combination of fuzzy numbers representing expert opinions abstract expert opinions or imprecise estimates of a physical variable are expressed as fuzzy numbers and five techniques for combining these numbers into a single fuzzy number estimate are developed seven characteristics of the combination technique are defined namely agreement preservation order independence transformation variance possibility conservation possibility interval conservation relationship between uncertainty of individual estimates and overall uncertainty and desirability of resultant estimate the five techniques listed in increasing order of preference are 1 crisp weighting 2 fuzzy weighting 3 minimal fuzzy extension 4 convex fuzzy extension and 5 mixed linear extension an example of estimating nitrate concentration in ground water illustrates the approach the cases of equally versus unequally reliable estimates are distinguished and guidelines for choice of combination technique are provided

a new approach to fuzzy regression models with application to business cycle analysis recently fuzzy regression analysis has been largely applied in the modeling of economic or financial data however those data often exhibit certain kinds of linguistic terms for instance very good a little reclining or stable in the business cycle or the growth rate of gdp etc the goal of this paper is to construct a fuzzy regression model by fuzzy parameters estimation using the fuzzy samples it deals with imprecise measurement of observed variables fuzzy least square estimation and nonparametric methods this is different from the assumptions as well as the estimation techniques of the classical analysis empirical results demonstrate that our new approach is efficient and more realistic than the traditional regression analysis

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

modeling temporal functions with granular regression and fuzzy rules modeling of temporal functions has been studied extensively in last few decades temporal functions or time series are found practically in the gamut of applications ranging from engineering analysis to financial and commercial transactions numerous time series models been proposed and they can be found in the relevant time series literature deterministic and stochastic models have dominated much of the research in this area nonetheless these models have their limitations and particularly specific models solve specific problem domains therefore there is no general mechanism that can address the issues of modeling of temporal functions granular information is now being used to address a few of the problems in the theory of time series this paper proposes two models that use the concepts of regression and interleaved information granules intervals and fuzzy sets to identify the structure existing in a given time series in brevity we are attempting to combine regression and fuzzy rules to model temporal systems

cartan subalgebras for non principal twisted groupoid c algebras abstract renault proved in 2008 22 theorem 5 2 that if g is a topologically principal groupoid then c 0 g 0 is a cartan subalgebra in c r g for any twist over g however there are many groupoids which are not topologically principal yet their twisted c algebras admit cartan subalgebras this paper gives a dynamical description of a class of such cartan subalgebras by identifying conditions on a 2 cocycle c on g and a subgroupoid s g under which c r s c is cartan in c r g c when g is a discrete group we also describe the weyl groupoid and twist associated to these cartan pairs under mild additional hypotheses

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

linear regression analysis for fuzzy input and output data using the extension principle abstract the method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed the membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators in order to obtain the membership value of any given value taken from the fuzzy least squares estimator optimization problems have to be solved we also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data

the study of jacobi and cyclic jacobi matrix eigenvalue problems using sturm liouville theory abstract we study the eigenvalues of matrix problems involving jacobi and cyclic jacobi matrices as functions of certain entries of particular interest are the limits of the eigenvalues as these entries approach infinity our approach is to use the recently discovered equivalence between these problems and a class of sturm liouville problems and then to apply the sturm liouville theory

affine buildings tiling systems and higher rank cuntz krieger algebras to an r dimensional subshift of finite type satisfying certain special properties we associate a c algebra a this algebra is a higher rank version of a cuntz krieger algebra in particular it is simple purely infinite and nuclear we study an example if is a group acting freely on the vertices of an a2 building with finitely many orbits and if is the boundary of that building then c o is the algebra associated to a certain two dimensional subshift

dependence of the nth sturm liouville eigenvalue on the problem abstract we consider the nth eigenvalue as a function on the space of self adjoint regular sturm liouville problems with positive leading coefficient and weight functions the discontinuity of the nth eigenvalue is completely characterized

