global existence and nonexistence of solution for cauchy problem of multidimensional double dispersion equations abstract in this paper we consider the cauchy problem of multidimensional generalized double dispersion equations u t t u u t t 2 u f u where f u a u p by potential well method we prove the existence and nonexistence of global weak solution without establishing the local existence theory and we derive some sharp conditions for global existence and lack of global existence solution

global existence and nonexistence of solution for cauchy problem of two dimensional generalized boussinesq equations abstract in this paper we consider the cauchy problem of two dimensional generalized boussinesq type equation u t t u u t t 2 u f u 0 under the assumption that f u is a function with exponential growth at infinity and under some assumptions on the initial data we prove the existence and nonexistence of global weak solution there are very few works on boussinesq equation with nonlinear exponential growth term by potential well theory

quantity of information comparison between information systems 1 non fuzzy states abstract in statistical theory experiments or probabilistic information systems are supposed to be informative since they reduce the amount of uncertainty associated with the states of nature for the case that the available information systems are vague fuzzy information systems h tanaka t okuda and k asai have proven using the measure of information as provided by entropy that the fuzzy information systems are informative too now we wish to state and to study a criterion in order to compare fuzzy information systems by the quantity of information of a fuzzy information system defined by tanaka et al in this first paper we consider the situation where we require information about the original state space non fuzzy state space the second paper will deal with the situation where we require only information on certain vague states fuzzy states

a note on interval estimation with fuzzy data abstract in this note we formulate the problem of interval estimation when the experimental outcomes cannot be exactly perceived but they may be assimilated with fuzzy information then we suggest a method to derive crude confidence intervals but always possible to apply

possibilistic decisions and fuzzy statistical tests the paper deals with the problem of the interpretation of the results of statistical tests in terms of the theory of possibility the well known concept in statistics of the observed test size p also known as p value and significance has been given a new possibilistic interpretation and generalised for the case of imprecisely defined statistical hypotheses and vague statistical data the proposed approach allows a practitioner to evaluate the test results using intuitive concepts of possibility necessity or indifference

a method for convex curve approximation abstract in this paper a new sandwich method is introduced to approximate a convex curve in r2 this method requires only function evaluation and the solution of a number of scalar optimization problems a quadratic convergence property of the method is established that is the total number of optimization problems solved is bounded by a constant multiple of the square root of the inverse of the given error an application to approximation of the efficient frontier of a bi criteria convex quadratic network program is given

approximation methods for non convex curves based on the triangle sandwich and block sandwich methods two approximation methods for non convex curves are considered in this paper numerical algorithms corresponding to these methods are developed and quadratic convergence properties of two methods in the original space are established application is given to the approximation of an efficient frontier of a bi criteria optimization problem

testing fuzzy hypotheses with crisp data abstract in this paper an approach is presented how statistical tests originally constructed to examine crisp hypotheses can also be applied to fuzzily formulated hypotheses in particular criterions and are proposed generalizing the probabilities of the errors of type i and type ii respectively the general approach is applied to one and two sided gaus tests here diagrams are given to determine the critical values in the most popular cases of 0 01 and 0 05 if in addition the value of is fixed in advance the sample size of a one or two sided gaus test can be obtained using supplementary graphs

travelling wave solutions for a generalized double dispersion equation abstract we analyze the generalization of a double dispersion equation by means of the theory of symmetry reductions of partial differential equations we consider travelling wave reductions depending on the form of an arbitrary function we present some explicit solutions soliton solutions kinks and anti kinks

existence and blow up of solution of cauchy problem for the generalized damped multidimensional boussinesq equation we consider the existence both locally and globally in time and the blow up of solutions for the cauchy problem of the generalized damped multidimensional boussinesq equation

a global attractor for the elastic waveguide model in rn abstract this paper studies the longtime behavior of solutions to the elastic waveguide model in r n u t t u u t t 2 u u t u t u g x u f x it proves that when the space dimension n 5 under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity x h 2 h 1 h 2 h with 0 1 a global attractor which is connected

the fuzzy hyperbolic inequality index associated with fuzzy random variables the aim of this paper is focussed on the quantification of the extent of the inequality associated with fuzzy valued random variables in general populations for this purpose the fuzzy hyperbolic inequality index associated with general fuzzy random variables is presented and a detailed discussion of some of the most valuable properties of this index extending those for classical inequality indices is given two examples illustrating the computation of the fuzzy inequality index are also considered some comments and suggestions are finally included

