaries on flow in heterogeneous aquifers we derive general equations governing the statistical moments of hydraulic head for steady state flow by perturbation expansions due to their mathematical complexity we solve the moment equations by the numerical technique of finite differences the numerical approach has flexibility in handling moderately irregular geometry different boundary conditions various trends in the mean log hydraulic conductivity spatial variabilities in the magnitude and direction of mean flow and different covariance functions all of which are important factors to consider for real world applications the effect of boundaries on the first two statistical moments involving head is strong and persistent for example in the case of stationary log hydraulic conductivity the head variance is always finite in a bounded domain while the head variance may be infinite in an unbounded domain as in many other stochastic models the statistical moment equations are derived under the assumption that the variance of log hydraulic conductivity is small accounting for a spatially varying large scale trend in the log hydraulic conductivity field reduces the variance of log hydraulic conductivity although this makes the conductivity field nonstationary and significantly increases the mathematical complexity in the problem it justifies the small variance assumption for many aquifers

stochastic modeling of macrodispersion in heterogeneous porous media a method for the prediction of dispersion processes of inert solutes occurring in heterogeneous porous media is presented its main features are as follows 1 the velocity field is assumed to be a space random function its moments are expressed through the physical parameters of the log transmissivity and head random fields by linearizing the flow equation the random velocity being a linear function of the head and log transmissivity which are assumed to be jointly multivariate normal mvn is thus also mvn its pdf is completely defined by its first two moments 2 the statistics of the dispersion process are obtained by the particle tracking method through monte carlo simulations which are based on gaussian conditioning the method is applied to the borden natural gradient tracer test freyberg 1986 showing favorable results

a smooth model of decision making under ambiguity we propose and axiomatize a model of preferences over acts such that the decision maker prefers act f to act g if and only if e e u f e e u g where e is the expectation operator u is a vn m utility function is an increasing transformation and is a subjective probability over the set of probability measures that the decision maker thinks are relevant given his subjective information a key feature of our model is that it achieves a separation between ambiguity identified as a characteristic of the decision maker s subjective information and ambiguity attitude a characteristic of the decision maker s tastes we show that attitudes towards risk are characterized by the shape of u as usual while attitudes towards ambiguity are characterized by the shape of we also derive x 1 e x as the special case of constant ambiguity aversion ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures this characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by epstein zhang 2001 and ghirardato marinacci 2002 one advantage of this model is that the welldeveloped machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes the model is also distinct from many in the literature on ambiguity in that allows smooth rather than kinked indifference curves this leads to different behavior and improved tractability while still sharing the main features e g ellsberg s paradox etc the maxmin eu model e g gilboa and schmeidler 1989 with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion two illustrative applications to portfolio choice are offered

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

fuzzy valued probability in this paper the main result is introduction of fuzzy valued probability restricted with respect to probability selectors in order to treat a highly imprecise probability system the fuzzy valued probability is defined over the measurable space as a fuzzy valued set function which is not additive in classical sense but it is additive with respect to restricted arithmetics some properties and the connection with fuzzy valued measure are discussed also an application in markov decision process with imprecise information is presented

data imprecision under λ geometry model introducing a model called geometry for handling a dynamic form of imprecision which allows the precision changes applications of the geometry model in facility locations and designing robust algorithms are discussed proposing efficient algorithms for solving the problem of axis aligned bounding box under geometry model proposing efficient algorithms for solving the proximity problems under the geometry model an essential assumption in most algorithms in computational geometry is that the input data is precise which is not always true in real world problems in this paper we introduce a model called geometry model for handling a dynamic form of imprecision which allows the precision changes in the input data of geometric problems also we study two families of basic computational geometry problems under this model axis aligned bounding box aabb and proximity problems for a set of n imprecise points where each point is modeled by a convex polygonal region with o k representation complexity we propose an o n log n log k m time algorithm to solve the largest aabb problem where m is the maximum number of corner defining functions when the largest aabb is defined by points on its corners also we propose an o n log n nk k2 log k k time algorithm for finding the smallest aabb under the assumption that the regions are disjoint we show that the algorithms are optimal when k is o log n further we propose o n2k log nk nk time algorithms for finding the closest and furthest pair problems and present a lower bound of n2 for the closest pair problem when k is constant

on fuzzy measure and fuzzy integral on fuzzy set abstract on a fuzzy algebra of fuzzy sets we discuss some structural characteristics of a fuzzy measure the pseudo autocontinuity and some other concepts for a fuzzy measure are introduced and the relations between these cre discussed for the case of fuzzy sets riesz s theorems and lebesgue s theorems for a sequence of measurable functions are proved the concept of the fuzzy integral on a fuzzy set is given and some properties of fuzzy integrals on fuzzy sets are studied finally we prove some convergence theorems of a sequence of fuzzy integrals on fuzzy sets

inference by aggregation of evidence with applications to fuzzy probabilities abstract optimal aggregation plays an important role towards developing a theory of aggregation of fuzzy concepts based on non additive set functions and nonlinear choquet or fuzzy integrals this paper presents a framework supporting such aggregations and argues that such a framework is useful to decision making based on distributed sources of evidence

