algorithms for solving fuzzy relational equations in a probabilistic setting abstract we discuss methods suitable for finding approximate solutions to fuzzy relational equations defined in finite universe of discourse and taking the form of either a system of equations x k r y k k 1 2 k with r being unknown fuzzy relation or a single equation x r y with x being looked for the key idea of the proposed algorithms is to incorporate some statistics concerning the solution of a single equation and utilize it in the final process of approximation of the unknown fuzzy relation set numerical considerations support the established algorithms

decomposition of extremal length and a proof of shen s conjecture on qed constant and boundary dilatation in this paper we study the relations among various constants of quasiextremal distance qed domains in the plane in particular we give an affirmative answer to shen s conjecture about the relation between the qed constant m omega and the boundary dilatation h omega this leads to the conclusion that for a large class of domains the equality m omega 1 r omega conjectured by garnett and yang does not hold where r omega is the quasiconformal reflection constant

an efficient decomposition of the expectation of the maximum for the multivariate normal and related distributions abstract in structural dynamic discrete choice models monte carlo integration has been the only way to evaluate the expectation of the maximum when errors are normally distributed in this paper however i show that the expectation of the maximum can be decomposed as a linear combination of multivariate normal cdfs for related distributions such as the multivariate t distribution this expectation has a similar decomposition my computational results show speed benefits of my proposed method for models with a low number of choices although the speed gains are contingent on the use of analytical derivatives as opposed to numerical derivatives

numerical analysis on fuzzy relation equations with various operators abstract in this study we investigate the properties of the approximate solutions of fuzzy relation equations for composite operators defined by max min hamacher and its special case disjunctive sum conjunctive product a quasi newton method is adopted to find the solutions apart from particular issues relevant to individual operators comparisons among the various operators are made

fuzzy linear systems abstract fuzzy linear systems of equations and inequalities over a bounded chain are studied both from theoretical and computational points of view a unified approach is presented for solving such systems completed with polynomial time algorithms the main results are concerned with establishing the consistency of the system computing all kinds of solutions or marking the contradictory equations respectively inequalities if the system is inconsistent applications in fuzzy linear programming multivalued logic fuzzy matrix equations or inequalities fuzzy relation equations or inclusions fuzzy automata and medicine are presented

fuzzy relational equations and the inverse problem abstract the inverse problem concerned with fuzzy relations is investigated the conditions for the existence of a solution are shown and an analytical solution is given a method for the improvement of the solution is proposed

convexly combined fuzzy relational equations and several aspects of their application to fuzzy information processing abstract this paper presents some theoretical results on a set of the convexly combined fuzzy relational equations represented in the form x k 2 x k r y k k 1 2 k where x k and y k denote fuzzy sets r and 2 fuzzy relations the sup min compositional operator the inf max one and a fuzzy convex combinator whose complement is furthermore we propose a method to formulate the fuzzy information processing approximately by means of the convexly combined fuzzy relational equations focusing our attention on the modeling of fuzzy input output systems normality of fuzzy sets characterizing fuzzy input fuzzy logical aspects of systems and association between fuzzy information finally it is suggested that the proposed method is suitable for the modelling of several types of fuzzy systems

possibilistic linear systems and their application to the linear regression model abstract it is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linear regression analysis by possibilistic linear models linear regression by a possibilistic model is called possibilistic linear regression this is a new interpretation of fuzzy linear regression and also includes a new method by which interval analysis can be done in fuzzy numbers

revealing logical dependencies in fuzzy data with the aid of multilevel fuzzy relational equations in this paper the idea is discussed to connect given fuzzy input and output data via a hidden layer of intermediate data this idea is on the one hand treated using cascaded systems of fuzzy relational equations and is on the other hand approached from a numerical perspective

resolution of composite interval valued fuzzy relation equations abstract in this study we investigate the properties and the solution procedure of composite interval valued fuzzy relation equations with max min operator this is a generalization of existing constant valued fuzzy relation problems the study includes both theoretical development and numerical analyses it is concluded that our proposed methodology not only solves the existing fuzzy relation equations but also reveals the necessary and sufficient conditions for more general problems therefore this study facilitates the understanding of solution structure and wider applications

on several definitions of the differential of a fuzzy mapping abstract several definitions of the differential of a fuzzy function are discussed in the restricted framework of fuzzy mappings from r to r

