reduction of a nilpotent fuzzy matrix abstract a problem of reducing fuzzy matrices is considered and some results are obtained with regard to nilpotent matrices first reduction of irreflexive and transitive matrices is examined and then the results are applied to nilpotent matrices nilpotent matrices are matrices which represent acyclic graphs and the graphs are used to represent consistent systems the results are useful for simplification of various systems with fuzzy transitivity

stabilization of parameter estimation for kriging based approximation with empirical semivariogram abstract this paper discusses stabilization of an optimization procedure to determine an appropriate semivariogram parameter using the empirical semivariogram for kriging based approximation from a viewpoint of a computational cost for constructing a surrogate model a semivariogram fitting approach using the empirical semivariogram can be usable for the parameter estimation of a semivariogram function however instability of the optimization procedure for determination of the semivariogram parameter may be observed in some cases and it causes to generate an invalid surrogate model for this problem a simple technique for stabilization of the optimization for the parameter determination is proposed in this paper the proposed approach employs a normalization technique of input data with respect to values of variables and an objective function the proposed method is applied to some numerical examples and the numerical results illustrate validity and effectiveness of the proposed method

multiparametric response surface construction by means of proper generalized decomposition an extension of the parafac procedure abstract multidimensional problems are found in almost every scientific field in particular this is standard in parametric design inverse analysis in optimization and in metamodeling analysis whereby statistical or deterministic approximations of multiparametric solutions are built from the results of experimental campaigns or computer simulations multidimensional fitting or approximation of response functions exponentially increase their complexity and computational cost with the number of dimensions responding to the well known curse of dimensionality to reduce the order of complexity and make the solution of many parameter problems affordable we propose to combine the model reduction technique known as proper generalized decomposition pgd and the response surface rsm methodology as a proof of concept we have used a simple fitting procedure as it is least squares although other more complex fitting procedures may be easily included the combined algorithm is presented and its capabilities discussed in a set of multidimensional examples the data samples to be fit in each of these examples are obtained by means of appropriate discretizing the interval of interest for each design factor and then generating the output values exact or stochastically modified by means of virtual experiments to have an idea of the number of discretization points needed along each direction the taguchi s design of experiments is used the obtained results show evident improvements in computer time and accuracy when compared to other traditional multiparametric approximation techniques based on polynomial functions and the standard levenberg marquardt algorithm especially in problems with non linear behavior and with high number of design parameters further comparison was done with the parafac als algorithm the combination of pgd and rsm seems to be an appealing tool for accurately modelling multiparametric problems in almost real time if a sufficient set of previous off line results is available despite the intrinsic complexity of the problem and of the number of parameters involved

convergence of the power sequence of a nearly monotone increasing fuzzy matrix abstract by introducing a new classification the essential role of the principal diagonal elements for the convergence of the power sequence of a fuzzy matrix a is exported at the level of a itself the established theorems cover those of monotone or nearly monotone increasing fuzzy matrices the convergence index of matrices of this type is always less than or equal to n the results can be considered to be a generalization of the results obtained by some authors on the one hand and on the other it is more important that the results have laid the foundation for studying the convergence and oscillation for power sequence of an arbitrary fuzzy matrix in general furthermore as a typical case which needs to be considered the necessary and sufficient conditions for an increasing fuzzy matrix a to have the property a n 1 a n a n 1 were established and the typical form was represented

szpilrajn s theorem on fuzzy orderings fuzzy relation matrices are considered and the well known szpilrajn theorem on orderings is generalized to fuzzy orderings zadeh has already shown a generalized theorem but another generalization is given in matrix form some interesting operations on fuzzy matrices are introduced and their properties are mentioned briefly the theorem is represented in terms of the matrix operations the operations have many properties and are useful in the various applications of fuzzy matrices or fuzzy relations

an efficient algorithm for kriging approximation and optimization with large scale sampling data abstract this paper describes an algorithm to improve a computational cost for estimation using the kriging method with a large number of sampling data an improved formula to compute the weighting coefficient for kriging estimation is proposed the sherman morrison woodbury formula is applied to solving an approximated simultaneous equation to determine a weighting coefficient a profile of the matrix is reduced by sorting of given data applying the proposal formula to several examples indicates its characteristics as a numerical example layout optimization of a beam structure for eigenfrequency maximization is solved the results show an applicability and effectiveness of the proposed method

perturbation based successive approximate topology optimization for a displacement minimization problem abstract this paper discusses a new approach for displacement based topology optimization of continuum topology optimization of continuum can be performed with the optimization of material distribution this optimization problem will include a large number of design variables and it may require a high computational cost especially for computation of gradient components with respect to an objective function and determination of an appropriate updating increment a conventional approximate optimization technique may not be effective for this problem because it is a very large scale problem from this viewpoint a new optimization technique which is based on a successive approximation algorithm is proposed the proposed method consists of two main processes 1 a linear approximation for determination of an updating direction and 2 a nonlinear approximation for determining a scale coefficient of the updating vector the first approximation is performed using the perturbation based finite element analysis and the second approximation is performed using the kriging method in order to investigate effectiveness of the proposed method it is applied to some typical examples for topology optimization problem from the numerical results effectiveness and validity of the proposed method are discussed