on the spectral gap of some cayley graphs on the weyl group w bn abstract the laplacian of a weighted cayley graph on the weyl group w b n is a n n matrix with n 2 n n equal to the order of the group we show that for a class of weighted generating sets its spectral gap lowest nontrivial eigenvalue is actually equal to the spectral gap of a 2 n 2 n matrix associated to a 2n dimensional permutation representation of w n this result can be viewed as an extension to w b n of an analogous result valid for the symmetric group known as aldous spectral gap conjecture proven in 2010 by caputo liggett and richthammer

identification of large scale spatial trends in hydrologic data it is often useful to distinguish different scales of variability in hydrologic properties such as hydraulic conductivity in the simplest two scale case large scale variations can be viewed as a trend while small scale fluctuations about this trend can be viewed as a random residual this paper describes a method for estimating spatial trends from scattered field measurements the basic concept is to treat both the trend and the residual as stationary random functions these functions are distinguished by their spatial spectral or covariance properties which may be estimated from available data or simply hypothesized we present two versions of a general algorithm for estimating spatial trends 1 a discrete version which is useful in practical applications where data are limited and irregularly spaced and 2 a continuous version which can be used to study the effects of using incorrect spectral parameters applications of the discrete algorithm to both synthetically generated data and field measurements yield satisfactory trend estimates an analysis based on the continuous algorithm shows that the estimation error lower bound for these applications depends on two dimensionless ratios that is the scale disparity ratio of the trend and residual correlation scales and the signal to noise ratio ratio of the trend and residual variances these ratios may be used to evaluate the feasibility of trend estimation before field samples are actually collected

characterizing isometries on the order polytope with an application to the theory of fuzzy measures in this paper we study the group of isometries over the order polytope of a poset we provide a result that characterizes any isometry based on the order structure in the original poset from this result we provide upper bounds for the number of isometries over the order polytope in terms of its number of connected components finally as an example of application we recover the set of isometries for the polytope of fuzzy measures and the polytope of p symmetric measures when the indifference partition is fixed

fuzzy numbers and fuzzification of the choquet integral to deal with linguistic attributes in databases the integrand of the choquet integral should be allowed to assume fuzzy numbers this paper provides a detailed discussion on one fuzzification of choquet integral in which the integrand as well as the integration result is fuzzy numbers based on the extension principle it is a generalized choquet integral for fuzzy valued integrand interval valued integrand as well as the crisp valued integrand two numerical methods are provided to calculate the membership function of the integration value of this generalized choquet integral with respect to the fuzzy measure and the signed fuzzy measure respectively the presented generalized choquet integral with respect to signed fuzzy measure can act as an aggregation tool which is especially useful in many information fusing and data mining problems such as regression and classification where not only crisp data but also heterogeneous fuzzy data are involved

decision making with fuzzy probability assessments we discuss the idea of a fuzzy probability assessment the association a collection of fuzzy probabilities with the outcomes of a random experiment fuzzy probability assessments often result from the linguistic specification of probabilities as provided by human experts the question of consistency of the fuzzy probability assessment is considered finally the problem of decision making selecting a best alternative action in the face of a fuzzy probability assessment is investigated here we focus on the issue of obtaining the expected payoff of alternatives in the face of a fuzzy probability assessment in the course of solving this problem we develop a representation of an effective probability distribution in the face of a fuzzy probability assessment

stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers 2 impervious boundary the spatial variability of the head h in a two dimensional flow in the vicinity of an impervious boundary is investigated this study is a continuation of a previous one rubin and dagan 1988 which dealt with the influence of a given head boundary by representing h and the log transmissivity y as space random function and by solving the flow equation first order closed form analytical expressions for the head variogram and the head log transmissivity y covariance are developed these expressions offer the means to evaluate the influence of the boundary on the joint y h random field the assumption of unbounded domain is examined and it is found to be a good approximation at distances larger than three log transmissivity integral scales from the boundary by using conditional probabilities a simple method to estimate the statistical moments close to the boundary is presented it requires the knowledge of the moments of y and h in the unbounded domain only the method is compared with the exact analytical solution showing favorable results

sharp phase transition in the random stirring model on trees we establish that the phase transition for infinite cycles in the random stirring model on an infinite regular tree of high degree is sharp that is we prove that there exists d 0 such that for any d ge d 0 the set of parameter values at which the random stirring model on the rooted regular tree with offspring degree d almost surely contains an infinite cycle consists of a semi infinite interval the critical point at the left hand end of this interval is at least d 1 tfrac 1 2 d 2 and at most d 1 2d 2

stochastic analysis of head spatial variability in bounded rectangular heterogeneous aquifers groundwater flow through bounded rectangular aquifers is analyzed in a stochastic framework new analytical expressions of the head covariance and variance and the log transmissivity head cross covariance are derived for the simplified first order problem effects of different boundary conditions the aquifer size and the log transmissivity correlation scale upon head moments are studied the results are compared to analytical half plane solutions demonstrating significant differences in several cases finally the problem is solved numerically using the monte carlo simulation method the realizations of the log transmissivity field are generated in two different ways through comparisons with the analytical results the accuracy of the numerical methods is shown to be excellent

stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers 1 constant head boundary the spatial variability of log transmissivity y and head h in aquifers assumes a major role in determining the solutions of the direct flow problem as well as of the inverse problem investigation of the joint y h variability has been cast in the past in numerical and analytic frames analytic solutions for the y h statistical moments in two dimensions assumed the flow to occur in an unbounded domain in this study exact analytical expressions for the y h moments are derived which account for the presence of a given head boundary in a half plane this result is achieved by a first order approximation and for an exponential y covariance the result offers the opportunity to examine the effects of boundaries on the semivariogram of h and on the y h cross covariance the assumption of unbounded domain is examined and shown to be accurate at distances larger than two y integral scales from the boundary by using conditional probabilities a general and simple method to estimate the moments close to the boundary is presented it requires the knowledge of the moments of y and h in the unbounded domain only the method is compared with the exact analytic solution showing excellent results

an existence theorem for fuzzy utility functions a new elementary proof first our paper consists in extending the ponsard s result to a convex set of objects by giving conditions under which a fuzzy complete preorder can be represented by a numerical function here we propose a new proof based on a fuzzy definition for topological separability basically the utility function we obtain is formally identical using homeomorphism of 0 1 and r and to a standard one but its foundations and thus the interpretation are different because of behavior fuzziness on the one hand and perfect separability property of a fuzzy preordered set on the other second we prove that it is always possible to exhibit an implicit fuzzy model that is hidden behind the standard one by means of the way the boolean standard models rank the elements of the quotient set

a note on head and velocity covariances in three dimensional flow through heterogeneous anisotropic porous media a procedure for the characterization of the head and velocity fields for saturated flow in heterogeneous statistically anisotropic formations is developed the fields are characterized through a series of spatial covariances as well as the velocity head velocity log conductivity and head log conductivity cross covariances all these functions are given in terms of the parameters which characterize the input log conductivity field and the average head garadient a general procedure is outlined followed by explicit derivation of head and velocity covariances for heterogeneous statistically anisotropic formations closed form analytic results are obtained for the statistically isotropic formations while the results for the anisotropic ones required taking quadrature over analytic expressions the results may be used for transport predictions and for conditioning on measurements and may be particularly useful for testing of numerical codes

a behavioral model for linguistic uncertainty abstract the paper discusses the problem of modelling linguistic uncertainty which is the uncertainty produced by statements in natural language for example the vague statement mary is young produces uncertainty about mary s age we concentrate on simple affirmative statements of the type subject is predicate where the predicate satisfies a special condition called monotonicity for this case we model linguistic uncertainty in terms of upper probabilities which are given a behavioural interpretation as betting rates possibility measures and probability measures are special types of upper probability measure we evaluate zadeh s suggestion that possibility measures should be used to model linguistic uncertainty and the bayesian claim that probability measures should be used our main conclusion is that when the predicate is monotonic possibility measures are appropriate models for linguistic uncertainty we also discuss several assessment strategies for constructing a numerical model

stochastic analysis of three dimensional flow in a bounded domain a commonly accepted first order approximation of the equation for steady state flow in a fully saturated spatially random medium has the form of poisson s equation this form allows for the advantageous use of green s functions to solve for the random output hydraulic heads in terms of a convolution over the random input the logarithm of hydraulic conductivity a solution for steady state three dimensional flow in an aquifer bounded above and below is presented consideration of these boundaries is made possible by use of green s functions to solve poisson s equation within the bounded domain the medium hydraulic conductivity is assumed to be a second order stationary random process as represented by a simple three dimensional covariance function upper and lower boundaries are taken to be no flow boundaries the mean flow vector lies entirely in the horizontal dimensions the resulting hydraulic head covariance function exhibits nonstationary effects resulting from the imposition of boundary conditions comparisons are made with existing infinite domain solutions

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

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

a behavioural model for vague probability assessments i present an hierarchical uncertainty model that is able to represent vague probability assessments and to make inferences based on them this model can be given an interpretation in terms of the behaviour of a modeller in the face of uncertainty and is based on walley s theory of imprecise probabilities it is formally closely related to zadeh s fuzzy probabilities but it has a different interpretation and a different calculus through rationality coherence arguments the hierarchical model is shown to lead to an imprecise first order uncertainty model that can be used in decision making and as a prior in statistical reasoning

decision making with interval probabilities handling uncertainty by interval probabilities is recently receiving considerable attention by researchers interval probabilities are used when it is difficult to characterize the uncertainty by point valued probabilities due to partially known information most of researches related to interval probabilities such as combination marginalization condition bayesian inferences and decision assume that interval probabilities are known how to elicit interval probabilities from subjective judgment is a basic and important problem for the applications of interval probability theory and till now a computational challenge in this work the models for estimating and combining interval probabilities are proposed as linear and quadratic programming problems which can be easily solved the concepts including interval probabilities interval entropy interval expectation interval variance interval moment and the decision criteria with interval probabilities are addressed a numerical example of newsvendor problem is employed to illustrate our approach the analysis results show that the proposed methods provide a novel and effective alternative for decision making when point valued subjective probabilities are inapplicable due to partially known information

mixing of the symmetric exclusion processes in terms of the corresponding single particle random walk we prove an upper bound for the e mixing time of the symmetric exclusion process on any graph g with any feasible number of particles our estimate is proportional to trw g ln v e where v is the number of vertices in g and trw g is the 1 4 mixing time of the corresponding single particle random walk this bound implies new results for symmetric exclusion on expanders percolation clusters the giant component of the erdos renyi random graph and poisson point processes in rd our technical tools include a variant of morris s chameleon process