approximation of convex curves with application to the bicriterial minimum cost flow problem abstract an approximation of an explicity or implicity given convex curve in the plane is given by two piecewise linear outer and inner curves to compute these three rules for choosing the supporting points are proposed and it is shown for two of them that the projective distance between inner and outer approximation decreases quadratically with the number of supporting points this method is applied to approximate the efficient point curve of the bicriterial minimum cost flow problem which is a piecewise linear convex curve that may have an exponential number of breakpoints in the worst case

combining ambiguous evidence with respect to ambiguous a priori knowledge part ii fuzzy logic abstract this paper describes fuzzy conditioned dempster shafer fcds theory a probability based calculus for dealing with possibly imprecise and vague evidence when the underlying a priori knowledge base is itself possibly imprecise and vague fcds has the same general form as existing fuzzy dempster shafer theories fcds however employs a finite level zadeh fuzzy logic and a dempster shafer like combination operator which is conditioned to reflect the influence of any a priori knowledge base which can be modeled by a belief measure on finite level fuzzy sets we show that fcds is grounded in probability theory specifically in the theory of random fuzzy sets we also show that it is a generalization of bayesian theory to the case when both evidence and a priori knowledge are imprecise and vague we show that fcds is consistent with the lattice structure of zadeh s min max fuzzy logic and that in particular it possesses an analog of the familiar mobius transform

the fuzzy decision problem an approach to the problem of testing statistical hypotheses with fuzzy information abstract this paper is devoted to the problems of testing statistical hypotheses about an experiment when the available information from its sampling is vague when the information supplied by the experimental sampling is exact the problems of testing statistical hypotheses about the experiment can be regarded as a particular statistical decision problem in addition decision procedures may be used in problems of testing hypotheses in a similar manner the problem of testing statistical hypotheses about an experiment when the available sample information is vague is approached in this paper as a particular fuzzy decision problem as defined by tanaka okuda and asai this approach assumes that the previous information about the experiment can be expressed by means of certain conditional probabilistic information whereas the present information about it can be expressed by means of fuzzy information the preceding framework allows us to extend the notion of risk function and some nonfuzzy decision procedures to the fuzzy case and particularize them to the problem of testing finally several illustrative examples are presented

simulation of random fuzzy variables an empirical approach to statistical probabilistic studies with fuzzy experimental data in this paper we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy valued random variables this simulation was carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sampled fuzzy data to the population mean or an expected value of the random fuzzy variable like the well known strong law of large numbers and the law of iterated logarithm since the theoretical results have recently been proved this simulation analysis represents a complementary study in which we can determine sample sizes providing us with suitable approximations finally future directions regarding statistical inference with fuzzy data and other applications are commented

the cauchy problem for a class of the multidimensional boussinesq type equation abstract in this paper we study the cauchy problem for a class of the multidimensional boussinesq type equation u t t u 2 u 2 u t t f u where f u a u p or a u p 1 u a 0 is a constant first we establish a local existence theorem for the solution then for m 1 n 1 m 2 3 4 n 3 we prove the existence of a global h m solution finally we prove the global nonexistence and finite time blow up of the solution

global attractor for a nonlinear wave equation arising in elastic waveguide model abstract the paper studies the longtime behavior of solutions to the initial boundary value problem ibvp for a nonlinear wave equation arising in an elastic waveguide model u t t u u t t 2 u u t g u f x it proves that when the space dimension n 5 under rather mild conditions the dynamical system associated with the above mentioned ibvp possesses a global attractor which is connected and has finite fractal and hausdorff dimension

bootstrap method for some estimators based on fuzzy data abstract the bootstrap efron ann statist 7 1979 1 26 is a simple and straightforward method for calculating approximated biases standard deviations confidence intervals and so forth in almost any nonparametric estimation problem in this paper we consider another example namely fuzzy data and use the bootstrap to answer several questions concerning the minimum inaccuracy estimator corral and gil stochastica 8 1984 63 81 a what is the standard error of this estimator b what is a reasonable confidence interval for such an estimate the validity of bootstrap method is investigated using a real data and computer simulation

global existence and blow up of solutions for a general class of doubly dispersive nonlocal nonlinear wave equations this study deals with the analysis of the cauchy problem of a general class of nonlocal nonlinear equations modeling the bi directional propagation of dispersive waves in various contexts the nonlocal nature of the problem is reflected by two different elliptic pseudodifferential operators acting on linear and nonlinear functions of the dependent variable respectively the well known doubly dispersive nonlinear wave equation that incorporates two types of dispersive effects originated from two different dispersion operators falls into the category studied here the class of nonlocal nonlinear wave equations also covers a variety of well known wave equations such as various forms of the boussinesq equation local existence of solutions of the cauchy problem with initial data in suitable sobolev spaces is proven and the conditions for global existence and finite time blow up of solutions are established