transitivity of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called a path algebra transitivity of generalized fuzzy matrices is defined and some properties of transitivity are shown especially properties of the composition of transitive fuzzy matrices representing transitive fuzzy relations are examined by introducing a third operation on the semiring with two operations the transitivity is closely related to metrics distances ultrametrics and so on

on the power sequence of a fuzzy matrix iii a detailed study on the power sequence of matrices of commonly used types abstract focusing on the behavior of the principal diagonal elements of ak a new classification has been introduced which is called circularly k dominating in turns out that the convergence index or the oscillating index of the power sequence of an n n fuzzy matrix of the circularly k dominating type is bounded by nk n k from above and if it is oscillating then the period index pa is a factor of k the fuzzy matrices of the 2 dominating type were discussed in detail it was shown that the 2 dominating type is a more general class than those have been discussed before and the results established for matrices of 2 dominating type is as good as the results obtained for controllable matrices therefore most commonly used types of fuzzy matrices can be examined under the framework of 2 dominating matrices and the convergence index or oscillating index can be estimated based on the results

a linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing a discrete event system is a system whose behavior can be described by means of a set of time consuming activities performed according to a prescribed ordering events correspond to starting or ending some activity an analogy between linear systems and a class of discrete event systems is developed following this analogy such discrete event systems can be viewed as linear in the sense of an appropriate algebra the periodical behavior of closed discrete event systems i e involving a set of repeatedly performed activities can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra this problem is numerically solved by an efficient algorithm which basically consists of finding the shortest paths from one node to all other nodes in a graph the potentiality of this approach for the performance evaluation of flexible manufacturing systems is emphasized the case of a flowshop like production process is analyzed in detail

on the sequence of consecutive powers of a fuzzy matrix with max archimedean t norms in the literature the limiting behavior of powers of a fuzzy matrix has been studied with max product composition pang and guu proposed a simple and effective characterization for the limiting behavior with the notion of asymptotic period in this paper we shall extend pang and guu s work to the realm with the max archimedean t norm composition to which the max product belongs moreover some sufficient conditions for the powers to converge in finitely many steps will be established

on the oscillating power sequence of a fuzzy matrix abstract the properties of an oscillating power sequence of an n n fuzzy matrix have been studied the necessary and sufficient conditions have been established for a power sequence to be oscillatory furthermore the oscillation index was detailed to some degree especially for some typical boolean matrices it is also shown that the period index set of the power sequences of fuzzy matrices of order n is not bounded from above by a power of n for all integers n

convergence of max arithmetic mean powers of a fuzzy matrix fuzzy matrices provide convenient representations for fuzzy relations on finite universes in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper the max arithmetic mean composition is considered for the fuzzy relations we show that the max arithmetic mean powers of a fuzzy matrix always are convergent

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

structural optimization using kriging approximation an optimization method using kriging approximation is applied to a structural optimization problem the method involves two main processes the first is a space estimation process that uses the kriging method and the second is an optimization process the use of the kriging method makes it easier to perform the approximation optimization as an example of the estimation performed as part of structural optimization a response surface for layout optimization of beam reinforcement is estimated to evaluate the applicability of the kriging method kriging estimation is compared with neural network approximation as a numerical example the optimization of a stiffened cylinder for an eigenfrequency problem is illustrated the obtained results clearly show the applicability of the method

residuation in fuzzy algebra and some applications abstract the system 0 1 max min has a number of well known applications many of which involve the inversion of linear relations we show the advantage of residuation theory for this process and apply it to the analysis of the problem of chebychev approximation

a note on the sequence of consecutive powers of a nonnegative matrix in max algebra abstract in this note we shall consider the sequence of consecutive powers in max algebra of a nonnegative matrix with each element less than or equal to 1 the notion of asymptotic period is defined to study the limiting behavior of this sequence a simple and effective characterization for the asymptotic period of the sequence is given

convergence of powers for a fuzzy matrix with convex combination of max min and max arithmetic mean operations fuzzy matrices have been proposed to represent fuzzy relations on finite universes since thomason s paper in 1977 showing that powers of a max min fuzzy matrix either converge or oscillate with a finite period conditions for limiting behavior of powers of a fuzzy matrix have been studied it turns out that the limiting behavior depends on the algebraic operations employed which usually in the literature includes max min max product max archimedean t norm max t norm max arithmetic mean operations respectively in this paper we consider the powers of a fuzzy matrix with convex combination of max min and max arithmetic mean operations we show that the powers of such a fuzzy matrix are always convergent

note on convergence of powers of a fuzzy matrix we show by example that a theorem in thomason j math anal appl 57 1977 476 also recently quoted in imai et al fuzzy sets and systems 109 2000 405 about the convergence of fuzzy matrices is false