a new fuzzy programming method to derive the priority vector from an interval reciprocal comparison matrix in this paper we discuss the interval reciprocal comparison matrices and suggest a new fuzzy programming method nfpm to derive the priority vector from an interval reciprocal comparison matrix based on mikhailov s membership function we first give a membership function which is used to measure the decision maker s satisfaction degree for the priority vector derived from each interval constraint then by using the membership function we propose a new fuzzy programming method to get the most satisfaction degree of each priority vector the nfpm has many prominent characteristics especially it is capable of deriving the priority vector from a consistent or inconsistent interval reciprocal comparison matrix moreover the nfpm can overcome some drawbacks of mikhailov s fuzzy programming method fpm for inconsistent interval reciprocal comparison matrices finally several examples are given to illustrate the applicability and advantage of the proposed method

iterative refinement of possibility distributions by learning for pixel based classification this paper proposes an approach referred as iterative refinement of possibility distributions by learning irpdl for pixel based image classification the irpdl approach is based on the use of possibilistic reasoning concepts exploiting expert knowledge sources as well as ground possibilistic seeds learning the set of seeds is constructed by incrementally updating and refining the possibility distributions synthetic images as well as real images from the rider breast mri database are being used to evaluate the irpdl performance its performance is compared with three relevant reference methods region growing semi supervised fuzzy pattern matching and markov random fields the irdpl performance in terms of recognition rate 87 3 is close to the markovian method 88 8 that is considered to be the reference in pixel based image classification irpdl outperforms the other two methods respectively at the recognition rates of 83 9 and 84 7 in addition the proposed irpdl requires fewer parameters for the mathematical representation and presents a reduced computational complexity

stochastic analysis of spatial variability in two dimensional steady groundwater flow assuming stationary and nonstationary heads two dimensional steady groundwater flow in a confined aquifer with spatially variable transmissivity t is analyzed stochastically using spectral analysis and the theory of intrinsic random functions conditions that ensure a stationary statistically homogeneous head process are derived and using two convenient forms for the covariance function of the ln t process the head covariance function is studied in addition the head variogram is obtained for a particular nonstationary case and the asymptotic head variogram is derived under very general conditions results are compared to those obtained by gelhar 1976 for one and two dimensional phreatic flow and bakr et al 1978 for one and three dimensional confined flow multidimensional flow analysis results in a significantly reduced head variance the head correlation remains high over much greater distances than the ln t correlation the variogram obtained when stationary heads are assumed is identical to that obtained for nonstationary heads for dimensionless lag distances up to 2 times the correlation scale of the log transmissivity the variogram for nonstationary heads continues to grow logarithmically as lag distance increases independent of the form of the input covariance in the nonstationary case the conditions for stationarity are contrasted with the corresponding results obtained for the one and three dimensional cases of gutjahr and gelhar 1981 the head variance calculated from the stationary theory is found to agree with that of previous monte carlo simulations

from fuzzy set theory to non additive probabilities how have economists reacted abstract in this paper we are going to try to conduct a comparative review of the two programmes devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second while putting forward some explanations and conjecture as to their development and their future in section 1 we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of general equilibrium as it is the programme on which ponsard worked the most in section 2 we shall seek to show that the second programme devoted to the introduction of nonadditive probabilities in decision theory on the contrary has attempted to come up with independent findings this would explain why this last programme has managed to fit into topics at a standstill or in crisis easily which is undeniably the case of the standard theory of decision making while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model in the case of the first programme one might thus speak of an extension principle and in the second case of a resolution principle

fuzzy expected utility abstract the aim of this paper is to state the foundations of fuzzy decision theory under uncertainty attention is focused on the analysis of a fuzzy expected utility given a fuzzy decision problem which does not rest on a borel field but on a weak borel field and according to the information available we shall use successively the probability and the possibility of a fuzzy subset when the imprecise preference structure of the decision maker verifies four axioms we can determine a function of fuzzy expected utility this latter is a numerical translation of the imprecise preferences of the decision maker in an uncertain world

applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy ahp the lack of consistency in decision making can lead to inconsistent conclusions in fuzzy analytic hierarchy process fuzzy ahp method it is difficult to ensure a consistent pairwise comparison furthermore establishing a pairwise comparison matrix requires nx n 1 2 judgments for a level with n criteria alternatives the number of comparisons increases as the number of criteria increases therefore the decision makers judgments will most likely be inconsistent to alleviate inconsistencies this study applies fuzzy linguistic preference relations fuzzy linprera to construct a pairwise comparison matrix with additive reciprocal property and consistency in this study the fuzzy ahp method is reviewed and then the fuzzy linprera method is proposed finally the presented method is applied to the example addressed by kahraman et al c kahraman d ruan i dogan fuzzy group decision making for facility location selection information sciences 157 2003 135 153 this study reveals that the proposed method yields consistent decision rankings from only n 1 pairwise comparisons which is the same result as in kahraman et al research the presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy ahp method

flow in heterogeneous media displaying a linear trend in the log conductivity the purpose of this study is to derive a general solution for the problem of flow in nonstationary geological formations where the nonstationary manifests itself in the form of a spatial trend in the mean log conductivity a stochastic frame of reference is adopted to account for the spatial variability of the hydraulic conductivity for a complete stochastic description we derive the expected values and spatial covariances of the hydraulic head and the fluid flux vector as well as a relation between the expected values of the head and the fluxes these expressions are obtained using a perturbation expansion of the log conductivity about its nonstationary mean and they are correct to the first order in the variance of the log conductivity the expressions we derive are applicable for any space dimensionality and for arbitrary orientation of the trend in space a general methodology is outlined for derivation of these expressions for any type of spatial covariance and for demonstration explicit results are obtained for a gaussian isotropic covariance 16 refs 6 figs

on the convergence of the fuzzy valued functional defined by μ integrable fuzzy valued functions in this paper in the sense of sugeno s fuzzy measure we first introduce the integrable fuzzy valued function define the fuzzy valued functional a kind of new fuzzy integral and then we discuss some important elementary properties with respect to this kind of functional finally we give its convergence theorem

