fuzzy risk analysis based on similarity measures of generalized fuzzy numbers in this paper we present a new method for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers firstly we present a method called the simple center of gravity method scgm to calculate the center of gravity cog points of generalized fuzzy numbers then we use the scgm to propose a new method to measure the degree of similarity between generalized fuzzy numbers the proposed similarity measure uses the scgm to calculate the cog points of trapezoidal or triangular generalized fuzzy numbers and then to calculate the degree of similarity between generalized fuzzy numbers we also prove some properties of the proposed similarity measure and use an example to compare the proposed method with the existing similarity measures the proposed similarity measure can overcome the drawbacks of the existing methods we also apply the proposed similarity measure to develop a new method to deal with fuzzy risk analysis problems the proposed fuzzy risk analysis method is more flexible and more intelligent than the existing methods due to the fact that it considers the degrees of confidence of decisionmakers opinions

attractors and asymptotic stability for fuzzy dynamical systems abstract in this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on the main results are in section 4 see theorem 21 and we give an illustrative example in the last section

stochastic inversion for electromagnetic geophysics practical challenges and improving convergence efficiency traditional deterministic geophysical inversion algorithms are not designed to provide a robust evaluation of uncertainty that reflects the limitations of the geophysical technique stochastic inversions which do provide a sampling based measure of uncertainty are computationally expensive and not straightforward to implement for nonexperts nonstatisticians our results include stochastic inversion for magnetotelluric and controlled source electromagnetic data two markov chain sampling algorithms metropolis hastings and slice sampler can significantly decrease the computational expense compared to using either sampler alone the statistics of the stochastic inversion allow for 1 variances that better reveal the measurement sensitivities of the two different electromagnetic techniques than traditional techniques and 2 models defined by the median and modes of parameter probability density functions which produce amplitude and phase data that are consistent with the observed data in general pa

a fuzzy approach to select the location of the distribution center abstract the location selection of distribution center dc is one of the most important decision issues for logistics managers owing to vague concept frequently represented in decision data a new multiple criteria decision making method is proposed to solve the distribution center location selection problem under fuzzy environment in the proposed method the ratings of each alternative and the weight of each criterion are described by linguistic variables which can be expressed in triangular fuzzy numbers the final evaluation value of each dc location is also expressed in a triangular fuzzy number by calculating the difference of final evaluation value between each pair of dc locations a fuzzy preference relation matrix is constructed to represent the intensity of the preferences of one plant location over another and then a stepwise ranking procedure is proposed to determine the ranking order of all candidate locations finally a numerical example is solved to illustrate the procedure of the proposed method at the end of this paper

shape preserving additions of fuzzy intervals abstract triangular norm based additions preserving the lr shape of lr fuzzy intervals are studied the connection between t norm based additions preserving the linearity of fuzzy intervals and additions preserving lr shape for invertible shapes l and r is given a possibility of controlling the growth of the spread during the calculations with lr fuzzy intervals is shown

estimation of a fuzzy regression model using fuzzy distances regression analysis is a powerful statistical tool that has many applications in different areas the problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input output data crisp or fuzzy however we realize that in general most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances minimizing a real error function and the interpretation of fuzzy data as possibility distributions the main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers the new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error the estimation process in general can be considered easier to apply in practice and it is not limited to triangular fuzzy numbers numerical examples are provided to illustrate the usefulness and applicability of these results and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory

on a new methodology for ranking fuzzy numbers and its application to real economic data abstract ranking fuzzy numbers plays an important role in the decision process several strategies can be found in the abundant literature existing on this topic which can be basically classified into two main groups approaches based on the so called ranking indices and based on fuzzy binary relations ranking indices are functions from fuzzy numbers to real values these defuzzification methods are critiqued by its implicit information loss which leads to results that might not be consistent with human intuition in certain cases in a fuzzy context approaches based on binary relations can be considered more suitable solutions following this strategy this paper introduces a new technique for ranking fuzzy numbers which is applicable to the whole set of fuzzy numbers it is proved that many desired properties in particular we give several new properties are satisfied and numerical examples show reasonable results the developed technique is very easy to compute and interpret in practice and it overcomes certain shortcomings that appear when applying other more complex algorithms in the case of triangular or trapezoidal fuzzy numbers the procedure is particularly simple and intuitive finally a real life example involving data of chinese economy is also carried out

trapezoidal approximations of fuzzy numbers the problem of the trapezoidal approximation of fuzzy numbers is discussed a set of criteria for approximation operators is formulated these constraints can be used for direct operator derivation a new nearest trapezoidal approximation operator preserving expected interval is suggested

representation and application of fuzzy numbers abstract in this paper we present the theoretical background of fuzzy numbers connected with the possibility and dempster shafer theories we describe some types of representation of fuzzy numbers and we study the notions of the distance and orders between fuzzy numbers based on these representations the second part is devoted to the application of fuzzy numbers in data analysis artificial intelligence and decision making