dealing with uncertainties in engineering problems using only available data abstract this paper is the second in the series of three addressing the problem of how to deal with uncertainties in the modelings of engineering problems using only available data the problem of the heat exchanger was selected as the example because it is sufficiently complex but still simple so that the difficulties and ideas will be apparent there are various theories on how to treat the uncertainties in the first paper in the series we use only the fuzzy set respectively the possibility theory in this paper we use the fuzzy approach for some model parameters and the probability approach for the others the third paper will use the bayesian theory

fuzzy hypothesis testing for a population proportion based on set valued information abstract in this paper we propose fuzzy hypothesis testing for a proportion with crisp data as the exact generalized one tailed hypergeometric test with fuzzy non complementary hypotheses and incorporate the conventional hypergeometric test with crisp hypotheses into its framework in particular we formulate hypotheses as ontic or epistemic fuzzy sets since we assume that presumptions regarding the true population proportion can be expressed in the conjunctive or disjunctive reading further we suggest modeling of membership functions in terms of cost or frequency due to considerations of user s priorities or incomplete knowledge in relation to hypotheses formulation considering a hypothesis as union of its crisp and fuzzy areas we illustrate via real life examples that in contrast to classical test theory fuzzy hypothesis testing provides an additional partial and gradual consideration of the indifference zone for both complementary and non complementary hypotheses the test concept is introduced for both test methods a test of significance and an alternative test and leads to a crisp test decision considering further cost aspects like the sample size the generalized error criteria are derived and interpreted in relation to both hypotheses additionally a corresponding sensitivity analysis is presented for one of the most promising test types

on fuzzy bayesian inference abstract the paper combines methods from bayesian statistics with ideas from fuzzy set theory to generalize bayesian methods both for samples of fuzzy data and for prior distributions with non precise parameters applying the principle of propagation of fuzziness we introduce a fuzzy valued likelihood function bayes theorem for both fuzzy data and fuzzy priors a fuzzy bayes estimator fuzzy predictive densities and distributions and fuzzy h p d regions

bayesian reliability analysis for fuzzy lifetime data lifetime data are important in reliability analysis classical reliability estimation is based on precise lifetime data it is usually assumed that observed lifetime data are precise real numbers however some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers thus it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers bayesian methods have proved to be very useful when the sample size is small there is little study on bayesian reliability estimation based on fuzzy lifetime data most of the reported works in this area is limited to single parameter lifetime distributions in this paper we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi parameter lifetime distributions an artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction the genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level this method can be used to determine the membership functions of the bayesian estimates of multi parameter distributions the effectiveness of the proposed method is illustrated with normal and weibull distributions

the fuzzy estimators of fuzzy parameters based on fuzzy random variables abstract the concept for fuzzy estimators of fuzzy parameters in fuzzy random variables is proposed in this paper due to the resolution identity the construction of a fuzzy number from a family of closed intervals is developed the construction of the fuzzy estimators of fuzzy parameters from the known conventional estimators inherits evidently from the aforementioned technique in the meantime we prove that the fuzzy estimator is a fuzzy random variable in order to provide the notion of fuzzy expectation and variance of fuzzy estimator the computational procedure is also provided by solving the related nonlinear programming problems that are transformed from the original problem for the purpose of evaluation of the membership values of the fuzzy estimates

global existence and asymptotic behaviour of solutions for the generalized boussinesq equation abstract in this paper we prove the existence and the uniqueness of global solution for the cauchy problem for the generalized boussinesq equation under some assumptions we also show that the l norm of small solution of the cauchy problem for the generalized boussinesq equation decays to zero as t tends to the infinity

bayesian estimation in forest surveys when samples or prior information are fuzzy abstract fuzzy phenomena are frequently encountered in forestry due to the complexity of the systems under investigation in this paper existing inference methods are presented to accommodate situations in which random events take place in fuzzy circumstances fuzzy concepts are incorporated into these commonly accepted approaches to account for uncertainties used by factors other than randomness which traditional statistical approaches deal primarily with based on two extensions of likelihood functions for fuzzy samples bayesian estimates are generalized for use when sample information and prior distribution of parameters are fuzzy the estimators are developed for some typical membership functions for fuzzy samples and fuzzy priors applications are illustrated using examples for forestry