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

optimizing the convergence rate of the quantum consensus motivated by the recent advances in the field of quantum computing quantum systems are modeled and analyzed as networks of decentralized quantum nodes which employ distributed quantum consensus algorithms for coordination in the literature both continuous and discrete time models of the algorithm have been proposed this paper aims at optimizing the convergence rate of the discrete time quantum consensus algorithm over a quantum network with n qudits the induced graphs are categorized in terms of the partitions of integer n by arranging them as the schreier graphs it is shown that the original optimization problem reduces to optimizing the second largest eigenvalue modulus of the weight matrix exploiting the specht module representation of partitions of n the aldous conjecture is generalized to all partitions of integer n implying that the spectral gap of all resultant induced graphs is the same the spectral radius of the laplacian is obtained from the feasible least dominant partition in the hasse diagram of integer n by analytically addressing the semidefinite programming formulation of the problem closed form expressions for the optimal results are provided for a wide range of topologies

on the existence of subjective upper and lower probabilities consistency between preference under uncertainty modeled by choquet expected utility theory and preference under imprecise risk a particular situation of uncertainty characterized by the existence of objective upper and lower probabilities modeled by linear utility theory is shown to imply that the choquet capacity must coincide on the imprecisely probabilized events with a fixed linear combination of their upper and lower probabilities this result is used to derive conditions for the existence of subjective upper and lower probabilities on all the events

subjective probabilities on subjectively unambiguous events this paper suggests a behavioral definition of subjective ambiguity in an abstract setting where objects of choice are savage style acts then axioms are described that deliver probabilistic sophistication of preference on the set of unambiguous acts in particular both the domain and the values of the decision maker s probability measure are derived from preference it is argued that the noted result also provides a decision theoretic foundation for the knightian distinction between risk and ambiguity

macrodispersion in a radially diverging flow field with finite peclet numbers 1 perturbation theory approach we study the transport behavior of a tracer in a radially diverging heterogeneous velocity field making use of homogenization theory we derive effective transport equations these effective transport equations are very similar to those defined on the local scale however the local transport parameters such as local dispersion coefficients are replaced by effective dispersion coefficients for smoothly varying heterogeneous media explicit results for effective radial dispersion coefficients are derived starting with the purely advective transport behavior infinite peclet numbers we extend our calculations to transport with finite peclet numbers we find that the impact of molecular diffusion on the effective dispersivity differs from the impact of local dispersion including local dispersion leads to effective dispersivities which are constant and equivalent to the effective dispersivities found in uniform flow configurations in contrast effective dispersivities including diffusion are not constant but depend on the radial distance we compare the results found by homogenization theory with those derived by neuweiler et al this issue by standard method of moments

density fluctuations for exclusion processes with long jumps we show that the stationary density fluctuations of exclusion processes with long jumps whose rates are of the form c pm y x 1 alpha where c pm depends on the sign of y x are given by a fractional ornstein uhlenbeck process for alpha in 0 frac 3 2 when alpha frac 3 2 we show that the density fluctuations are tight in a suitable topology and that any limit point is an energy solution of the fractional burgers equation previously introduced in gubinelli and jara stoch partial differ equ anal comput 1 2 325 350 2013 in the finite volume setting

spectral analysis of random to random markov chains abstract we compute the eigenvalues and eigenspaces of random to random markov chains we use a family of maps which reveal a remarkable recursive structure of the eigenspaces yielding an explicit and effective construction of all eigenbases starting from bases of the kernels

objective and subjective rationality in a multiple prior model a decision maker dm is characterized by two binary relations the first reflects choices that are rational in an objective sense the dm can convince others that she is right in making them the second relation models choices that are rational in a subjective sense the dm cannot be convinced that she is wrong in making them in the context of decision under uncertainty we propose axioms that the two notions of rationality might satisfy these axioms allow a joint representation by a single set of prior probabilities and a single utility index it is objectively rational to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set it is subjectively rational to choose f rather than g if and only if the minimal expected utility of f with respect to all priors in the set is at least as high as that of g in other words the objective and subjective rationality relations admit respectively a representation a la bewley 2002 and a la gilboa and schmeidler 1989 our results thus provide a bridge between these two classic models as well as a novel foundation for the latter