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

two dimensional discrete fuzzy numbers and applications in this paper the concept of two dimensional discrete fuzzy numbers is presented based on the idea of representation theorem of one dimensional discrete fuzzy numbers then a sufficient condition is proposed which makes a fuzzy set on r2 become a two dimensional discrete fuzzy number and the representations of joint membership function and the two edge membership functions of two dimensional discrete fuzzy number are given some special two dimensional discrete fuzzy numbers are also defined and then some weak orders in the two dimensional discrete fuzzy number space are set up based on the mass centers and the degree of ambiguities of two dimensional discrete fuzzy numbers and their properties are also investigated at last some practical examples are included to demonstrate the effectiveness and potential of the theoretic results obtained

a fused cp factorization method for incomplete tensors low rank tensor completion methods have been advanced recently for modeling sparsely observed data with a multimode structure however low rank priors may fail to interpret the model factors of general tensor objects the most common method to address this drawback is to use regularizations together with the low rank priors however due to the complex nature and diverse characteristics of real world multiway data the use of a single or a few regularizations remains far from efficient and there are limited systematic experimental reports on the advantages of these regularizations for tensor completion to fill these gaps we propose a modified cp tensor factorization framework that fuses the l 2 norm constraint sparseness l 1 norm manifold and smooth information simultaneously the factorization problem is addressed through a combination of nesterov s optimal gradient descent method and block coordinate descent here we construct a smooth approximation to the l 1 norm and tv norm regularizations and then the tensor factor is updated using the projected gradient method where the step size is determined by the lipschitz constant extensive experiments on simulation data visual data completion intelligent transportation systems and gps data of user involvement are conducted and the efficiency of our method is confirmed by the results moreover the obtained results reveal the characteristics of these commonly used regularizations for tensor completion in a certain sense and give experimental guidance concerning how to use them

on the specificity of a possibility distribution abstract the specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation as such it is a measure of amount of uncertainty or information we investigate a number of issues related to specificity measures we discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution we describe unifying view for constructing specificity measures we look at the relationship of the specificity of a distribution and its negation we consider the case where the base set is continuous

an application of fuzzy sets in students evaluation existing two systems of evaluation of students answerscripts grading method and traditional marking method are considered and a better method of evaluation called fem is suggested fem is a computer based fuzzy approach where a vector valued marking is used finally fem is generalized and the generalized method is called gfem in which a matrix valued marking is adopted the paper shows a good and successful application of fuzzy set theory initiated by zadeh in 1965

ranking fuzzy numbers based on decomposition principle and signed distance by using the decomposition principle and the crisp ranking system on r we construct a new ranking system for fuzzy numbers which is very realistic and also matching our intuition as in r

fuzzy regression models using the least squares method based on the concept of distance fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment in order to increase the explanatory performance of the model the least squares method is applied to determine the numeric coefficients based on the concept of distance unlike most existing approaches the numeric coefficients in the proposed model can have negative values the proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few alpha cuts the proposed approach is not limited to triangular fuzzy numbers it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods comparisons with existing methods show that based on the total estimation error using the mean squared error and kim and bishu s criterion the explanatory performance of the proposed model is satisfactory

convergence of slice sampler markov chains we analyse theoretical properties of the slice sampler we find that the algorithm has extremely robust geometric ergodicity properties for the case of just one auxiliary variable we demonstrate that the algorithm is stochastically monotone and we deduce analytic bounds on the total variation distance from stationarity of the method by using foster lyapunov drift condition methodology

set valued choquet integrals revisited this paper performs a further investigation on the set valued choquet integral given by jang and kwon fuzzy sets and systems 112 2000 233 some incorrect properties are revised it is pointed out that the definition for convergence of sequence of sets or set valued functions is unreasonable by using the usual kuratowski s convergence some new convergence theorems for the set valued choquet integral are shown meanwhile some other properties are obtained