kriging based approximate stochastic homogenization analysis for composite materials abstract this paper describes a novel method for a stochastic analysis of a multiscale homogenization problem an inhomogeneous material such as a composite material has a complex microstructure and sometimes it has an uncertainty in geometry or a material property of a microstructure this microscopic uncertainty will cause dispersion of a macroscopic homogenized material property of a composite material in order to analyze this problem an approximation based stochastic analysis approach is developed the proposed method uses a flexible approximation technique and variable transformation of a probabilistic density function in this paper the kriging method is used for approximation and integral estimation of a probabilistic density function as a numerical example a stochastic response analysis for a homogenized elastic tensor and homogenized elastic constants of a unidirectional fiber reinforced composite material is performed using the monte carlo simulation the perturbation based homogenization method and the proposed method uncertainties in material properties and geometry of a microstructure of a unidirectional fiber reinforced composite plate are taken into account from the numerical results validity and effectiveness of the proposed method are shown

canonical form of a transitive fuzzy matrix some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive matrix is given using the properties as a special case an open problem concerning idempotent matrices of kim and roush is solved in our results a nilpotent matrix and a symmetric matrix play an important role we decompose a transitive matrix into the sum of a nilpotent matrix and a symmetric matrix then we obtain a canonical form of the transitive matrix

on the asymptotic period of powers of a fuzzy matrix in our prior study we have examined in depth the notion of an asymptotic period of the power sequence of an nxn fuzzy matrix with max archimedean t norms and established a characterization for the power sequence of an nxn fuzzy matrix with an asymptotic period using analytical decomposition methods in this paper by using graph theoretical tools we further give an alternative proof for this characterization with the notion of an asymptotic period using graph theoretical tools we additionally show a new characterization for the limit behaviour and then derive some results for the power sequence of an nxn fuzzy matrix with an asymptotic period

error analysis of algorithms for computing the projection of a point onto a linear manifold the accumulation of rounding errors in methods used to compute the projection of a point onto a linear manifold is studied the methods are based on modified gram schmidt householder and givens orthogonal factorizations

dioids and semirings links to fuzzy sets and other applications besides the classical algebraic structures of groups rings and fields which have long been the almost exclusive reference concepts used in mathematical modelling other algebraic structures such as dioids and semirings have emerged in the last two or three decades in connection with modelling and solving a rich variety of non classical problems e g in decision analysis fuzzy set theory operations research automatic control and mathematical physics the present paper aims at providing an overview of applications of dioid and semiring structures stressing links with fuzzy sets and emphasizing linear algebraic problems solving linear systems computing eigenvalues and eigenvectors non classical path finding problems using algebras of endomorphisms and connections between dioid structure and nonlinear analysis in view of solving problems in mathematical physics

on applying kriging based approximate optimization to inaccurate data abstract this paper describes a new approach for the use of kriging based approximate optimization with inaccurate data a conventional kriging system is applicable to several kinds of complex systems however there are some difficulties in applying a kriging based system to a noisy system therefore this paper proposes a new approach for kriging based estimation with inaccurate data the principal idea is summarized as an improvement of a semivariogram and determining process of its parameters by applying the proposed method to some numerical examples the applicability of the kriging system to an approximate optimization system of inaccurate data is investigated the applicability and problems in applying the kriging system to inaccurate data are discussed and numerical results illustrate the validity and effectiveness of the proposed method

on the max nilpotent t norm powers of a fuzzy matrix fuzzy matrices have been proposed to represent fuzzy relations in finite universes various studies have evaluated the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions indicating that the limiting behavior of the powers of a fuzzy matrix depends on its composition in this paper max nilpotent composition is considered for the fuzzy relations we demonstrate that the max nilpotent powers of a fuzzy matrix either converge or oscillate in a finite period moreover the max nilpotent t norm powers of a fuzzy matrix a are p periodic if and only if the powers of an associated boolean matrix a c are p periodic finally necessary and sufficient conditions are proposed for nilpotent fuzzy matrices that exhibit max nilpotent composition

convergence of powers of a fuzzy transitive matrix convergence of powers of a fuzzy transitive matrix is considered and some conditions for convergence are given under the max min operation on fuzzy matrices a fuzzy transitive matrix is a matrix which represents a fuzzy transitive relation and has many interesting properties the conditions for convergence of fuzzy matrices are examined under a special operation which is essential to reduction of fuzzy matrices or fuzzy systems given results show graph theoretic properties of fuzzy matrices and are useful when we consider convergence of systems represented by fuzzy matrices

convergence eigen fuzzy sets and stability analysis of relational matrices abstract if stable control applications are formulated with a max product composition then instability in the relational matrix under any conditions is undesirable this paper reviews the stability analysis of relational matrices combined with the max min composition 19 and then presents an analysis of the stability of relational matrices combined with the max product composition this analysis includes results defining the convergence properties of the relational matrix determination of the eigen fuzzy sets of the stable matrices and algorithmic solutions for several important cases a method is also presented to stabilize unstable relational matrices for some control applications