aleatoric and epistemic uncertainty in groundwater flow and transport simulation 1 the characterization of aleatory hydrogeological parameter uncertainty has traditionally been accomplished using probability theory however when consideration is given to epistemic as well as aleatory uncertainty probability theory is not necessarily appropriate this is especially the case where expert opinion is regarded as a suitable source of information when experts opine upon the uncertainty of a parameter value both aleatoric and epistemic uncertainties are introduced and must be modeled appropriately a novel approach to expert provided parameter uncertainty characterization can be defined that bridges an historical gap between probability theory and fuzzy set theory herein a random set a generalization of a random variable is employed to formalize expert knowledge and fuzzy sets are used to propagate this uncertainty to model estimates of contaminant transport the resultant random set based concentration estimates are shown to be more general than the corresponding random variable estimates in some cases the random set based results are shown as upper and lower probabilities that bound the corresponding random variable s cumulative distribution function

global existence and asymptotic behavior of solution for the rosenau equation with hydrodynamical damped term abstract we consider the cauchy problem for rosenau equation with hydrodynamical damped term in n dimensional space under smallness condition on the initial data we prove the global existence and asymptotic behavior of the solution in the time weighted sobolev spaces by the contraction mapping principle

fuzzy hypotheses testing in the framework of fuzzy logic abstract testing hypotheses about the probability distribution underlying the available empirical data is one of the fundamental data analytic tasks in any application domain basically it consists in checking the null hypothesis that the probability distribution a priori assumed to belong to a certain set of distributions actually belongs to some its narrow subset which must be precisely delimited in advance however sometimes there are not enough clues for such a precise delimitation especially if the purpose of the data analysis is explorative a situation encountered increasingly often due to the growing amount of routinely collected data and the increasing importance of data mining that is why generalizations of statistical hypotheses testing to vague hypotheses have been investigated for more than a decade so far based on the most straightforward approach to replace the set defining the null hypothesis by a fuzzy set in this paper a principally different approach is presented motivated by the observational logic and its success in automated knowledge discovery its key idea is to view statistical testing of a fuzzy hypothesis as the application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data the theoretical principles of the approach are explained and its first implementations are briefly sketched

a note on the operativeness of neyman pearson tests with fuzzy information abstract in a previous paper we have studied the extension of the neyman pearson optimality criterion of testing statistical hypotheses when the available experimental information involves fuzzy imprecision this extension usually becomes unmanageable for small samples nevertheless we will verify that when the sample size is large enough the application of the central limit theorem determines an operative extension

global attractor for the generalized double dispersion equation abstract the paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t u u t t 2 u u t g u f x the main result is concerned with nonlinearities g u with supercritical growth in that case we construct a subclass g of the limit solutions and show that it has a weak global attractor especially in non supercritical case the weak topology becomes strong the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space

cauchy problem for the generalized benney luke equation this paper is concerned with the study of the cauchy problem associated with an n dimensional generalized benney luke equation utt m u utt 2u 2 u ut ut u u p u 0 where n 1 2 3 4 we prove the existence and the uniqueness of the global solution of the cauchy problem for the 0 case by using energy conservation law and give the existence and the nonexistence of the global solution of the cauchy problem for the 0 case by constructing the stable set and the unstable set

testing statistical hypotheses with vague data a definition of fuzzy test for testing statistical hypotheses with vague data is proposed then the general method for the construction of fuzzy tests for hypotheses concerning an unknown parameter against one sided or two sided alternative hypotheses is shown this fuzzy test contrary to the classical approach leads not to the binary decision to reject or to accept given null hypothesis but to a fuzzy decision showing a grade of acceptability of the null and the alternative hypothesis respectively however it is a natural generalization of the traditional test i e if the data are precise not vague we get a classical statistical test with the binary decision a measure of fuzziness of the considered fuzzy test is suggested and the robustness of that test is also discussed

cauchy problem of the generalized double dispersion equation abstract in this paper the existence and the uniqueness of the global solution for the cauchy problem of the generalized double dispersion equation are proved the blow up of the solution for the cauchy problem of the generalized double dispersion equation is discussed by the concavity method under some conditions