some theoretical aspects of fuzzy relation equations describing fuzzy systems abstract this paper contains some theoretical results on fuzzy relation equations and applications to analysis of fuzzy systems as well as identification and control problems if ai 1 i k are fuzzy inputs b is a fuzzy output and r is a fuzzy relation describing the system the above problems are illustrated by means of a max min multidimensional equation of type b a 1 a k r furthermore we investigate some properties of fuzzy systems described by fuzzy relation equations focusing our attention on energy and entropy measures of fuzziness of solutions of the class of equations under discussion

fuzzy arithmetic with requisite constraints abstract the purpose of this paper is to show that the standard fuzzy arithmetic does not take into account known constraints when applied to states of linguistic variables these constraints referred to as requisite constraints represent additional information when they are ignored as in the standard fuzzy arithmetic the obtained results exhibit in general information deficiency it is thus important as argued in the paper to revise fuzzy arithmetic to take relevant requisite constraints into account some typical requisite constraints are overviewed with a more extensive examination of the requisite equality constraint crisp or fuzzy

on the existence of minimal solutions for fuzzy equations with tolerances abstract we investigate the existence of minimal elements of solution sets for fuzzy equation problems with tolerances where the cardinality of the basic spaces of fuzzy inputs and outputs of an object need not be finite it turns out the semi continuity of applied membership functions plays a central role crisp models with fuzzy parameters are considered as well

antithetic acceleration of monte carlo integration in bayesian inference abstract it is proposed to sample antithetically rather than randomly from the posterior density in bayesian inference using monte carlo integration conditions are established under which the number of replications required with antithetic sampling relative to the number required with random sampling is inversely proportional to sample size as sample size increases the result is illustrated in an experiment using a bivariate vector autoregression

algebraic characteristics of extended fuzzy numbers abstract extended fuzzy numbers previously called fuzzy intervals are discussed by using the resolution identity and the extension principle the regularity and the spread are defined for describing the algebraic properties of extended fuzzy numbers arithmetic operations on level set intervals are suggested instead of general set operations in order to reduce the amount of computation a sufficient and necessary condition for solving a x c is derived the exact solution for a x c is obtained finally a a a fuzzification of the crisp 0 which is a natural extension from the nonfuzzy field is proved

building confidence interval based fuzzy random regression models in real world regression analysis statistical data may be linguistically imprecise or vague given the co existence of stochastic and fuzzy uncertainty real data cannot be characterized by using only the formalism of random variables in order to address regression problems in the presence of such hybrid uncertain data fuzzy random variables are introduced in this study to serve as an integral component of regression models a new class of fuzzy regression models that is based on fuzzy random data is built and is called the confidence interval based fuzzy random regression model ci frrm first a general fuzzy regression model for fuzzy random data is introduced then using expectations and variances of fuzzy random variables sigma confidence intervals are constructed for fuzzy random input output data the ci frrm is established based on the sigma confidence intervals the proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming therefore we resort to some heuristics finally an illustrative example is provided

solution of a system of linear equations with fuzzy numbers in this paper the interval nature of fuzzy numbers is revealed by showing that many interesting results from classical interval analysis transfer also into the fuzzy case the paper deals with a solution of a fuzzy interval system of linear equations i e a system in which fuzzy intervals numbers appear instead of crisp numbers

solution of fuzzy equations with extended operations abstract assuming that is any operation defined on a product set x y and taking values on a set z it can be extended to fuzzy sets by means of zadeh s extension principle given a fuzzy subset c of z it is here shown how to solve the equation a b c or a b c when a fuzzy subset a of x or a fuzzy subset b of y is given the methodology we provide includes as a special case the resolution of fuzzy arithmetical operations i e when stands for or extended to fuzzy numbers fuzzy subsets of the real line the paper is illustrated with several examples in fuzzy arithmetic

