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

the s differentiability of a fuzzy valued mapping several approaches to define the differential of fuzzy valued mappings can be found in the literature in this paper we introduce a new concept of differential of a fuzzy valued mapping which is based on the notion of differential of the support function associated with such a mapping properties of the new concept as well as the relation between it and previous approaches are also analyzed in detail

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

noise compensation arrangement adaptive speech recognition is improved by extracting an estimate of the background noise during unknown speech input and using the noise estimate to modify the noiseless prestored reference speech signals for comparison with the input averaged values of autocorrelation coefficient and toeplitz matrix elements representative of noise frames and prestored reference frames are used to calculate the lpc predictor signals

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

uncertain alternating renewal process and its application uncertain process is a sequence of uncertain variables indexed by time and space first this paper presents a kind of uncertain process known as the uncertain alternating renewal process whose alternating interarrival times are uncertain variables then it proves an uncertain alternating renewal theorem on the limit value of average working rate finally an application of the alternating renewal theorem is discussed

existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non lipschitzian condition abstract this paper makes a research into a class of fuzzy stochastic differential equations fsdes driven by a continuous local martingale under the non lipschitzian condition such equations can be useful in modelling of hybrid systems where the phenomena are subjected to two kinds of uncertainties randomness and fuzziness simultaneously the solutions of fsdes are the fuzzy stochastic processes and their uniqueness is considered to be in a strong sense thus the existence and uniqueness of solutions to fsdes under the non lipschitzian condition is first proven and the continuity of solutions to fsdes with respect to the initial data or the coefficients of the equations is investigated

pairwise compatibility graphs a survey a graph g v e is a pairwise compatibility graph pcg if there exists an edge weighted tree t and two nonnegative real numbers d min and d max such that each leaf u of t is a node of v and there is an edge u v in e if and only if d min leq d t u v leq d max where d t u v is the sum of weights of the edges on the unique path from u to v in t in this article we survey the state of the art concerning this class of graphs and some of its subclasses

the l average value and the fuzzy expectation of a fuzzy random variable abstract the concepts of fuzzy random variable and the associated fuzzy expected value have been introduced by puri and ralescu as an extension of measurable set valued functions random sets and of the aumann integral of these functions respectively on the other hand the average function has been suggested by campos and gonzalez as an appropriate function to rank fuzzy numbers in this paper we are going to analyze some useful properties concerning the average value of the expectation of a fuzzy random variable and some practical implications of these properties are also commented on

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

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

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

almost periodic solutions of fuzzy systems we prove the existence of almost periodic solutions and asymptotically almost periodic solutions for the fuzzy functional differential equations moreover we consider uniform stable and uniformly asymptotically stable of almost periodic solutions for the fuzzy system

exact leaf powers we define and study the new notion of exact k leaf powers where a graph g v g e g is an exact k leaf power if and only if there exists a tree t v t e t an exact k leaf root of g whose set of leaves equals v g such that email protected e g holds for u email protected v g if and only if the distance of u and v in t is exactly k this new notion is closely related to but different from leaf powers and neighbourhood subtree tolerance graphs we prove characterizations of exact 3 and 4 leaf powers which imply that such graphs can be recognized in linear time and that also the corresponding exact leaf roots can be found in linear time furthermore we characterize all exact 5 leaf roots of chordless cycles and derive several properties of exact 5 leaf powers

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

strong law of large numbers for t normed arithmetics we prove a strong law of large numbers for sequences of pairwise i i d fuzzy random variables addition is given by the extension principle associated with a general continuous triangular norm our result includes the slln for levelwise sums obtained when the chosen triangular norm is the minimum

the intersection operation in light of joint observables and bell inequalities in operational probability theory operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs in this paper we first explain the need to extend the concept of the intersection operation in the light of the concept of joint observables then we tried to determine the basic features that characterize any possible definition of the intersection operation furthermore we tried to know if there is a relation between the definitions of the intersection operation of both fuzzy and operational probability theories these relations are used first to find a suitable suggestion to define the intersection operation second they are used besides the studies made on bell inequalities in fuzzy probability theory to find the conditions that should be satisfied by the intersection operation to ensure the possibility of the violation of bell inequalities in operational probability theory

the complete inclusion structure of leaf power classes let k 2 be an integer and g v e be a finite simple graph a tree t is a k leaf root of g if v is the set of leaves of t and for any two distinct x y v the distance between x and y in t is at most k if and only if xy e we say that g is a k leaf power if there is a k leaf root of g the main result of this paper is that for all 2 k

higher level fuzzy numbers arising from fuzzy regression consider a fuzzy random variable y with expectation symbol b x where b is an unknown fuzzy number and an unknown real number for n observations yi xi there is a model yi b xi ei i 1 2 n where ei are fuzzy valued errors independently and identically distributed in some sense the aim is to obtain estimates of b when all fuzzy numbers are triangular and the ei are uniformly distributed maximum likelihood estimators emerge naturally as a special form of higher level fuzzy number thus mle can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness

b fuzzy probabilities abstract we treat b fuzzy probabilities in nonstandard frameworks by the methods based on boolean valued models and especially boolean powers these formal methods apart from the difficulties associated with the formal model itself give a simple and powerful theory for fuzzy probability spaces and fuzzy random variables essentially everything is reduced to a transfer principle however one can also work using classical methods of proofs we first give the necessary background on nonstandard frameworks within these frameworks we develop boolean fuzzy probabilities and fuzzy random variables

fuzziness and randomness in an optimization framework abstract a semi infinite approach for linear programming in the presence of fuzzy random variable coefficients is described as a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained numerical examples are provided for the sake of illustration

linear programming with fuzzy random variable coefficients abstract linear programming with fuzzy random variable coefficients is introduced by discussing a practical engineering problem in order to study the solution of the linear programming with fuzzy random variable coefficients we discuss the simplex algorithm for linear programming with random variable coefficients furthermore the solution and distribution problem of this new fuzzy random programming are studied

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

compatibility between fuzzy set operations and level set operations applications to fuzzy difference abstract three types of binary operation between any two fuzzy sets are proposed in this paper the concept of 0 level set of fuzzy set plays an important role for defining the binary operations between two fuzzy sets according to the decomposition theorem of fuzzy sets the consistency between the membership functions and level sets should be rigorously verified when the binary operation between two fuzzy sets is defined by using their level sets the consistency is investigated thoroughly in this paper for the purpose of guaranteeing the existence of such binary operations moreover we also propose the so called hausdorff difference between any two fuzzy sets to define the difference of any two fuzzy numbers

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

neuro fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets abstract this paper presents the results of using type 2 fuzzy sets to assist in the pre processing of data for use with neuro fuzzy clustering for classification of sports injuries in the lower leg this research is concerned with the analysis of bone scans from stress related injuries to the tibia of particular interest is whether neural network based clustering techniques can help the consultant in classifying the images the work was motivated by the situation where there is a relatively small amount of relevant data and difficulties are faced by consultants in classifying the various types of injuries for this particular problem the consultant s interpretation of the image lends itself to representation using type 2 fuzzy sets this research sets out to address whether with fuzzy neuro clustering techniques some insights may be provided to the consultant that they can use along with their experience and knowledge the results of this approach indicate that the use of neural clustering using a type 2 representation can improve the classification of shin images

a fuzzy approach for multiresponse optimization an off line quality engineering problem abstract multiresponse optimization techniques are used to identify settings of process parameters that make the product s performance close to target values in the presence of multiple quality characteristics in this study a fuzzy multiresponse optimization procedure is proposed to search an appropriate combination of process parameter settings based on multiple quality characteristics or responses fuzzy regression models are first used to model the relations between process parameters and responses the possibility distributions of the prediction responses are then obtained the problem is reduced to a multiobjective optimization problem with fuzzy objectives a strategy of optimizing the most possible response values and minimizing the deviations from the most possible values is proposed we consider not only the most possible value but also the imprecision of the prediction responses through a die casting example we show how to use our approach to reach an appropriate machine setting which simultaneously optimize both casting quality and die life

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

acoustic category mean value calculating apparatus and adaptation apparatus each time a matching unit 22 finishes a matching at a time i between feature vectors of input speech which have been converted by an analyzer 1 and feature vectors of reference patterns stored in a reference pattern memory 2 and goes to a matching at a next time i 1 a feature vector integrator 24 multiplies the feature vectors of the input speech or the reference patterns by a weight w1 in each of acoustic categories successively integrates products stores integrated values in respective frames of the reference patterns in feature vector accumulating buffers 26 and integrates and stores weights w1 in feature vector weight counters 27 corresponding to the respective acoustic categories when the feature vector integrator 24 finishes integrating and storing processes corresponding to the final matching process a mean value calculator 28 divides the values stored in the final frames in the feature vector accumulating buffers 26 by the values stored in the feature vector weight counters 27 and outputs the quotients as mean values in the respective acoustic categories of the input speech or the reference patterns an adaptation unit 55 adapts one or both of the input speech or the reference patterns using the mean values

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

continuous speech recognition method and device in a system for recognizing a continuous speech pattern based on a speech pattern entered through a microphone a feature vector alpha i is extracted by a feature extraction unit and a feature vector beta jn is read out from a reference pattern memory a first recursive operation unit dpm1 computes a set of similarity measures sn i j between the feature vectors a maximum similarity measure at a time point i is determined and produced by a first decision unit dsc1 and is stored in a maximum similarity memory max a second recursive operation unit dmp2 computes a reversed similarity measure based on a computed result g v l and the output from said maximum similarity measure memory a second decision unit determines a boundary vmax a word wu based on data u vmax 1 obtained by the boundary v is stored as nx x 1 y in an order reversing unit rev the order reversing unit finally reverses the order of data and produces an output nx x 1 y

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

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

limit theorems for fuzzy random variables a strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables whose values are fuzzy sets with compact levels the proofs are based on embedding theorems as well as on probability techniques in banach space