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

fuzzy preference based rough sets preference analysis is an important task in multi criteria decision making the rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations the existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria in this paper we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria fuzzy preference relations are incorporated into a fuzzy rough set model which leads to a fuzzy preference based rough set model the measure of attribute dependency of the pawlak s rough set model is generalized to compute the relevance between criteria and decisions the definitions of upward dependency downward dependency and global dependency are introduced algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets

novel weighted averages versus normalized sums in computing with words in this paper some properties of novel weighted averages that are related to the concepts of possibility theory are examined it is shown that novel weighted averages have certain interpretations in terms of addition of interactive interval or fuzzy constraints to do this alternative forms of novel weighted averages are provided in particular an alternative form of novel weighted averages represented by the extension principle is determined it is shown that when fuzzy set models of words are obtained by collecting data from subjects in a computing with words setting interactive addition of fuzzy sets is not a well defined method and the optimization problems related to it may have no solutions although interactive addition is recommended in the literature for solving multicriteria decision making problems and for dealing with uncertain probabilities on the other hand novel weighted averages perform a specific normalization that guarantees that they always exist

modeling attitude to risk in human decision processes an application of fuzzy measures abstract several models of the human decision process have been proposed classical examples of which are utility theory and prospect theory in recent times the theory of fuzzy measures and integrals has emerged as an alternative meriting further investigation specifically one is interested in the degrees of disjunction and conjunction and the veto and favor indices that represent the tolerance measure of the decision maker though several theoretical expositions have appeared in contemporary literature empirical studies applying these concepts to the real world are scarce this paper reports two studies based on a model of strategic telecommunication investment decisions from a research work involving a survey of executives the first study involves building fuzzy models corresponding to each individual decision maker with the results grouped based on the decision makers propensity to risk as determined by their degrees of disjunction the shapley indices and the interaction effects are determined for each pooled dataset corresponding to each group to contrast this approach with those of conventional nomothetic comparisons of decision policies the decision makers are grouped based on a clustering analysis of the individual linear regression models the data for each cluster are pooled and the fuzzy measures learned from the dataset are analyzed for comparison purposes the results not only serve as a demonstration of fuzzy measure analysis as a viable approach to studying qualitative decision making but also provide useful methodological insights into applying fuzzy measures to strategic investment decisions under risk

using the nonstationary spectral method to analyze flow through heterogeneous trending media this paper describes a nonstationary spectral theory for analyzing flow in a heterogeneous porous medium with a systematic trend in log hydraulic conductivity this theory relies on a linearization of the groundwater flow equation but does not require the stationarity assumptions used in classical spectral theories the nonstationary theory is illustrated with a two dimensional analysis of a linear trend aligned with the mean flow direction in this case closed form solutions can be obtained for the effective hydraulic conductivity head covariance and log conductivity head cross covariance the effective hydraulic conductivity decreases from the geometrical mean as the mean slope of the log conductivity increases trending leads to a reduction of head variance and a structural change in the head covariance and the log conductivity head cross covariance such changes have important implications for measurement conditioning or cokriging methods which rely on the head covariance and log conductivity head covariance the nonstationary spectral analysis is also compared with classical spectral analysis this comparison indicates that the classical spectral method correctly predicts the normalized head covariance in a linear trending media the stationary spectral method fails to capture the qualitative influence of trends on the effective hydraulic conductivity and the log conductivity head cross covariance although the magnitude of the error is relatively small for realistic values of the mean log conductivity slope the stationary and nonstationary results are the same when there is no trend in log conductivity the trending conductivity example illustrates that the nonstationary spectral method has all the capabilities of the classical spectral approach while not requiring as many restrictive assumptions

a multiscale probabilistic collocation method for subsurface flow in heterogeneous media 1 owing to the spatial variability of the media properties uncertainty quantification for subsurface flow and solute transport usually requires high resolution simulations in this work a multiscale probabilistic collocation method mspcm is developed for solving such problems in a computationally efficient manner the subsurface flow problem is cast in a stochastic framework and probabilistic collocation strategy is used to represent the original stochastic differential equation the resulting equations are a set of decoupled deterministic equations with respect to collocation points a multiscale finite element method is utilized to solve these deterministic problems on a coarse mesh coarse scale basis functions are constructed on a field in which the conductivity varies spatially at each set of stochastic collocation points the coarse scale solution is then obtained by solving a modified coarse formulation that takes into account the fine scale heterogeneity the fine scale solution is reconstructed after the coarse scale solution is available since the pcm and multiscale finite element method are implemented at different levels the mspcm inherits their respective advantages in which a stochastic problem is decomposed by fewer realizations and is solved on a coarser grid the performance of the proposed method is demonstrated with numerical examples the capability of mspcm in reproducing the probability density functions pdfs of head and velocity is investigated the numerical results show that the mspcm with proper coarsening level is able to capture small scale heterogeneity with a coarse mesh and to generate satisfactory probability density functions of head and velocity

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

decision analysis based on fused double exponential possibility distributions abstract in this paper the possibility grades given by an expert are approximated by double possibility distributions called upper and lower possibility distributions to characterize uncertainty knowledge from this expert the upper and lower possibility distributions have some similarities to upper and lower approximations in rough set theory multi source knowledge from multiple experts is represented by a set of exponential possibility distributions based on the consistency index defined by the possibility measure of each pair of possibility distributions a fusion model is proposed to integrate multiple possibility distributions into a new one representing a refined knowledge as an application a portfolio selection problem with multiple experts is considered

exact eigenspectrum of the symmetric simple exclusion process on the complete complete bipartite and related graphs we show that the infinitesimal generator of the symmetric simple exclusion process recast as a quantum spin ferromagnetic heisenberg model can be solved by elementary techniques on the complete complete bipartite and related multipartite graphs some of the resulting infinitesimal generators are formally identical to homogeneous as well as mixed higher spins models the degeneracies of the eigenspectra are described in detail and the clebsch gordan machinery needed to deal with the arbitrary spin s representations of the su 2 is briefly developed we mention in passing how our results fit within the related questions of a ferromagnetic ordering of energy levels and a conjecture according to which the spectral gaps of the random walk and the interchange process on finite simple graphs must be equal