extremal function for capacity and estimates of qed constants in rn abstract this paper is devoted to the study of some fundamental problems on modulus and extremal length of curve families capacity and n harmonic functions in the euclidean space r n one of the main goals is to establish the existence uniqueness and boundary behavior of the extremal function for the conformal capacity cap a b of a capacitor in r n this generalizes some well known results and has its own interests in geometric function theory and potential theory it is also used as a major ingredient in this paper to establish a sharp upper bound for the quasiextremal distance or qed constant m of a domain in terms of its local boundary quasiconformal reflection constant h a bound conjectured by shen in the plane along the way several interesting results are established for modulus and extremal length one of them is a decomposition theorem for the extremal length a b of the curve family joining two disjoint continua a and b in a domain

an alternative approach to the resolution of fuzzy relation equations abstract in this paper we propose a solution procedure by means of a quasi characteristic matrix the matrix is so defined that not only the solution set can be determined but also the type of solution set such as the non empty set full set unique minimal solution and unique solution can be identified before the solution set is determined therefore it provides an insight into the structure of fuzzy relation equations

sets of solution set invariant coefficient matrices of simple fuzzy relation equations abstract a set of coefficient matrices which are invariant to a solution set of a simple fuzzy relation equation is considered the equipollency of the cardinal numbers of solution sets of simple fuzzy relation equations for two constant vectors is also shown

fuzzy relation equations theory as a basis of fuzzy modelling an overview abstract we give a wide overview on the applications of fuzzy relation equations theory to decision making processes to the construction of preference relations and to knowledge engineering mainly fuzzy control and fuzzy pattern recognition general theoretical results and methodological aspects are pointed out

likelihood approximation by numerical integration on sparse grids the calculation of likelihood functions of many econometric models requires the evaluation of integrals without analytical solutions approaches for extending gaussian quadrature to multiple dimensions discussed in the literature are either very specific or suffer from exponentially rising computational costs in the number of dimensions we propose an extension that is very general and easily implemented and does not suffer from the curse of dimensionality monte carlo experiments for the mixed logit model indicate the superior performance of the proposed method over simulation techniques

the set of fuzzy rational numbers and flexible querying a fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership this notion can be viewed as a generalization of the concepts of set fuzzy set and bag the set of fuzzy integers n f provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed in the field of databases the use of fuzzy bags is motivated by their ability to manage both quantities and preferences however n f becomes too restricted a framework when dealing with queries based on difference or division operations so a more general structure based on the set of fuzzy relative integers z f in which exact differences can be performed has been first developed in this paper we carry on with this approach and we extend z f to the set of fuzzy rational numbers q f this context leads to define a closed system of multiplicative operations and allows to perform exact divisions applied to flexible querying of databases q f and the notion of division on fuzzy numbers allow to generalize the relational division they define a sound basis for queries involving ratios between quantities

solutions of algebraic equations involving generalized fuzzy numbers abstract this paper deals with algebraic equations involving generalized fuzzy numbers with continuous membership functions the generalized fuzzy number defined in this paper is a general name for fuzzy numbers fuzzy intervals crisp numbers and interval numbers three important properties of the generalized fuzzy numbers with continuous membership functions are introduced as the basis for deriving the solvability criterion the sufficient and necessary condition for solving a x c is derived the sufficient and necessary condition for solving a x c and a x c when a and c are nonzero generalized fuzzy numbers is also derived in this paper instead of the inverse operation method which fails for fuzzy sets inverse operations on the boundary points of level set intervals for continuous membership functions are used when the derived criteria of solvability are satisfied a unique solution rather than a solution set is obtained

convex combinations of generalized fuzzy relational equations abstract convex combinations of two fuzzy relational equations are studied these equations are built with compositions of the type conorm norm and norm conorm this study is a generalization of the works of ohsato and sekigushi previous results concerning usual fuzzy relational equations lead to the development of convexly combined equations first conditions for the existence of solutions are studied then the resolution of equations is discussed finally the concept of pseudo solutions of a system of several equations is introduced

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

lower solutions of systems of fuzzy equations lower solutions of a system of fuzzy equations are determined by lower solutions of each equation the result is applied to fuzzy relation equations so that they are decomposed to simple fuzzy relation equations

an algorithm for solving fuzzy relation equations with max t composition operator this paper studies the problem of solving a max t composite finite fuzzy relation equation where t is a special class of pseudo t norms if the equation is solvable then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value under these conditions some minimal solutions of the system can be obtained easily some procedures are also proposed in order to simplify the original system the simplified system is then decomposed if possible into several subsystems with smaller dimensions which are very easy to solve furthermore a method is presented to solve each subsystem by combining the method and those procedures an efficient algorithm is proposed to obtain the set of feasible solutions of the original system two examples are also given to illustrate the algorithm

on the set of solutions of composite fuzzy relation equations in this paper we introduce some algorithms which have minimization properties about the fuzziness of solutions in the maxmin fuzzy relation equations