instability and stability properties of traveling waves for the double dispersion equation abstract in this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation u t t u x x a u x x x x b u x x t t u p 1 u x x for p 1 a b 0 the main characteristic of this equation is the existence of two sources of dispersion characterized by the terms u x x x x and u x x t t we obtain an explicit condition in terms of a b and p on wave velocities ensuring that traveling wave solutions of the double dispersion equation are strongly unstable by blow up in the special case of the boussinesq equation b 0 our condition reduces to the one given in the literature for the double dispersion equation we also investigate orbital stability of traveling waves by considering the convexity of a scalar function we provide analytical as well as numerical results on the variation of the stability region of wave velocities with a b and p and then state explicitly the conditions under which the traveling waves are orbitally stable

kendall s rank correlation on quantized data an interval valued approach kendall s rank correlation coefficient also called kendall s is an efficient and robust way for identifying monotone relationships between two data sequences however when applied to digital data the high number of ties yields inconsistent results due to quantization here we propose an extension of kendall s that considers an epistemic view of a sequence of quantized data each sample is supposed to be the quantized version of an original value that is a real number we come up with an imprecise defined as the interval containing all values that could have been computed on sequences of original values before quantization we propose a very simple and straightforward algorithm to compute this interval valued we prove the exactness of the bounds and propose an experiment that illustrates the need for such an extension

statistical tests for fuzzy data abstract in this paper we investigate the impacts of vague and imprecise data on the statistical task of hypotheses testing test results are evaluated with respect to this ambiguity the issue of how to aggregate fuzzy data to a fuzzy sample vector is discussed and different eventualities are considered their consequences on the test results are compared the domain of the used test statistics is extended to fuzzy sample vectors by the means provided in the first part of this paper different methods for the defuzzification of the obtained fuzzy test results are discussed and the fuzzy nature of the classical verification task for statistical hypotheses is studied in this context a way of how to overcome the general insufficiency of statistical tests of being conclusive only in one direction is proposed by admitting fuzzy results

a bi objective median location problem with a line barrier the multiple objective median problem momp involves locating a new facility with respect to a given set of existing facilities so that a vector of performance criteria is optimized a variation of this problem is obtained if the existing facilities are situated on two sides of a linear barrier such barriers like rivers highways borders or mountain ranges are frequently encountered in practice in this paper theory of an momp with line barriers is developed as this problem is nonconvex but specially structured a reduction to a series of convex optimization problems is proposed the general results lead to a polynomial algorithm for finding the set of efficient solutions the algorithm is proposed for bicriteria problems with different measures of distance

global existence of cauchy problem for boussinesq paradigm equation in this paper we study the cauchy problem for the boussinesq paradigm equation u t email protected b email protected t email protected email protected email protected u where f u email protected u p new functionals are introduced and their sign preserving properties under the flow of the equation are studied the existence of a global weak solution with supercritical initial energy is proved the explicit value of the critical energy constant is found

the fuzzy decision problem an approach to the point estimation problem with fuzzy information abstract this paper is devoted to the extension of the bayesian method for the point estimation when the available information is vague in the nonfuzzy case the parametric estimation can be approached as a particularization in the statistical decision problem this motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem defined by tanaka okuda and asia in this way concepts in the fuzzy decision problem are first expressed in the estimation terminology then on the basis of these concepts we shall introduce some notions and state some interesting results finally several illustrative examples will be exposed

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

performance characteristics of the fuzzy sign detector in this paper fuzzy statistical techniques are introduced into the optimum signal detection problems the likelihood ratio for fuzzy detection of known signals is obtained as a special case of the fuzzy signal detector a fuzzy set theoretic approach to sign detection of known signals is considered specifically the test statistic of the fuzzy sign detector for known signals is obtained some properties of the fuzzy sign nonlinearity which constitutes the fuzzy sign detector are also described finally the performance characteristics of the fuzzy sign detector are investigated and compared to those of the crisp sign detector

statistical hypotheses testing for fuzzy data the method of handling fuzziness upon the usual method of statistical hypotheses testing is proposed we transact the h level set of fuzzy data for the sake of invoking usual method of statistical hypotheses testing we propose the decision rules that are used to accept or reject the null and alternative hypotheses with the notions of degrees of optimism and pessimism by solving optimization problems we also provide a computational procedure and an example to clarify the discussions in this paper

a study of defuzzification with experts knowledge for deteriorating repairable systems abstract this paper presents ideas on the applications of fuzzy concepts to decision making for deteriorating repairable systems a non homogeneous poisson process nhpp with a power law intensity function is used in this study in general classical bayesian decision methods presume that future states of nature can be characterized as probability events however we do not know what the future will entail probabilistically so we devise a method to consider experts opinions which are usually the absence of sharply defined criteria and to develop a fuzzy bayesian decision process for dealing with such situations two cases of the discrimination problem with deteriorating repairable systems are studied 1 fuzzy states and exact information and 2 fuzzy states and fuzzy information the fuzzy decomposition and arithmetic derivation of the experts opinion are presented to facilitate the development of the bayesian decision process for deteriorating repairable systems

similarity of personal preferences theoretical foundations and empirical analysis we study the problem of defining similarity measures on preferences from a decision theoretic point of view we propose a similarity measure called probabilistic distance that originates from the kendall s tau function a well known concept in the statistical literature we compare this measure to other existing similarity measures on preferences the key advantage of this measure is its extensibility to accommodate partial preferences and uncertainty we develop efficient methods to compute this measure exactly or approximately under all circumstances these methods make use of recent advances in the area of markov chain monte carlo simulation we discuss two applications of the probabilistic distance in the construction of the decision theoretic video advisor diva and in robustness analysis of a theory refinement technique for preference elicitation

advocating the use of imprecisely observed data in genetic fuzzy systems in our opinion and in accordance with current literature the precise contribution of genetic fuzzy systems to the corpus of the machine learning theory has not been clearly stated yet in particular we question the existence of a set of problems for which the use of fuzzy rules in combination with genetic algorithms produces more robust models or classifiers that are inherently better than those arising from the bayesian point of view we will show that this set of problems actually exists and comprises interval and fuzzy valued datasets but it is not being exploited current genetic fuzzy classifiers deal with crisp classification problems where the role of fuzzy sets is reduced to give a parametric definition of a set of discriminant functions with a convenient linguistic interpretation provided that the customary use of fuzzy sets in statistics is vague data we propose to test genetic fuzzy classifiers over imprecisely measured data and design experiments well suited to these problems the same can be said about genetic fuzzy models the use of a scalar fitness function assumes crisp data where fuzzy models a priori do not have advantages over statistical regression

asymptotic properties of least squares estimation with fuzzy observations this paper deals with the asymptotic properties of the least squares estimators for fuzzy linear regression models with fuzzy triangular input output and random error terms the asymptotic normality and strong consistency of the fuzzy least squares estimator flse are investigated a confidence region based on a class of flses is proposed the asymptotic relative efficiency of flses with respect to the crisp least squares estimators is also provided and a numerical example is given some simulation results are also presented to illustrate the behavior of flses

bayesian sequential test for fuzzy parametric hypotheses from fuzzy information abstract this paper is devoted to the sequential problem of testing fuzzy hypotheses concerning an experiment the outcomes of which provide fuzzy information this problem will be formalized as a special fuzzy sequential decision problem to which it is possible to extend the bayes nonfuzzy decision procedures when the bayesian framework is assumed

a fuzzy statistical test of fuzzy hypotheses abstract a fuzzy hypothesis is introduced and a testing method of a fuzzy hypothesis is proposed for random data the proposed test produces a conclusion which is also fuzzy some applications of the fuzzy statistical test are demonstrated particularly the test of the difference of two population means is considered in detail and the fuzzy hypothesis that two population means are nearly equal is tested by the proposed procedure

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

non asymptotic fuzzy estimators based on confidence intervals abstract in this paper we study and generalize the method of fuzzy estimation which is based on confidence intervals we provide definitions and the corresponding formulas the method we propose allows new additional ways in constructing fuzzy estimators in particular instead of constructing fuzzy estimators as the exact set of confidence intervals of the parameters to be estimated we generalize them in such a way that we eliminate discontinuities and ensure compact support preserving the statistically derived triangular shape of the estimators our approach is particularly useful in critical situations where subtle fuzzy comparisons between almost equal statistical quantities have to be made an example of this application is provided

a bayesian approach to fuzzy hypotheses testing in statistical decisions we may come across imprecise fuzzy concepts one important case is a situation where we are interested in testing the hypotheses that are fuzzy rather than crisp in this paper we consider and analyze the testing of fuzzy hypotheses on the basis of a bayesian approach we illustrate our method by some examples and compare it with previous works on this topic

nonparametric rank based statistics and significance tests for fuzzy data nonparametric rank based statistics depending only on linear orderings of the observations are extended to fuzzy data the approach relies on the definition of a fuzzy partial order based on the necessity index of strict dominance between fuzzy numbers which is shown to contain in a well defined sense all the ordinal information present in the original data a concept of fuzzy set of linear extensions of a fuzzy partial order is introduced allowing the approximate computation of fuzzy statistics alpha cutwise using a markov chain monte carlo simulation approach the usual notions underlying significance tests are also extended leading to the concepts of fuzzy p value and graded rejection of the null hypothesis quantified by a degree of possibility and a degree of necessity at a given significance level this general approach is demonstrated in two special cases kendall s rank correlation coefficient and wilcoxon s two sample rank sum statistic

an optimal adaptive algorithm for the approximation of concave functions motivated by the study of parametric convex programs we consider approximation of concave functions by piecewise affine functions using dynamic programming we derive a procedure for selecting the knots at which an oracle provides the function value and one supergradient the procedure is adaptive in that the choice of a knot is dependent on the choice of the previous knots it is also optimal in that the approximation error in the integral sense is minimized in the worst case

pointwise estimates of global small solutions to the generalized double dispersion equation abstract in this paper we investigate the initial value problem for the generalized double dispersion equation in r n under suitable conditions global classical solutions are proved for n 3 and n 1 respectively moreover pointwise estimates of global classical solutions are established when n 3 and n is an odd integer by fourier splitting frequency technique

global existence and optimal time decay estimates of solutions to the generalized double dispersion equation on the framework of besov spaces abstract we investigate the initial value problem for the generalized double dispersion equation in any dimensions inspired by 28 for the hyperbolic system of first order pdes we develop littlewood paley pointwise energy estimates for the dissipative wave equation of high order furthermore with aid of the frequency localization duhamel principle we establish the global existence and optimal decay estimates of solutions in spatially critical besov spaces our results could hold true for any dimensions n 1 indeed the proofs are different in case of high dimensions and low dimensions owing to interpolation tricks

global existence to generalized boussinesq equation with combined power type nonlinearities abstract the cauchy problem to the generalized boussinesq equation with combined power type nonlinearities is studied global solvability or finite time blow up of the solutions with subcritical initial energy is proved by means of the sign preserving property of the nehari functional for generalized lienard or generalized bernoulli nonlinear terms the critical energy constant is explicitly evaluated a new method that can be considered as a modification of the potential well method is developed the performed numerical experiments support the theoretical results

c fuzzy numbers and a dual of extension principle in this paper we introduce and investigate the concept of c fuzzy numbers we extend the algebraic operations on c fuzzy numbers and specially study the properties of these operations on lr type c fuzzy numbers in addition a dual of extension principle is introduced it is shown that the algebraic operations with c fuzzy numbers have a representation based on the dual of extension principle

on statistically inference for fuzzy data with applications to descriptive statistics abstract the object of this paper is to discuss how fuzziness of data is propagated when statistical inference for samples of non precise data is carried out first fuzzy data and fuzzy samples are defined subsequently the method of propagation of fuzziness as used in previous work for specific stochastic models is formulated in rather general terms this method may be applied to any statistical method which leads to a result that may be expressed as a function f x 1 x n of the data x 1 x n it is proved that this method is equal to determining the images of a family of compact subsets of the sample space under the function f this equivalence is utilized in order to perform propagation of fuzziness in practice finally this approach is applied to some concepts of descriptive statistics such as fuzzy sample mean fuzzy sample variance and to the empirical distribution function of a fuzzy sample

existence and asymptotic stability of time periodic solutions to the generalized double dispersion equation with periodic external force abstract in this paper we investigate the generalized double dispersion equation with periodic external force in r n we prove the existence and uniqueness of time periodic solutions that have the same period as the external force in some suitable function space for the space dimension n 3 the proof is based on the spectral analysis for the solution operator and the contraction mapping theorem in addition we also discuss the time asymptotic stability of the time periodic solutions by continuous argument

combined rank tests for randomly censored paired data abstract many authors have dealt with the problem of extending ordinary two sample rank tests to cases where censoring occurs albers and akritas 1987 proposed simple tests for this purpose based on the idea of making separate rankings for uncensored and censored observations and subsequently combining the resulting two rank statistics similarly some papers appeared that studied the problem of censoring for the paired data case rather than the two sample case this article indicates how the approach of albers and akritas can be adapted to the paired data case the tests involved are not based on the ranks of the differences but the differences of the ranks in the pooled sample in this way use is made of interblock information the asymptotic distribution of the new statistic is obtained under the null hypothesis and contiguous location alternatives by way of example wilcoxon and savage type scores are introduced that are optimal for logistic location and exponential scale alternatives respecti

two sample hypothesis tests of means of a fuzzy random variable abstract in this paper we will consider some two sample hypothesis tests for means concerning a fuzzy random variable in two populations for this purpose we will make use of a generalized metric for fuzzy numbers and we will develop an exact study for the case of normal fuzzy random variables and an asymptotic study for the case of simple general fuzzy random variables

the effect of transformations on the approximation of univariate convex functions with applications to pareto curves in the literature methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed we study the effect of the use of increasing convex or increasing concave transformations on the approximation of univariate convex functions in this paper we show that these transformations can be used to construct upper and lower bounds for nonconvex functions moreover we show that by using such transformations of the input variable or the output variable we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations we show that these transformations can be applied to the approximation of a convex pareto curve that is associated with a convex bi objective optimization problem

potential well method for cauchy problem of generalized double dispersion equations abstract in this paper we study cauchy problem of generalized double dispersion equations u t t u x x u x x t t u x x x x f u x x where f u u p p 1 or u 2 k k 1 2 by introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions but also obtain the invariance of some sets and vacuum isolating of solutions in addition the global existence and finite time blow up of solutions for problem with critical initial conditions e 0 d i u 0 0 or i u 0 0 are proved

global existence of solution for cauchy problem of multidimensional generalized double dispersion equations abstract we study the cauchy problem of a class of multidimensional generalized double dispersion equations u t t u u t t 2 u k u t f u we prove the global existence of weak solution under some assumptions on the nonlinear term and the initial data

on the use of zadeh s probabilistic definition for testing statistical hypotheses from fuzzy information abstract a statistical hypothesis is an assertion about the distribution of an experiment we consider the study of the problem of testing a statistical hypothesis that is the problem of concluding whether or not the hypothesis is correct on the basis of data from the experiment when its outcomes do not provide exact but rather fuzzy information for establishing optimality criteria of testing we will use the definition of probability of a fuzzy event given by zadeh in order to extend both neyman pearson and bayes theories to the fuzzy framework then we will analyze several properties for the new criteria particularly the goodness of optimal procedures in both the fuzzy and the nonfuzzy situation will be compared for each criterion finally we will apply the extended criteria for testing simple hypotheses this application leads us to prefer bayesian procedures to neyman pearson procedures in the fuzzy context

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

a fuzzy decision problem based on the generalized neyman pearson criterion korea science and engineering foundation kosef under grant 893 0801 011 2 and korea advanced institute of science and technology kaist under an internal grant

multiple objective minimum cost flow problems a review in this paper theory and algorithms for solving the multiple objective minimum cost flow problem are reviewed for both the continuous and integer case exact and approximation algorithms are presented in addition a section on compromise solutions summarizes corresponding results the reference list consists of all papers known to the authors which deal with the multiple objective minimum cost flow problem

asymptotic profile of solutions to the double dispersion equation abstract in this paper we investigate the initial value problem for the double dispersion equation in r n decay estimate and asymptotic profile of solutions to the corresponding linear problem are established the asymptotic profile of solutions to the corresponding linear problem is given by the convolution of the fundamental solutions of heat and free wave equations moreover the asymptotic profile of solutions shows the decay estimate of solutions to the corresponding linear problem obtained in this paper is optimal under some conditions finally global existence and optimal decay estimate of solutions to the nonlinear problem are also established

application of fuzzy naive bayes and a real valued genetic algorithm in identification of fuzzy model we present a method to identify a fuzzy model from data by using the fuzzy naive bayes and a real valued genetic algorithm the identification of a fuzzy model is comprised of the extraction of if then rules that is followed by the estimation of their parameters the involved parameters include those which determine the membership function of fuzzy sets and the certainty factors of fuzzy if then rules in our method as long as the fuzzy partition in the input output space is given the certainty factor of each rule is computed with the fuzzy conditional probability of the consequent conditioned on the antecedent by using the fuzzy naive bayes which is a generalization of naive bayes the fuzzy model involves the rules characterized by the highest values of certainty factors the certainty factor of each rule is the fuzzy conditional probability and it reflects the inner relationship between the antecedent and the consequent in order to improve the accuracy of the fuzzy model the real valued genetic algorithm is incorporated into our identification process this process concerns the optimization of the membership functions occurring in the rules we just involve the parameters of membership function of the fuzzy sets into the real valued genetic algorithm since the certainty factor of each rule can be computed automatically the performance of the model is shown for the backing truck problem and the prediction of mackey glass time series