triangular norms on partially ordered sets in this paper several methods to construct triangular norms on partially ordered sets are proposed these methods include 1 constructing triangular norms on the poset of closed intervals of a given bounded poset 2 constructing triangular norms via galois connections between bounded posets based on a categorical analysis of the construction of triangular norms on closed intervals via monotone functions and their pseudo inverses 3 constructing triangular norms on function spaces between partially ordered sets

fuzzy cardinality and the modeling of imprecise quantification abstract the concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners a systematic investigation of this notion is performed which unifies and improves previous attempts the cardinality of a fuzzy set viewed as a fuzzy integer is related to scalar cardinality indices the closely related question of the probability of a fuzzy event is dealt with lastly the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

a generalization of hukuhara difference and division for interval and fuzzy arithmetic we propose a generalization of the hukuhara difference first the case of compact convex sets is examined then the results are applied to generalize the hukuhara difference of fuzzy numbers using their compact and convex level cuts finally a similar approach is suggested to attempt a generalization of division for real intervals and fuzzy numbers applications to solving interval and fuzzy linear equations and fuzzy differential equations are shown

a new linguistic computational model based on discrete fuzzy numbers for computing with words in recent years several different linguistic computational models for dealing with linguistic information in processes of computing with words have been proposed however until now all of them rely on the special semantics of the linguistic terms usually fuzzy numbers in the unit interval and the linguistic aggregation operators are based on aggregation operators in 0 1 in this paper a linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model in this framework no underlying membership functions are needed and several aggregation operators defined on the set of all discrete fuzzy numbers are presented these aggregation operators are constructed from aggregation operators defined on a finite chain in accordance with the granularity of the linguistic term set finally an example of a multi expert decision making problem in a hierarchical multi granular linguistic context is given to illustrate the applicability of the proposed method and its advantages

some applications of the study of the image of a fuzzy number in this paper we present a characterization of the image of a fuzzy number in terms of the extremes of its level sets then we deduce some consequences we show some relationships between the image of two fuzzy numbers and the images of their usual operations and it is proved that the continuity of some fuzzy numbers is preserved under the usual operations as applications we introduce a fuzzy regression model involving a parametric family of fuzzy semidistances between fuzzy numbers with finite image and an ordering process of fuzzy numbers with compact support that satisfies specificity type properties

parallelized tensor train learning of polynomial classifiers in pattern classification polynomial classifiers are well studied methods as they are capable of generating complex decision surfaces unfortunately the use of multivariate polynomials is limited to kernels as in support vector machines because polynomials quickly become impractical for high dimensional problems in this paper we effectively overcome the curse of dimensionality by employing the tensor train tt format to represent a polynomial classifier based on the structure of tts two learning algorithms are proposed which involve solving different optimization problems of low computational complexity furthermore we show how both regularization to prevent overfitting and parallelization which enables the use of large training sets are incorporated into these methods the efficiency and efficacy of our tensor based polynomial classifier are then demonstrated on the two popular data sets u s postal service and modified nist

possibilistic linear regression analysis for fuzzy data abstract fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined recently it has become important to deal with fuzzy data in connection with expert knowledge three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data since our formulations can be reduced to linear programming problems the merit of our formulations is to be able to obtain easily fuzzy parameters in possibilistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters this approach can be regarded as a fuzzy interval analysis in a fuzzy environment

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

aggregation of subjective evaluations based on discrete fuzzy numbers in this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail these aggregation functions are constructed from discrete aggregation functions defined on a finite chain and they are applied to the aggregation of subjective evaluations

using discrete fuzzy numbers in the aggregation of incomplete qualitative information in this article discrete fuzzy numbers are used to model complete and incomplete qualitative information and some methods to aggregate this kind of information are proposed when the support of discrete fuzzy numbers is a closed interval of the chain l n 0 1 n they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms on the other hand when the support is not an interval of l n the corresponding discrete fuzzy number can be interpreted as an incomplete linguistic expert valuation in order to aggregate this kind of information we propose two different methods one of them deals with the construction of aggregation functions on the set of discrete fuzzy numbers from discrete aggregation functions defined on l n the other one presents several procedures for estimating the missing information based on the so called discrete associations finally the proposed aggregation methods are used in a multi expert decision making problem and a concrete example is given

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

a comparison between gauss newton and markov chain monte carlo based methods for inverting spectral induced polarization data for cole cole parameters we have developed a bayesian model to invert spectral induced polarization sip data for cole cole parameters using markov chain monte carlo mcmc sampling methods we comparedtheperformanceofthemcmc basedstochasticmethod with an iterative gauss newton based deterministic method for cole cole parameter estimation through inversion of syntheticandlaboratorysipdata thegauss newton basedmethod canprovideanoptimalsolutionforgivenobjectivefunctionsunder constraints but the obtained optimal solution generally dependsonthechoiceofinitialvaluesandtheestimateduncertainty information often is inaccurate or insufficient in contrast the mcmc based inversion method provides extensive global informationonunknownparameters suchasthemarginalprobability distribution functions from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method in addition the results obtained with the mcmc method are independent of the choice of initial values becausethemcmc basedmethoddoesnotexplicitlyofferasingleoptimalsolutionforgivenobjectivefunctions thedeterministic and stochastic methods can complement each other forexample thestochasticmethodcanbeusedfirsttoobtainthe mediansofunknownparametersbystartingfromanarbitraryset of initial values the deterministic method then can be initiated using the medians as starting values to obtain the optimal estimatesofthecole coleparameters

evaluating students answerscripts using fuzzy numbers associated with degrees of confidence this paper presents a new approach for evaluating students answerscripts using fuzzy numbers associated with degrees of confidence of the evaluator the satisfaction levels awarded to the questions of students answerscripts are represented by fuzzy numbers associated with degrees of confidence between zero and one the arithmetic operations between the alpha cuts of fuzzy numbers are used to evaluate the total mark of each student where alpha isin 0 1 the proposed method can overcome the drawbacks of the methods presented by biswas 1994 and chen and lee 1999 it can evaluate students answerscripts in a more flexible and more intelligent manner

aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations abstract in this paper we propose a method to construct aggregation functions on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers from a couple of discrete aggregation functions the interest on these discrete fuzzy numbers lies on the fact that they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms finally a linguistic decision making model based on a pair of aggregation functions defined on discrete fuzzy numbers is given

fuzzy sets with triangular norms and their cardinality theory the most advanced and adequate approach to the question of cardinality of a fuzzy set seems to be that offering a fuzzy perception of cardinality the resulting convex fuzzy sets of usual cardinals of nonnegative integers in the finite case are then called generalized cardinal numbers three types of them are of special interest and importance namely fgcounts flcounts and fecounts in this paper first we show that their original forms are suitable only for fuzzy sets with the classical min and max operations second we propose an appropriate generalization to fuzzy sets with triangular norms and conorms further we investigate the resulting generalized fgcounts flcounts and fecounts from the viewpoint of the corresponding equipotency relations inequalities and arithmetical operations

low rank tensor train coefficient array estimation for tensor on tensor regression the tensor on tensor regression can predict a tensor from a tensor which generalizes most previous multilinear regression approaches including methods to predict a scalar from a tensor and a tensor from a scalar however the coefficient array could be much higher dimensional due to both high order predictors and responses in this generalized way compared with the current low candecomp parafac cp rank approximation based method the low tensor train tt approximation can further improve the stability and efficiency of the high or even ultrahigh dimensional coefficient array estimation in the proposed low tt rank coefficient array estimation for tensor on tensor regression we adopt a tt rounding procedure to obtain adaptive ranks instead of selecting ranks by experience besides an ell 2 constraint is imposed to avoid overfitting the hierarchical alternating least square is used to solve the optimization problem numerical experiments on a synthetic data set and two real life data sets demonstrate that the proposed method outperforms the state of the art methods in terms of prediction accuracy with comparable computational complexity and the proposed method is more computationally efficient when the data are high dimensional with small size in each mode

the median of a random fuzzy number the 1 norm distance approach in quantifying the central tendency of the distribution of a random fuzzy number or fuzzy random variable in puri and ralescu s sense the most usual measure is the aumann type mean which extends the mean of a real valued random variable and preserves its main properties and behavior although such a behavior has very valuable and convenient implications extreme values or changes of data entail too much influence on the aumann type mean of a random fuzzy number this strong influence motivates the search for a more robust central tendency measure in this respect this paper aims to explore the extension of the median to random fuzzy numbers this extension is based on the 1 norm distance and its adequacy will be shown by analyzing its properties and comparing its robustness with that of the mean both theoretically and empirically

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

jensen and chebyshev inequalities for pseudo integrals of set valued functions set valued functions are an important mathematical notion and play a crucial role in several practical areas at the same time pseudo analysis as a background allows extension of some classical mathematical notions to the forms that are highly applicable in some nonstandard situations this paper focuses on pseudo integration of set valued functions which is generalization of aumann s research and corresponding extensions of the jensen and chebyshev integral inequalities to the set valued case since the integral inequalities in question are widely used in various aspects of mathematics the main motivation for the presented research lies in the possibility of expanding the applicability of these inequalities by combining the properties of set valued functions with pseudo analysis

bayesian linearized avo inversion a new linearized avo inversion technique is developed in a bayesian framework the objective is to obtain posterior distributions for p wave velocity s wave velocity and density distributions for other elastic parameters can also be assessed for example acoustic impedance shear impedance and p wave to s wave velocity ratio the inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the zoeppritz equation the solution is represented by a gaussian posterior distribution with explicit expressions for the posterior expectation and covariance hence exact prediction intervals for the inverted parameters can be computed under the specified model the explicit analytical form of the posterior distribution provides a computationally fast inversion method tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero with realistic noise levels acoustic impedance was the best determined parameter

canonical representations of discrete fuzzy numbers in this paper we obtain two canonical representations of discrete fuzzy numbers in particular it is shown that any discrete fuzzy number can be represented by a triangular or a block discrete fuzzy number having the same value ambiguity and fuzziness as the original number

multi criteria decision making involving uncertain information via fuzzy ranking and fuzzy aggregation functions abstract many advances in artificial intelligence and machine learning are based on decision making especially in uncertain settings due to its possible applications decision making is currently a broad field of study in many areas like computation economics and business management the first techniques appeared in scenarios where information was modeled by real numbers in all cases one of the key steps in such processes was the summarization of the available information into a few values that helped the decision maker to complete this task in this paper we introduce a novel multi criteria decision making methodology in the fuzzy context in which weights and experts opinions may be translated by linguistic labels are stated as triangular fuzzy numbers to do that we take advantage of a recently presented fuzzy binary relation whose properties are according to human intuition and we carry out a study of the main properties that an aggregation function a mapping to sum up information must satisfy in the fuzzy framework the presented procedure makes a final decision based on parabolic fuzzy numbers not triangular and this will be shown in an illustrative example

ranking fuzzy numbers based on the areas on the left and the right sides of fuzzy number in this paper a novel method based on the areas on the left and the right sides of fuzzy numbers is proposed for ranking fuzzy numbers the merits of the results given here is to overcome certain shortcomings in the recent literature that mostly does not end in the right ordering of fuzzy numbers the method also has very easy and simple calculations compared to other methods moreover numerical examples are given to compare the proposed method with other existing ones

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

sums of fuzzy set of summands abstract we investigate the addition operation on fuzzy numbers with a fuzzy set of summands this is a natural generalization of the corresponding operation which involves a crisp set of summands it is shown that the resulting set is a type 2 fuzzy set we construct a type 2 membership function of this set the sum type 2 fuzzy set can be decomposed according to secondary membership grades into the corresponding collection of fuzzy numbers it helps to represent the addition operation on fuzzy numbers with a fuzzy set of summands in a form which is convenient for a proper understanding and applications illustrative examples are given

reservoir parameter identification using minimum relative entropy based bayesian inversion of seismic ava and marine csem data a stochastic joint inversion approach for estimating reservoir fluid saturations and porosity is proposed the approach couples seismic amplitude variation with angle ava and marine controlled source electromagnetic csem forward models into a bayesian framework which allows for integration of complementary information to obtain minimally subjective prior probabilities required for the bayesian approach the principle of minimum relative entropy mre is employed instead of single value estimates provided by deterministic methods the approach gives a probability distribution for any unknown parameter of interest such as reservoir fluid saturations or porosity at various locations the distribution means modes and confidence intervals can be calculated providing a more complete understanding of the uncertainty in the parameter estimates the approach is demonstrated using synthetic and field data sets results show that joint inversion using seismic and em data gives better estimates of reservoir parameters than estimates from either geophysical data set used in isolation moreover a more informative prior leads to much narrower predictive intervals of the target parameters with mean values of the posterior distributions closer to logged values

two ways to quantify uncertainty in geophysical inverse problems we present two approaches to invert geophysical measurements and estimate subsurface properties and their uncertainties when little is known a priori about the size of the errors associated with the data we illustrate these approaches by inverting first arrival traveltimes of seismic waves measured in a vertical well to infer the variation of compressional slowness in depth first we describe a bayesian formulation based on probability distributions that define prior knowledge about the slowness and the data errors we use an empirical bayes approach where hyperparameters are not well known ahead of time e g the variance of the data errors and are estimated from their most probable value given the data the second approach is a non bayesian formulation that we call spectral in the sense that it uses the power spectral density of the traveltime data to constrain the inversion e g to estimate the variance of the data errors in the spectral approach we vary assumptions made about the characteristics of the slowness signal and evaluate the resulting slowness estimates and their uncertainties this approach is computationally simple and starts from a few assumptions these assumptions can be checked during the analysis on the other hand it requires evenly spaced traveltime measurements and it cannot be extended easily e g to data that have gaps in contrast the bayesian framework is based on a general theory that can be generalized immediately but it is more involved computationally despite the conceptual and practical differences we find that the two approaches give the same results when they start from the same assumptions the allegiance to a bayesian or non bayesian formulation matters less than what one is willing to assume when solving the inverse problem

defending against strategic manipulation in uninorm based multi agent decision making abstract we consider the problem of multi agent group decision making we describe the possible use of the uninorm aggregation operator as a way of combining individual agents preference functions to obtain a group preference function we then discuss the possibility of an agent using a type of strategic manipulation of the preference information it provides in order to get the group to select its most preferred alternative a mechanism is then suggested for modifying the construction of the group decision function to defend against this type of strategic manipulation in addition to considering the case where the preference information is provided numerically we consider the case of ordinal preference information

hukuhara derivative of the fuzzy expected value in this paper we establish sufficient conditions to guarantee the exchange of the fuzzy expected value for a fuzzy random variable depending on certain parameter and its hukuhara derivative with respect to the parameter main results are obtained for two different sets of general conditions one of them requiring measurability conditions with respect to the product space the fuzzy random variable is defined from and the second one just requiring conditions over the projections of the fuzzy random variables

variational bayesian inversion of synthetic 3d controlled source electromagnetic geophysical data abstractinversion of controlled source electromagnetic data is dealt with for a geophysical application the goal is to retrieve a map of conductivity of an unknown body embedded in a layered underground from measurements of the scattered electric field that results from its interaction with a known interrogating wave this constitutes an inverse scattering problem whose associated forward problem is described by means of electric field domain integral equations the inverse problem is solved in a bayesian framework in which prior information is introduced via a gauss markov potts model this model describes the body as being composed of a finite number of different materials distributed into compact homogeneous regions the posterior distribution of the unknowns is approached by means of the variational bayesian approximation as a separable distribution that minimizes the kullback leibler divergence with respect to the posterior law thus we get a parametric model for the distributions of the induced cu

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

robust and accelerated bayesian inversion of marine controlled source electromagnetic data using parallel tempering bayesian methods can quantify the model uncertainty that is inherent in inversion of highly nonlinear geophysical problems in this approach a model likelihood function based on knowledge of the data noise statistics is used to sample the posterior model distribution which conveys information on the resolvability of the model parameters because these distributions are multidimensional and nonlinear we used markov chain monte carlo methods for highly efficient sampling because a single markov chain can become stuck in a local probability mode we run various randomized markov chains independently to some extent this problem can be mitigated by running independent markov chains but unless a very large number of chains are run biased results may be obtained we got around these limitations by running parallel interacting markov chains with annealed or tempered likelihoods which enable the whole system of chains to effectively escape local probability maxima we tested this approach using a transdimensional algorithm where the number of model parameters as well as the parameters themselves were treated as unknowns during the inversion this gave us a measure of uncertainty that was independent of any particular parameterization we then subset the ensemble of inversion models to either reduce uncertainty based on a priori constraints or to examine the probability of various geologic scenarios we demonstrated our algorithms fast convergence to the posterior model distribution with a synthetic 1d marine controlled source electromagnetic data example the speed up gained from this new approach will facilitate the practical implementation of future 2d and 3d bayesian inversions where the cost of each forward evaluation is significantly more expensive than for the 1d case

a new fuzzy arithmetic in this paper we first present fuzzy numbers with a new parametric form based on this representation a new fuzzy arithmetic is defined and applied to fuzzy linear equations and fuzzy calculus

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas

occam s inversion a practical algorithm for generating smooth models from electromagnetic sounding data the inversion of electromagnetic sounding data does not yield a unique solution but inevitably a single model to interpret the observations is sought we recommend that this model be as simple or smooth as possible in order to reduce the temptation to overinterpret the data and to eliminate arbitrary discontinuities in simple layered models to obtain smooth models the nonlinear forward problem is linearized about a starting model in the usual way but it is then solved explicitly for the desired model rather than for a model correction by parameterizing the model in terms of its first or second derivative with depth the minimum norm solution yields the smoothest possible model rather than fitting the experimental data as well as possible which maximizes the roughness of the model the smoothest model which fits the data to within an expected tolerance is sought a practical scheme is developed which optimizes the step size at each iteration and retains the computational efficiency of layered models resulting in a stable and rapidly convergent algorithm the inversion of both magnetotelluric and schlumberger sounding field data and a joint magnetotelluric resistivity inversion demonstrate the method and show it to have practical application

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

extension of discrete t norms and t conorms to discrete fuzzy numbers the aim of this paper is to extend a monotone operation defined on a discrete setting to a closed binary operation on the partially ordered set a 1 of discrete fuzzy numbers whose support is a subset of natural numbers moreover we study several properties like the monotonicity commutativity associativity or the boundary condition when the extended operation is a discrete t norm or a discrete t conorm defined on a finite chain l 0 1 n n also we study the frank s equation for t norms and t conorms defined on a special subset of a 1 finally we propose an application to obtain consensus opinion based on discrete fuzzy weighted normed operators

a fuzzy regression model based on finite fuzzy numbers and its application to real world financial data different sources of imprecision and uncertainty are encountered in practical problems and thus many elements may need to be imprecisely observed defined or treated in this setting one of the most successfully applied techniques to describe possible relationships between fuzzy variables is the regression methodology in this paper we introduce a fuzzy regression procedure involving a class a fuzzy numbers defined by some level sets called finite fuzzy numbers we give a characterization of the image of a finite fuzzy number in terms of the extremes of its level sets and we present a parametric family of fuzzy semidistances between them that let us to consider a total fuzzy error of estimation described as a fuzzy sum of squares of residuals in particular cases the estimation process consists in finding a regression model that minimizes in a fuzzy sense such fuzzy error although spreads of finite fuzzy numbers can take some values very close to zero which complicate the task of finding nonnegative models the presented algorithm is able to guarantee that the predicted response is a fuzzy variable finally a numerical example based on fuzzy economic data of china is given to illustrate the use of the proposed method

new methods for students evaluation using fuzzy sets in an earlier work biswas 1995 presented two methods for the application of fuzzy sets in students answerscripts evaluation in this paper we extend his work to propose two new methods for evaluating students answerscripts using fuzzy sets the proposed methods can overcome the drawbacks in biswas 1995 due to the fact that they do not need to perform the complicated matching operations and they can evaluate students answerscripts in a more fair manner

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

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

a unified approach to asymptotic behaviors for the autoregressive model with fuzzy data we propose a unified estimator for the autoregressive model with fuzzy input output variables based on the least squares method the least squares estimation is investigated in presence of a unified r distance defined on the space of fuzzy numbers we investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization which reduces to the asymptotic properties under those distances when the distances are the special cases of r distance some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of r distance

measures of specificity over continuous spaces under similarity relations we introduce the concept of specificity and indicate its importance as a measure of uncertainty for information represented using fuzzy sets or possibility distributions we provide formal measures of specificity for variables whose domain is an interval of the real line similarity relations are discussed and formalized the class of width based similarity relations is introduced we extend the measure of specificity to allow for the effect of an underlying similarity relationship the manifestation of this extension for a number of different similarity relations is investigated particularly notable results are obtained for width based similarity relationships more generally we note the connection between the size of a granule of information and its uncertainty motivated by this we investigate the effect of a similarity relationship on the perception of distance in the underlying space and use this to develop an extension of the specificity measure