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

finite fuzzy relation equations with unique solution in complete brouwerian lattices abstract we characterize finite fuzzy relation equations having a unique solution for sake of completeness we first recall some results already established in foregoing papers in the context of the linear lattices new results are established in the general setting of the complete brouwerian lattices suitable examples illustrate the theorems obtained

equations with fuzzy numbers abstract assuming that is any operation defined in the real number set it can be extended to the fuzzy sets by zadeh s extension principle in this paper we study which conditions have to be verified by the cuts of the fuzzy numbers f and g in order that the equation f x g has a solution by the way we study some properties of the function h g f considered by e sanchez

fuzzy quantifiers in syllogisms direct versus inverse computations abstract a methodology for treating fuzzy quantifiers in natural languages has been proposed by l a zadeh this paper is centered on the intersection product syllogism where combination of quantifiers is related to multiplication of fuzzy numbers after recalling basic concepts it is shown that the use of a non standard fuzzy arithmetic can reduce fuzziness with regard to a direct computation of fuzzy quantifiers

a model for the prediction of diseases of firms by means of fuzzy relations the core of our proposal is the determination of a matrix of economic financial knowledge which states fuzzy relations between symptoms and causes in this case the symptoms of a firm can be represented by the diverse ratios which are in the end the indicators the analysts look at to make their predictions and suggestions on the other hand the diseases of the firm will be the causes to be determined which generate anomalies at the firm the ability to create such a matrix of economic financial knowledge implies that given the level of intensity of the chosen symptoms we can determine the extent to which the main problems or diseases affecting a firm s cost effectiveness and efficiency are present at the firm in order to act upon them with the utilization of the same one can be complemented the activity of the analyst of the business

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

on the existence of solutions of systems of fuzzy equations abstract a necessary and sufficient condition for the existence of solutions of a fuzzy equation given by e sanchez is extended to systems of fuzzy equations

difference distance and similarity as a basis for fuzzy decision support based on prototypical decision classes the use of prototypical decision classes as a basis for fuzzy decision support is outlined it is shown that given certain assumptions about the structure of both numeric and non numeric linguistic variables trapezoidal fuzzy sets can be used to model linguistic terms in particular the notion of a fuzzy index is introduced to model sets of linguistic terms for which there is no formal measurement scale the similarity between prototypes and input cases is measured as a function of the difference or distance between fuzzy sets the difference measure is itself a fuzzy set to reflect the underlying uncertainties in the original linguistic model similarity profiles for different decision classes are output as trapezoidal fuzzy sets the approach can be applied to the rapid development of decision aids using standard business software

inverse problem in fuzzy relational equations abstract the paper deals with the problem of handling fuzzy relational equations of the form x r y in the case of an empty solution set with respect to x x r y discussing the essence of the structure of the fuzzy relation r with respect to provided y algorithms have been proposed which enable us to modify the original equation i e the fuzzy set y in a way leading to its genuine solution or at least an approximate one it is explained how these modifications relax a set of constraints needed to be satisfied for any solvable equation a grade of the modification of the original problem is expressed in terms of distortion of the fuzzy set y which forms a cornerstone of the proposed procedures numerical examples are provided some aspects related to the area of diagnostic models in which these equations are studied are also treated

generalized solvability criteria for fuzzy equations abstract recently e sanchez has given a necessary and sufficient condition for the existence of a solution of a fuzzy a x c with the extension of a given binary operation in the universe of discourse using many valued logic we generalize this result and get a characterization also of the cases if a x c has only nearly a solution additionally we consider fuzzy relation equations and get similar results

s norm aggregation of infinite collections abstract the aggregation of membership values by means of the iterate application of an s norm is of cardinal relevance for the development of any general theory of approximate reasoning which relies on a sup t model for relation composition here we present a definition of s norm aggregation for possibly infinite collections which can be demonstrated to generalize previous approaches consistently it provides a common framework in which classical sup t and finite s t compositions can be analyzed as well as other significant cases general properties of the s norm aggregation concept its specialization for the class of continuous s norms and its relationship with fuzzy measure theory are discussed