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

extracting easily interpreted diagnostic rules abstract diagnosis support systems are often disregarded because of their high costs complicated inference and inability to modify the knowledge base the aim of this work is to propose a method that helps to resolve these problems by extracting diagnostic rules that can be easily interpreted and verified by experts the rules can be obtained from data even if the latter are imperfect which is usual in medical databases next intuitively clear reasoning is suggested to elaborate on the diagnosis rules are focal elements in the framework of the dempster shafer theory they include fuzzy sets in their premises thus a measure of imprecision as a fuzzy membership function and a measure of uncertainty as the basic probability value are used moreover a rule selection algorithm and a rule evaluation method that prevent some of the imperfections of the existing methods are proposed particular attention is paid to the evaluation of the extracted rule set according to its reliability and clarity for a human user experimental results obtained for popular medical data sets demonstrate the advantages of the proposed approach for each data set simple and readable rule sets are determined they provide comparable or better results than the approaches published so far

spectral gap for multi species exclusion processes we consider a multi species generalization of the symmetric simple exclusion process in homogeneous and non homogeneous hypercubes of zd in this model the hyperplanes of configurations with given numbers of particles of each species are not necessarily irreducible we give a sufficient condition of the dynamics to make them irreducible in addition assuming the irreducibility of them we show some estimates of the spectral gap the absolute value of the second largest eigenvalue of the generator which plays an important role in the study of hydrodynamic limit

computing spectral bounds of the heisenberg ferromagnet from geometric considerations we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperimetric problem holds then our proposed method of estimating the energy eigenvalues via approximating the edge isoperimetric properties of vertex induced subgraphs will yield a polynomial time algorithm for estimating the smaller energy eigenvalues of the heisenberg ferromagnet we give a polynomial time algorithm for computing upper bounds on some of the smaller energy eigenvalues in a spin 1 2 ferromagnetic heisenberg model with any graph g for the underlying interactions an important ingredient is the connection between heisenberg models and the symmetric products of g our algorithms for computing upper bounds are based on generalized diameters of graphs computing the upper bounds amounts to solving the minimum assignment problem on g which has well known polynomial time algorithms from the field of combinatorial optimization we also study the possibility of computing the lower bounds on some of the smaller energy eigenvalues of heisenberg models this amounts to estimating the isoperimetric inequalities of the symmetric product of graphs by using connections with discrete sobolev inequalities we show that this can be performed by considering just the vertex induced subgraphs of g if our conjecture for a polynomial time approximation algorithm to solve the edge isoperi

optimizing the convergence rate of the continuous time quantum consensus inspired by the recent developments in the field of distributed quantum computing distributed quantum systems are analyzed as networks of quantum systems this gives rise to the distributed quantum consensus algorithms focus of this paper is on optimizing the convergence rate of the continuous time quantum consensus algorithm over a quantum network with n qudits it is shown that the optimal convergence rate is independent of the value of d in qudits by classifying the induced graphs as the schreier graphs they are categorized in terms of the partitions of integer n the intertwining relation is established between one level dominant partitions in the hasse diagram of integer n based on this result the proof of the aldous conjecture is extended to all possible induced graphs and the original optimization problem is reduced to optimizing algebraic connectivity of the smallest induced graph utilizing the generalization of aldous conjecture it is shown that the convergence rates of the algorithm to both the consensus state and the reduced quantum state consensus are the same by providing the analytical solution to semidefinite programming formulation of the obtained problem closed form expressions for the optimal results are provided for a range of topologies

a linguistic multi criteria decision making approach based on logical reasoning in real decision making problems it is always more natural for decision makers to use linguistic terms to express their preferences opinions in a qualitative way among alternatives than to provide quantitative values additionally many of these decision making problems are under uncertain environments with vague and imprecise information involved following the idea of computing with words cww methodology we propose in this paper a linguistic valued qualitative aggregation and reasoning framework for multi criteria decision making problems where a linguistic valued algebraic structure is constructed for modelling the linguistic information involved in multi criteria decision making problems and a linguistic valued logic based approximate reasoning method is developed to infer the final decision making result this method takes the advantage of handling the linguistic information no matter totally ordered or partially ordered directly without numerical approximation and having a non classical logic as its formal foundation for decision making process

proof of aldous spectral gap conjecture aldous spectral gap conjecture asserts that on any graph the random walk process and the random transposition or interchange process have the same spectral gap we prove the conjecture using a recursive strategy the approach is a natural extension of the method already used to prove the validity of the conjecture on trees the novelty is an idea based on electric network reduction which reduces the problem to the proof of an explicit inequality for a random transposition operator involving both positive and negative rates the proof of the latter inequality uses suitable coset decompositions of the associated matrices with rows and columns indexed by permutations