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

a fuzzy systems approach in data envelopment analysis abstract the use of fuzzy set theoretic measures is explored here in the context of data envelopment analysis which utilizes a nonparametric approach to measure efficiency three types of fuzzy statics are employed here e g fuzzy mathematical programme fuzzy regression and fuzzy entropy to illustrate the types of decisions and solutions that are achievable when the data are vague and prior information is inexact and imprecise

a clustering algorithm for fuzzy model identification the fuzzy model proposed by takagi and sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules in this paper the model is firstly modified to make its identification easier based on the fuzzy c partition space four criteria are proposed for optimization of the model parameters following that a clustering algorithm composed of fuzzy c linear functions clustering and like fuzzy c means clustering is developed for minimizing the four criteria an identification scheme for rule s premise and consequence parameters is deduced from the clustering algorithm in succession finally four examples are demonstrated to verify the effectiveness of the proposed algorithm

kms states of self similar k graph c algebras abstract let g be a countable discrete amenable group and be a strongly connected finite k graph if g is a pseudo free and locally faithful self similar action which satisfies the finite state condition then the structure of the kms simplex of the c algebra o g associated to g is described it is either empty or affinely isomorphic to the tracial state space of the c algebra of the periodicity group per g of g depending on whether the perron frobenius eigenvector of is g equivariant as applications of our main results we also exhibit several classes of important examples

a new approach to the identification of a fuzzy model abstract this paper presents an approach which is useful for the identification of a fuzzy model the identification of a fuzzy model using input output data consists of two parts structure identification and parameter identification in this paper algorithms to identify those parameters and structures are suggested to solve the problems of conventional methods given a set of input output data the consequent parameters are identified by the hough transform and clustering method which consider the linearity and continuity respectively for the premise part identification the input space is partitioned by a clustering method the gradient descent algorithm is used to fine tune parameters of a fuzzy model finally it is shown that this method is useful for the identification of a fuzzy model by simulation

fuzzy ranking and quadratic fuzzy regression abstract three different ranking methods namely the overall existence ranking index oeri the approach proposed by diamond 1 and a new two step method based on oeri are used to estimate the distance between two fuzzy numbers this distance parameter is then used in the least square or quadratic regression nonlinear programming is used to solve the resulting quadratic regression equations with constraints and simulation is used to evaluate the performance of the approaches the criterion used to evaluate the performance is the average of the absolute difference between the estimated and the observed values it appears that the two step oeri obtains better results for the case of small sample size and diamond s approach gets better as the sample size increases

linear fuzzy regression abstract this paper presents an approach which is useful for regression analysis in the case of heterogeneity of a set of observations for which regression is evaluated the proposed procedure consists of two stages first for a set of observations fuzzy classification is determined due to this homogenous classes of observations which are of hyperellipsoidal shape are obtained then for each fuzzy class the so called linear fuzzy regression is evaluated in the paper the method of calculating linear fuzzy regression coefficients is given it is a generalized version of the least squares method the formula for the values of coefficients is given some properties of linear fuzzy regression are analyzed it is proved that in one and two dimensional cases the formulae are analogous to those for usual regression a measure of goodness of fit and the method of determination of the number of fuzzy classes are also given presented examples indicate the superiority of fuzzy regression in comparison to usual regression in the case of heterogenous observations

a fuzzy multiple linear regression based loss formula in electric distribution systems estimation of energy loss is an essential task for both operation and planning in electric distribution systems the energy losses are considered to be uncertain due to measurements a new method based on fuzzy c number clustering and fuzzy multiple linear regression analysis is proposed for developing energy loss formulas to estimate losses in this paper the proposed method is implemented with three stages a part of taipower distribution system in taipei is used for illustrating the performance of the proposed method

the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources abstract we catalogue the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph the primitive ideals in the cuntz krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group the cuntz krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic

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

a generalized cuntz krieger uniqueness theorem for higher rank graphs we present a uniqueness theorem for k graph c algebras that requires neither an aperiodicity nor a gauge invariance assumption specifically we prove that for the injectivity of a representation of a k graph c algebra it is sufficient that the representation be injective on a distinguished abelian c subalgebra a crucial part of the proof is the application of an abstract uniqueness theorem which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient c algebra each of which is the unique extension of a state on the distinguished abelian c subalgebra

sturm liouville problems with finite spectrum abstract for every positive integer n we construct a class of regular self adjoint and non self adjoint sturm liouville problems with exactly n eigenvalues these n eigenvalues can be located anywhere in the complex plane in the non self adjoint case and anywhere along the real line in the self adjoint case the latter complements the well known general result for right definite sturm liouville problems with an infinite number of eigenvalues which must go to infinity asymptotically like n2 does with an appropriate and natural interpretation of a zero the eigenfunctions have the usual zero properties