fuzzy relational structures the state of art fuzzy relational structures built with the aid of fuzzy sets and fuzzy relations constitute a fundamental class of constructs arising in fuzzy set theory they give rise to fuzzy relation equations in this paper we will develop the concepts of single and multilevel relational structures different logic operations will be discussed in detail aspects of the knowledge representation will be studied and illustrated with several schemes of applications

approximate solutions of fuzzy relational equations in the previous chs we have discussed various problems concerning solutions of fuzzy relation equations obviously an underlying assumption is that there exists a nonempty set of solutions a situation may occurr and indeed it is quite common in which no solution exists nevertheless even in this case one might be interested to obtain an approximate solution and know to which extent it can be viewed as a solution this stream of investigations is particularly interesting for applicational purposes contrary to the topics already discussed in the previous chs this is a field of research which has not been developed enough so far it concerns studies on solvability properties of fuzzy relation equations in this ch we shall try to answer by using several techniques the following basic question how difficult is it to attain a situation in which the system of equations has solutions and then how to measure this property

specificity shift in solving fuzzy relational equations abstract studied is a system of n fuzzy relational equations with a max t composition x k r y k where the input output fuzzy sets x k and y k are available while the fuzzy relation r needs to be determined the solution to these equations is derived through a new paradigm of specificity shift the main objective is to modify a level of specificity of the fuzzy sets relational constraint so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable in more detail the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets the optimization of the specificity levels is discussed in detail numerical studies are also included finally the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient based techniques

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

inference in dynamic discrete choice models with serially correlated unobserved state variables this paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables estimation of these models involves computing high dimensional integrals that are present in the solution to the dynamic program and in the likelihood function first the paper proposes a bayesian markov chain monte carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function second the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure

relations in fuzzy class theory this paper studies fuzzy relations in the graded framework of fuzzy class theory fct this includes i rephrasing existing work on graded properties of binary fuzzy relations in the framework of fuzzy class theory and ii generalizing existing crisp results on fuzzy relations to the graded framework our particular aim is to demonstrate that fuzzy class theory is a powerful and easy to use instrument for handling fuzzified properties of fuzzy relations this paper does not rephrase the whole theory of fuzzy relations instead it provides an illustrative introduction showing some representative results with a strong emphasis on fuzzy preorders and fuzzy equivalence relations

a fuzzy approach to stability of fuzzy controllers this paper deals with stability analysis of fuzzy controllers a new definition embedding the notion of stability into fuzzy set theory is suggested in this context the introduction of a gradual stability is discussed investigating stability needs a model of the process one of the essential assumptions for the model used here is that the process has an approximatively linear structure within a sufficiently small time interval t possible deviations between the model and the real system are taken into account by specifying fuzzy parameters for the sake of simplicity however only a simple version of the model is considered in the present paper moreover some facts about the influence of the defuzzifier and the inference engine on the stability statement are presented by using this model and the suggested definition of stability some criteria ensuring stability are derived

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

identification of fuzzy relational equations by fuzzy neural networks abstract although the identification of a fuzzy system by a feedforward neural network is obviously possible whenever the system was continuous however when we use fuzzy max min neural network some problems on the learning of the network arise in this paper we present a method to identify a fuzzy relation by a fuzzy max min neural network we adapt the learning algorithm backpropagation to learning of max min neural network by using one which we will denote as smooth derivative finally we present some examples and a comparison with a similar method

fuzzy phoneme recognition abstract first a scheme for pattern recognition is given in a learning step a relation between acoustic characteristics and the corresponding phoneme is computed using an inference rule next the phonemes are recognised as result of a fuzzy relation equation then the recognition quality is analysed by means of uncertainty measures specially sugeno s and possibility measures

interval linear systems as a necessary step in fuzzy linear systems this article clarifies what it means to solve a system of fuzzy linear equations relying on the fact that they are a direct extension of interval linear systems of equations already studied in a specific interval mathematics literature we highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals each of which based on a generalization of scalar equality to intervals each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals we also consider the smallest multidimensional intervals containing the solution sets we propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals this unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