stochastic modeling of groundwater flow by unconditional and conditional probabilities 1 conditional simulation and the direct problem mathematical modeling of groundwater flow in heterogeneous porous formations of large extent is investigated the formation properties hydraulic conductivity transmissivity as well as flow variables head specific discharge solute concentration are regarded as random variables subjected to uncertainty the main aim of the study is to analyze the influence of conditional probability of input variables upon the statistical structure of the dependent variables the unconditional probability density functions are supposed to be stationary multivariate normal while conditioning accounts for the measured values at a few points of the formation two problems of groundwater flow are discussed in part 1 conditional simulation and the direct problem for steady flow analytical results are obtained by using perturbation approximations average uniform head gradient flows as well as recharge and flow to wells are discussed in unconditional modeling the input variable the conductivity or transmissivity log is regarded as stationary and is represented by its constant mean and variogram the ensemble of formations on which statistical calculations are carried out represents all aquifers with same probability density distributions in conditional modeling the measured values at a few points are kept fixed and uncertainty prevails only at other points consequently statistical computations are performed for the subensemble of aquifers which preserve the measured values and as a result both input and output variables are nonstationary the main effect of conditioning is to reduce the variance i e the uncertainty of these variables this effect is particularly important in the case of flow toward wells application of the modeling method to field problems is outlined

indeterminate probabilities on finite sets this paper presents a quasi bayesian model of subjective uncertainty in which beliefs which are represented by lower and upper probabilities qualified by numerical confidence weights the representation is derived from a system of axioms of binary preferences which differs from standard axiom systems insofar as completeness is not assumed and transitivity is weakened confidence weighted probabilities may be elicited through the acceptance of bets with limited stakes a generalization of the operational method of de finetti the model is applicable to the reconciliation of inconsistent probability judgments and to the sensitivity analysis of bayesian decision models

functions defined on a set of z numbers abstract a wide class of problems in science and engineering requires mathematical formalization one of the important aspects in this regard is that we should account for various types of uncertainties which are simultaneously present in real world problems and result from imprecise and partially reliable information this mandates a need for a theoretical basis of uncertain functional dependencies the theories of interval valued functions functions of random variables and fuzzy functions are well developed the main disadvantage of these theories is that each of them can deal with only a single type of uncertainty in order to ground the formal basis for dealing with real world information zadeh suggested the concept of a z number as an ordered pair z a b of fuzzy numbers used to describe a value of a random variable x where a is a fuzzy constraint on values of x and b is a fuzzy value of probability measure of a unfortunately there is no study on functions of z numbers in existence in this paper for the first time we propose a general methodology for a construction of such functions on the basis of the extension principle applied to z numbers the proposed methodology is helpful in restricting the increase of uncertainty in computation the values of z valued functions some properties of functions of z numbers are considered we construct typical and commonly encountered functions such as addition of z numbers minimum of z numbers square root of z numbers and others a spectrum of examples is provided to illustrate the proposed approach

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

a stochastic analysis of steady state two phase flow in heterogeneous media 1 we present a novel approach to modeling stochastic multiphase flow problems for example nonaqueous phase liquid flow in a heterogeneous subsurface medium with random soil properties in particular with randomly heterogeneous intrinsic permeability and soil pore size distribution a stochastic numerical model for steady state water oil flow in a random soil property field is developed using the karhunen loeve moment equation klme approach and is numerically implemented an exponential model is adopted to define the constitutive relationship between phase relative permeability and capillary pressure the log transformed intrinsic permeability y x and soil pore size distribution b x are assumed to be gaussian random functions with a separable exponential covariance function the perturbation part of these two log transformed soil properties is then decomposed into an infinite series based on a set of orthogonal normal random variables xn the phase pressure capillary pressure and phase mobility are decomposed by polynomial expansions and the perturbation method combining these expansions of y x b x and dependent pressures the steady state water oil flow equations and corresponding boundary conditions are reformulated as a series of differential equations up to second order these differential equations are solved numerically and the solutions are directly used to construct moments of phase pressure and capillary pressure we demonstrate the validity of the proposed klme model by favorably comparing firstand second order approximations to monte carlo simulations the significant computational efficiency of the klme approach over monte carlo simulation is also illustrated

measures of uncertainty in expert systems abstract this paper compares four measures that have been advocated as models for uncertainty in expert systems the measures are additive probabilities used in the bayesian theory coherent lower or upper previsions belief functions used in the dempster shafer theory and possibility measures fuzzy logic special emphasis is given to the theory of coherent lower previsions in which upper and lower probabilities expectations and conditional probabilities are constructed from initial assessments through a technique of natural extension mathematically all the measures can be regarded as types of coherent lower or upper previsions and this perspective gives some insight into the properties of belief functions and possibility measures the measures are evaluated according to six criteria clarity of interpretation ability to model partial information and imprecise assessments especially judgements expressed in natural language rules for combining and updating uncertainty and their justification consistency of models and inferences feasibility of assessment and feasibility of computations each of the four measures seems to be useful in special kinds of problems but only lower and upper previsions appear to be sufficiently general to model the most common types of uncertainty

fuzzy linear spaces over valued fields abstract the concept of fuzzy linear spaces was introduced by nanda 3 the purpose of the present paper is to introduce some further concepts such as convex fuzzy sets etc in fuzzy linear spaces over any valued field