on various eigen fuzzy sets and their application to image reconstruction in this study we formulate and solve a problem of image reconstruction using eigen fuzzy sets treating images as fuzzy relations we propose two algorithms of generating eigen fuzzy sets that are used in the reconstruction process the first one corresponds to a convex combination of eigen fuzzy set equations i e fuzzy relational equations involving convex combination of max min and min max compositions in the case of the first algorithm various eigen fuzzy sets can be generated by changing the parameter controlling the convex combination of the corresponding equations the second algorithm generates various eigen fuzzy sets with respect to the original fuzzy relation using a permutation matrix a thorough comparison of the proposed algorithms and a conventional algorithm which reconstructs an image using the greatest and smallest eigen fuzzy sets is presented as well in the experiments 10 000 artificial images of size 5x5 pixels the approximation error in the case of the first second algorithm is decreased to 68 2 97 9 of that of the conventional algorithm respectively furthermore through the experimentation using real images extracted from standard image database sidba it is confirmed that the approximation error of the first algorithm is decreased to 41 5 of that of the conventional one

qed domains and ned sets in rn this paper contributes to the theory of quasiextremal distance or qed domains we associate with every qed domain d two qed constants m d and m d and exhibit how these constants reflect the geometry of d for example we give a geometric characterization for qed domains d with m d 2 and obtain some sharp estimates of qed constants m d and m d for different kinds of domains

defuzzification functionals of ordered fuzzy numbers defuzzification functionals which play the main role when dealing with fuzzy controllers and fuzzy inference systems for convex as well for ordered fuzzy numbers are discussed three characteristic conditions for them are formulated it is shown that most of the known defuzzification functionals satisfy them motivations for introducing the extended class of convex fuzzy numbers are presented together with operations on them

finite fuzzy relation equations with a unique solution in linear lattices abstract we characterize fuzzy relation equations possessing a unique solution the equations presented here involve fuzzy sets and fuzzy relations assuming values in a linear lattice and defined on finite sets a suitable example also shows that our main result generally does not hold if the fuzzy equations are assigned on complete brouwerian lattices not necessarily linear

some results in the setting of fuzzy relation equations theory abstract in this paper we point out certain theoretical aspects of fuzzy relation equations connecting some known results between composite and o fuzzy equations several theorems are obtained and some examples are provided too

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

sets of solution set equivalent coefficient matrices of fuzzy relation equations abstract a set of coefficient matrices which are equivalent to the solution set of a fuzzy relation equation is considered it is also shown that the cardinal numbers of solution sets of fuzzy relation equations for two constant vectors with the same partition on the index set are equal to each other

fuzzy set framework for development of a perception perspective abstract the question of perception attracts a lot of investigation concerning fundamental issues of knowledge representation and particularly application oriented techniques we clearly indicate the context dependent character of information processed in cognitive processes as opposed to statistical analysis in which no context is taken into account the problem being addressed here is translated into an optimization scheme under which algorithms of data analysis are worked out a general class of techniques dedicated to linguistic analysis of records of numerical data is introduced its essence relies on determining the level of data and fuzzy labels

a computationally practical simulation estimator for panel data in this paper i develop a practical extension of mcfadden s method of simulated moments estimator for limited dependent variable models to the panel data case the method is based on a factorization of the msm first order condition into transition probabilities along with the development of a new highly accurate method for similating these transition probabilities a series of monte carlo tests show that this msm estimator performs quite well relative to quadrature based ml estimators even when large numbers of quadrature points are employed the estimator also performs well relative to simulated ml even when a highly accurate method is used to simulate the choice probabilities in terms of computational speed complex panel data models involving random effects and arma errors may be estimated via msm in times similar to those necessary for estimation of simple random effects models via ml quadrature

approximately solving fuzzy relation equations some mathematical results and some heuristic proposals abstract fuzzy relation equations are intimately connected with the approach toward fuzzy control unfortunately systems of such equations are solvable only under quite restrictive conditions therefore a notion of approximate solution is discussed which applied also in cases where such systems do not have solutions for some types of fuzzy equations best possible approximate solutions are known for other types some strategies are considered to suitably guess approximate solutions furthermore that approach is applied to some types of cascaded fuzzy relation equations which are connected with ideas to join neural network structures with fuzzy control

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm