general chebyshev type inequalities for universal integral a new inequality for the universal integral on abstract spaces is obtained in a rather general form as two corollaries minkowski s and chebyshev s type inequalities for the universal integral are obtained the main results of this paper generalize some previous results obtained for special fuzzy integrals e g choquet and sugeno integrals furthermore related inequalities for seminormed integral are obtained

an algorithm for global minimization of linearly constrained concave quadratic functions we present an algorithm for the global minimization of a quadratic function x y xtqx htx dty over a polytope x y rn k ax by b x 0 y 0 where x h rn y d rk b rm and where a and b are m n and m k matrices respectively and q is an n n symmetric positive definite matrix we first consider the case where k 0 and construct a tight parallelpiped r containing by using an arbitrary set of q conjugate directions and by solving 2n linear programs we show that the convex envelope of with respect to r is linear and obtain an explicit formula for it we then describe a branch and bound algorithm in which the linearity of the convex envelope allows efficient lower bounding for the subproblems for each subproblem we obtain the linear convex envelope of over a smaller parallelepiped r with facets parallel to those of r then we obtain a lower bound by minimizing this convex envelope over r if is the optimal objective value for each e 0 the algorithm generates a sequence of feasible points zj with nonincreasing function values j and a nondecreasing sequence j of lower bounds to moreover if e 0 there exist j0 such that j j e for all j j0 and if e 0 j j converges to 0 the results are then generalized to the case where k is nonzero and possibly much larger than n preliminary computational results are also presented

componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

an fptas for optimizing a class of low rank functions over a polytope we present a fully polynomial time approximation scheme fptas for optimizing a very general class of non linear functions of low rank over a polytope our approximation scheme relies on constructing an approximate pareto optimal front of the linear functions which constitute the given low rank function in contrast to existing results in the literature our approximation scheme does not require the assumption of quasi concavity on the objective function for the special case of quasi concave function minimization we give an alternative fptas which always returns a solution which is an extreme point of the polytope our technique can also be used to obtain an fptas for combinatorial optimization problems with non linear objective functions for example when the objective is a product of a fixed number of linear functions we also show that it is not possible to approximate the minimum of a general concave function over the unit hypercube to within any factor unless p np we prove this by showing a similar hardness of approximation result for supermodular function minimization a result that may be of independent interest

measures of fuzzy sets and measures of fuzziness abstract the measures presented in this paper are defined by using weber s concept of decomposable measures m of crisp sets having in particular the archimedean decomposable operations in view section 2 measures m of fuzzy sets are introduced as integrals with respect to m for the archimedean cases weber s integral will be used as alternative to sugeno s and choquet s concepts section 3 what fuzziness means will be described by functions of fuzziness f another name entropy n functions with respect to a negation in addition to the types of functions of fuzziness which are induced by concave functions we discuss also the ones which are induced by fuzzy connectives section 4 now using m for measuring the importance of items and f for the fuzziness of the possible values of a fuzzy set m f serves us as a measure of the fuzziness f of the concepts of de luca and termini capocelli and de luca kaufmann knopfmacher loo gottwald dombi and under the restriction to the archimedean cases also the concepts of trillas and riera and yager turn out to be special cases section 5

the split levinson algorithm the classical levinson algorithm for computing the predictor polynomial relative to a real positive definite toeplitz matrix is shown to be redundant in complexity it can be broken down into two simpler algorithms either of which needs only to be processed this result can be interpreted in the framework of the theory of orthogonal polynomials on the real line as follows the symmetric and antisymmetric parts of the predictors relative to the sequence of toeplitz matrices constitute two families of polynomials orthogonal on the interval 1 1 with respect to some even weight functions it turns out that the recurrence relations for these orthogonal polynomials can be used efficiently to compute the desired predictor the resulting split levinson algorithm requires roughly one half the number of multiplications and the same number of additions as the classical levinson algorithm a simple derivation of cybenko s method for computing the pisarenko frequencies is obtained from the recurrence relations underlying the split levinson algorithm

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

on fuzzy measures defined by seminormed fuzzy integrals and semiconormed fuzzy integrals abstract in this paper we show that for the continuous t seminorms and continuous t semiconorms the properties of null addivity pseudo null addivity autocontinuity and pseudo autocontinuity of fuzzy measures g can be preserved by the fuzzy measures g h and g h defined by seminormed fuzzy integrals and semiconormed fuzzy integrals respectively at most under the conditions that x y 0 x y 0 and x y x y g can be preserved by the fuzzy measures g h under the condition that x y 0 x y 0

a unified approach to the monotone convergence theorem for nonlinear integrals abstract we present a unified approach to the monotone convergence theorem for nonlinear integrals such as the choquet the sipos the sugeno and the shilkret integral a nonlinear integral may be viewed as a nonlinear functional defined on a set of pairs of a nonadditive measure and a measurable function we thus formulate our general type of monotone convergence theorem for such a functional the key tool is a perturbation of functional that manages not only the monotonicity of the functional but also the small change of the functional value arising as a result of adding small amounts to a measure and a function in the domain of the functional our approach is also applicable to the lebesgue integral when a nonadditive measure is additive

a new accelerating method for globally solving a class of nonconvex programming problems abstract in this paper we combine the new global optimization method proposed by jiao h jiao a branch and bound algorithm for globally solving a class of nonconvex programming problems nonlinear anal 70 2 2008 1113 1123 with a suitable deleting technique to propose a new accelerating global optimization algorithm for solving a class of nonconvex programming problems np this technique offers a possibility to cut away a large part of the currently investigated region in which the global optimal solution of np does not exist and can be seen as an accelerating device for the global optimization algorithm of the nonconvex programming problems compared with the method in the above cited reference numerical results show that the computational efficiency is obviously improved by using this new technique in the number of iterations the required list length and the overall execution time of the algorithm

circulant preconditioners for complex toeplitz matrices the solution of n by n complex toeplitz systems a n x b by the preconditioned conjugate gradient method is studied the preconditioner c n is the circulant matrix that minimizes b n a n f over all circulant matrices b n the authors prove that if the generating function of a n is a 2 mu periodic continuous complex valued function without any zeros then the spectrum of the normalized preconditioned matrix c n 1 a n c n 1 a n will be clustered around one hence they show that if the condition number of a n is of o n alpha the conjugate gradient method when applied to solving the normalized preconditioned system converges in at most o alpha log n 1 steps thus the total complexity of the algorithm is o alpha n log 2 n 1 log n

a branch and bound algorithm for globally solving a class of nonconvex programming problems abstract a branch and bound algorithm is proposed for globally solving a class of nonconvex programming problems np for minimizing the problem linear lower bounding functions llbfs of objective function and constraint functions are constructed then a relaxation linear programming is obtained which is solved by the simplex method and which provides the lower bound of the optimal value the proposed algorithm is convergent to the global minimum through the successive refinement of linear relaxation of the feasible region and the solutions of a series of linear programming problems and finally the numerical experiment is reported to show the feasibility and effectiveness of the proposed algorithm

a new algorithm for solving toeplitz systems of equations abstract we present some recurrences that are the basis for an algorithm to invert an n n toeplitz system of linear equations with computational complexity o n log 2 n the recurrences used are closely related to the zohar trench and bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of toeplitz systems

generalized fuzzy integrals part i fundamental concepts abstract in this paper we introduce a definition of fuzzy integral which is a generalization of both s fuzzy integral defined by m sugeno and n fuzzy integral due to zhao ruhuaiand discuss the fundamen tal properties of this kind of fuzzy integral

a robust solution approach for nonconvex quadratic programs with additional multiplicative constraints in this paper a robust algorithm is proposed for globally solving a nonconvex quadratic programming problem p1 with several additional multiplicative constraints to our knowledge little progress has been made so far for globally solving problem p1 the proposed algorithm is based on a robust solution approach that provides an essential e optimal solution this solution is also stable under small perturbations of the constraints and it turns out that such a robust optimal solution is adequately guaranteed to be feasible and to be close to the actual optimal solution convergence of the algorithm is shown and three solved sample problems are given to illustrate the robust stability and feasibility of the present algorithm

some aspects of circulant preconditioners this paper studies circulant approximations of hermitian toeplitz matrices that are solutions of certain minimization problems relative to the frobenius norm the lub 1 or the lub infty norms the examinations supplement the family of the so called optimal and superoptimal preconditioners that have been proposed for the preconditioned conjugate gradient method for solving toeplitz systems t n x b for the new frobenius norm approximations it is shown that they can be computed in o n log n arithmetic operations and that the eigenvalues of the preconditioned linear equations are asymptotically clustered around 1 if t n is a leading principal submatrix of an infinite toeplitz matrix connected with a positive function of the wiener class

measures of fuzziness of fuzzy events abstract we prove some new results on two families of fuzzy integrals defined in a previous paper and by means of them we obtain entropy measures of fuzzy sets not necessarily finite which contain as particular cases the measures of batle and trillas and weber we define another measure of fuzziness which is a function of the previous ones and satisfies with slight restrictions de luca and termini s axioms

on the monotone convergence theorem for conormed seminormed fuzzy integral abstract in this paper under the condition that the t conorm and t seminorm are continuous we prove the monotone convergence theorem of conormed seminormed fuzzy integral for non decreasing monotone measurable function sequence also we show that the result cannot be extended to the case of the non increasing function sequence

fast computation of the discrete cosine transform and the discrete hartley transform a new factorization of the discrete hartley transform dht is presented it is used to derive new algorithms for the dht and the discrete cosine transform dct with reduced number of multiplications

estimation of speech spectral parameters in the presence of noise a speech analysis system includes a codebook 230 that stores speech spectral parameters corresponding to a speech spectral hypothesis the speech spectral hypothesis may be combined with a noise spectral hypothesis and the combined hypothesis compared to a sensed signal via a discriminant function 240 the discriminant function may be evaluated using the preconditioned conjugate gradient pcg process

optimum block adaptive filtering algorithms using the preconditioning technique we propose three block adaptive algorithms using the preconditioning technique the toeplitz preconditioned optimum block adaptive toba algorithm employs a preconditioner assumed to be toeplitz the symmetric successive overrelaxation ssor preconditioned optimum block adaptive soba algorithm uses a product of triangular matrices as a preconditioner and the circulant preconditioned oba coba algorithm is based on a circulant preconditioner it is also shown that their tracking properties and convergence rates are superior to those of the oba algorithm the self orthogonizing block adaptive filter sobaf and the normalized frequency domain oba nfoba algorithm

a new global optimization approach for convex multiplicative programming in this paper by solving the relaxed quasiconcave programming problem in outcome space a new global optimization algorithm for convex multiplicative programming is presented two kinds of techniques are employed to establish the algorithm the first one is outer approximation technique which is applied to shrink relaxation area of quasiconcave programming problem and to compute appropriate feasible points and to raise the capacity of bounding and the other one is branch and bound technique which is used to guarantee global optimization some numerical results are presented to demonstrate the effectiveness and feasibility of the proposed algorithm

left right semi uninorms and coimplications on a complete lattice in this paper we firstly discuss the deresidual operations of left right semi uninorms and show which properties they satisfy then we investigate the left and right semi uninorms induced by a coimplication and give some conditions such that the operations induced by a coimplication constitute left or right semi uninorms finally we demonstrate that the meet semilattice of all disjunctive right left distributive left right semi uninorms is order reversing isomorphic to the join semilattice of all right distributive coimplications which satisfy the neutrality principle

c g preconditioning for toeplitz matrices abstract we consider the problem of solving a toeplitz system of equations by conjugate gradient method when a sequence of nested toeplitz matrices is associated to a function the spectral behaviour of the matrices involved is closely related to the analytical properties of the generating function thus it is possible to devise efficient preconditioning techniques by using various functional approximation strategies this approach leads to attractive results in the case of ill conditioned matrices for which a wide class of preconditioners are proposed

an efficient algorithm for globally solving generalized linear multiplicative programming generalized linear multiplicative programming problems are difficult problems known to be n p hard and they frequently arise in various areas such as engineering economics finance etc at present most of the global optimization algorithms for this kind of problems are mainly developed based on those kinds of branch and bound algorithms in this study a new algorithm based on the concept of level set is presented for globally solving generalized linear multiplicative programming problems the proposed algorithm is concise and easy to implement so it is quite suitable for engineering applications finally the global convergence is presented and the practical efficiency of the algorithm is demonstrated by the numerical experiments

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

circulant preconditioners for toeplitz matrices with piecewise continuous generating functions the authors consider the solution of n by n toeplitz systems t sub n x b by preconditioned conjugate gradient methods the preconditioner c sub n is the t chan circulant preconditioner which is defined to be the circulant matrix that minimizes parallel b sub n t sub n parallel sub f over all circulant matrices b sub n for toeplitz matrices generated by positive 2 pi periodic continuous functions they have shown earlier that the spectrum of the preconditioned system c sup minus 1 sub n t sub n is clustered around 1 and hence the convergence rate of the preconditioned system is superlinear however in this paper they show that if instead the generating function is only piecewise continuous then for all epsilon sufficiently small there are o log n eigenvalues of c sup minus 1 sub n t sub n that lie outside the interval 1 epsilon 1 epsilon in particular the spectrum of c sup minus 1 sub n t sub n cannot be clustered around 1 numerical examples are given to verify that the convergence rate of the method is no longer superlinear in general 20 refs

level set algorithm for solving convex multiplicative programming problems multiplicative programming problems arise in many fields such as engineering finance economics and other fields globality of solutions for these problems is difficult hence in this paper the globality of the mutiplicative programming problem is discussed by the level set concept at the end of this paper an algorithm for solving these kinds of problems is presented

minimum concave cost production system a further generalization of multi echelon model we will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities the products at some facility are either sent to the next facility or stocked in the warehouse the amount of demand for the final products during periodi i 1 n are known in advance our problem is to minimize the sum of processing holding and backlogging cost all of which are assumed to be concave the origin of this model is the classical economic lot size problem of wagner and whitin and was extensively studied by zangwill this model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems the purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility we will propose an efficient o n4m algorithm for this class of problems

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

the convergence of dg fuzzy integrals abstract the definition of another kind of generalized fuzzy integrals is introduced by means of the so called generalized triangular conorm it is said to be dual generalized fuzzy integrals and is denoted by dg fuzzy integrals in this paper several equivalent forms of dg fuzzy integrals are given particularly the convergence theorem in fuzzy measure and the monotone convergence theorems are obtained

a behavioral foundation for fuzzy measures in savage 41 a behavioral foundation was given for subjective probabilities to be used in the maximization of expected utility this paper analogously gives a behavioral foundation for fuzzy measures to be used in the maximization of choquet expected utility this opens the way to empirical verification or falsification of fuzzy measures and frees them of their ad hoc character

a survey of weak connectives and the preservation of their properties by aggregations the aim of this paper is to choose diverse definitions of generalized logical connectives and to present them in a coherent order from the weakest to the richest such a rich list of notions allows us to consider the problem of admissible aggregations in the presented classes of unary and binary operations this gives a contribution to the discussion of tolerance analysis in soft computing decision making approximate reasoning and fuzzy control first we present a short survey of the development of mv logic s connectives next we discuss postulates used for generalized logical connectives finally we describe families of weak connectives and indicate the preservation of their properties by some aggregation functions

holder type inequality for sugeno integral two inequalities for the sugeno integral on abstract spaces are studied in rather general forms which generalize most of the results on the same topic obtained by other authors thus closing the series of papers on this topic as an application a holder type inequality is obtained finally some conclusions are drawn and some problems for further investigation are suggested

global minimization of a linearly constrained concave function by partition of feasible domain the problem of minimizing a concave function subject to linear inequality constraints may have many local solutions therefore finding the global constrained minimum is a computationally difficult problem a computational method is described which finds the global minimum of a smooth concave function over a polyhedron in rn the feasible domain is partitioned into a rectangular domain which can be excluded from further consideration and r 2n subdomains at least one of which contains the global minimum a known algorithm can be applied sequentially or in parallel to each of these r subdomains to compute the global minimum a method is also presented appendix b for the construction of nontrivial test problems for which the global minimum point is known given an arbitrary polyhedron and a selected vertex it is shown how to determine a concave quadratic function generally with many local minima with its global minimum at the selected vertex

a survey and some extensions of t chan s preconditioner abstract for any given n by n matrix an t chan s circulant preconditioner cf an proposed by t chan t chan an optimal circulant preconditioner for toeplitz systems siam j sci statist comput 9 1988 766 771 is defined to be the solution of min c n a n c n f over all n by n circulant matrices cn the cf an called the optimal circulant preconditioner by t chan has been proved to be a good preconditioner for a large class of structured systems a generalization of t chan s circulant preconditioner was given by huckle t huckle circulant and skew circulant matrices for solving toeplitz matrix problems siam j matrix anal appl 13 1992 767 777 which can be used for solving some general linear systems in this paper we review some old and develop some new properties of t chan s circulant preconditioner

sharp bounds of jensen type for the generalized sugeno integral abstract in this paper we provide two sided attainable bounds of jensen type for the generalized sugeno integral of any measurable function the results extend the previous results of roman flores et al for increasing functions and abbaszadeh et al for convex and concave functions we also give corrections of some results of abbaszadeh et al as a by product we obtain sharp inequalities for symmetric integral of grabisch to the best of our knowledge the results in the real valued functions context are presented for the first time here

transformation of the pseudo integral and related convergence theorems abstract in this paper a transformation of the pseudo integral into another pseudo integral is considered using the transformed pseudo integral monotone convergence theorems for the pseudo integral are obtained based on the reverse fatou s lemma for the pseudo integral the dominated convergence type theorem is proven

band preconditioners for block toeplitz toeplitz block systems abstract preconditioned conjugate gradient methods are employed to solve symmetric positive definite m by m block toeplitz with n by n toeplitz block systems am nx b where am n are generated by 2 periodic nonnegative functions with zeros serra has proposed using band block toeplitz with band toeplitz block matrices bm n with their external and internal bandwidths independent of m and n as preconditioners serra showed that if the hessians of the generating function at the zeros are positive definite then the condition number of b 1m nam n is uniformly bounded by a constant independent of m and n whereas the condition number of am n tends to infinity as m and n tend to infinity in this paper we provide a method for deriving band preconditioners for block toeplitz toeplitz block matrices numerical examples are given to illustrate the performance of the method

possibility and necessity integrals abstract in this paper we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures these confidence measures have a field of sets as their domain and a complete lattice as their codomain in introducing these integrals the analogy with the classical introduction of lebesgue integrals is explored and exploited it is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties in this way our dual classes of fuzzy integrals constitute a significant generalization of sugeno s fuzzy integrals a large number of important general properties of these integrals is studied furthermore and most importantly the combination of seminormed fuzzy integrals and possibility measures on the one hand and semiconormed fuzzy integrals and necessity measures on the other hand is extensively studied it is shown that these combinations are very natural and have properties which are analogous to the combination of lebesgue integrals and classical measures using these results the very basis is laid for a unifying measure and integral theoretic account of possibility and necessity theory in very much the same way as the theory of lebesgue integration provides a proper framework for a unifying and formal account of probability theory

aggregation functions construction methods conjunctive disjunctive and mixed classes in this second part of our state of the art overview on aggregation theory based again on our recent monograph on aggregation functions we focus on several construction methods for aggregation functions and on special classes of aggregation functions covering the well known conjunctive disjunctive and mixed aggregation functions some fields of applications are included

range division and linearization algorithm for a class of linear ratios optimization problems abstract this article interprets a range division and linearization algorithm for solving a class of fractional programming problems p with the sum or product of linear ratios objective function in the algorithm by dividing the outer space with respect to problem p into many polynomial rectangles the original non convex problem p is transformed and decomposed into a sequence of linear programming problems in order to improve the computational efficiency of the algorithm a new accelerating technique is introduced which deletes a large part of region of the outer space in which there exists no the optimal solution of p moreover the global convergence of the proposed algorithm is outlined and the computational complexity of it is investigated to demonstrate that it is a fully polynomial time approximation scheme finally the numerical computational results illustrate the feasibility and efficiency of the proposed algorithm

convexity conditions of kantorovich function and related semi infinite linear matrix inequalities the kantorovich function x tax x ta 1x where a is a positive definite matrix is not convex in general from a matrix or convex analysis point of view it is interesting to address the question when is this function convex in this paper we prove that the 2 dimensional kantorovich function is convex if and only if the condition number of its matrix is less than or equal to 3 22 thus the convexity of the function with two variables can be completely characterized by the condition number the upper bound 3 22 is turned out to be a necessary condition for the convexity of the kantorovich function in any finite dimensional spaces we also point out that when the condition number of the matrix which can be any dimensional is less than or equal to 5 26 the kantorovich function is convex furthermore we prove that this general sufficient convexity condition can be improved to 2 3 in 3 dimensional space our analysis shows that the convexity of the function is closely related to some modern optimization topics such as the semi infinite linear matrix inequality or robust positive semi definiteness of symmetric matrices in fact our main result for 3 dimensional cases has been proved by finding an explicit solution range to some semi infinite linear matrix inequalities

fft based preconditioners for toeplitz block least squares problems discretized two dimensional deconvolution problems arising e g in image restoration and seismic tomography can be formulated as least squares computations min b tx 2 where t is often a large scale rectangular toeplitz block matrix the authors consider solving such block least squares problems by the preconditioned conjugate gradient algorithm using square nonsingular circulant block and related preconditioners constructed from the blocks of the rectangular matrix t preconditioning with such matrices allows efficient implementation using the one dimensional or two dimensional fast fourier transform fft two block preconditioners related to those proposed by t chan and j olkin for square nonsingular toeplitz block systems are derived and analyzed it is shown that for important classes of t the singular values of the preconditioned matrix are clustered around one this extends the authors earlier work on preconditioners for toeplitz least squares iterations for one dimensiona

fuzzy sets and their operations ii among the basic operations which can be performed on fuzzy sets are the operations of union intersection complement algebraic product and algebraic sum in addition to these operations new operations called bounded sum and bounded difference were defined by l a zadeh to investigate the fuzzy reasoning which provides a way of dealing with the reasoning problems which are too complex for precise solution this paper investigates the algebraic properties of fuzzy sets under these nex operations of bounded sum and bounded difference and the properties of fuzzy sets in the case where these new operations are combined with the well known operations of union intersection algebraic product and algebraic sum

convex programs with an additional constraint on the product of several convex functions abstract in this paper we consider a special type of global optimization problem in which a convex function is minimized on x y where x is a convex set and y is a nonconvex set represented in terms of a product of p convex functions it is shown that this problem can be reduced to a p dimensional reverse convex program two outer approximation algorithms are proposed for solving the resulting problem computational experiments indicate that these algorithms can generate optimal solutions of fairly large scale linear programs with a constraint on the product of up to 4 linear functions

bilevel multiplicative problems a penalty approach to optimality and a cutting plane based algorithm bilevel programming has been proposed for dealing with decision processes involving two decision makers with a hierarchical structure they are characterised by the existence of two optimisation problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimisation problem in this paper we focus on the class of bilevel problems in which the upper level objective function is linear multiplicative the lower level one is linear and the common constraint region is a bounded polyhedron after replacing the lower level problem by its karush kuhn tucker conditions the existence of an extreme point which solves the problem is proved by using a penalty function approach besides an algorithm based on the successive introduction of valid cutting planes is developed obtaining a global optimal solution finally we generalise the problem by including upper level constraints which involve both level variables

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

toeplitz preconditioners for hermitian toeplitz systems abstract we propose a new type of preconditioners for hermitian positive definite toeplitz systems a n x b where a n are assumed to be generated by functions f that are positive and 2 periodic our approach is to precondition a n by the toeplitz matrix a n generated by 1 f we prove that the resulting preconditioned matrix a n a n will have clustered spectrum when a n cannot be formed efficiently we use quadrature rules and convolution products to construct nearby approximations to a n we show that the resulting approximations are toeplitz matrices which can be written as sums of circulant matrices as a side result we prove that any toeplitz matrix can be written as a sum of circulant matrices we then show that our toeplitz preconditioners t n are generalizations of circulant preconditioners and the way they are constructed is similar to the approach used in the additive schwarz method for elliptic problems we finally prove that the preconditioned systems t n a n will have clustered spectra around 1

semi copulas capacities and families of level sets we point out how capacities non additive measures can be used to provide explanations about the concept of bivariate ageing function the latter had been introduced to describe the family of the level sets of a survival function and motivated the interest toward the concept of semi copula

on a class of quadratic programs abstract this paper considers a class of quadratic programs where the constraints ae linear and the objective is a product of two linear functions assuming the two linear factors to be non negative maximization and minimization cases are considered each case is analyzed with the help of a bicriteria linear program obtained by replacing the quadratic objective with the two linear functions global minimum maximum is attained at an efficient extreme point efficient point of the feasible set in the solution space and corresponds to an efficient extreme point efficient point of the feasible set in the bicriteria space utilizing this fact and certain other properties two finite algorithms including validations are given for solving the respective problems each of these essentially consists of solving a sequence of linear programs finally a method is provided for relaxing the non negativity assumption on the two linear factors of the objective function

efficient numerical methods in non uniform sampling theory summary we present a new second generation reconstruction algorithm for irregular sampling i e for the problem of recovering a band limited function from its non uniformly sampled values the efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems the choice of adaptive weights can be seen as a simple but very efficient method of preconditioning further substantial acceleration is achieved by utilizing the toeplitztype structure of the system matrix this new algorithm can handle problems of much larger dimension and condition number than have been accessible so far furthermore if some gaps between samples are large then the algorithm can still be used as a very efficient extrapolation method across the gaps

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

design and analysis of toeplitz preconditioners the solution of symmetric positive definite toeplitz systems ax b by the preconditioned conjugate gradient pcg method was recently proposed by strang 1986 and analyzed by chan 1989 and chan and strang 1989 the convergence rate of the pcg method depends on the choice of preconditioners for the given toeplitz matrices the authors present a general approach to the design of toeplitz preconditioners based on the idea to approximate a partially characterized linear deconvolution with circular deconvolutions all resulting preconditioners can therefore be inverted via various fast transform algorithms with o n log n operations for a wide class of problems the pcg method converges in a finite number of iterations independent of n so that the computational complexity for solving these toeplitz systems is o n log n

on the eigenvectors of symmetric toeplitz matrices this paper presents a number of results concerning the eigenvectors of a symmetric toeplitz matrix and the location of the zeros of the filters eigenfilters whose coefficients are the elements of the eigenvectors one of the results is that the eigenfilters corresponding to the maximum and minimum eigenvalues if distinct have their zeros on the unit circle while the zeros of the other eigenfilters may or may not have their zeros on the unit circle even if the zeros of the eigenfilters of a matrix are all on the unit circle the matrix need not be toeplitz examples are given to illustrate the different properties

global optimization algorithms for linearly constrained indefinite quadratic problems abstract in this paper we consider the problem of finding the constrained global optimum of an indefinite quadratic function since such a function may have many local optima finding the global optimum is a computationally difficult problem we give an overview of the most important methods used which include benders decomposition concave programming approaches enumerative techniques and bilinear programming

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

an outcome space finite algorithm for solving linear multiplicative programming this paper presents an outcome space finite algorithm for solving linear multiplicative programming in each iteration of which a convex quadratic programming is only solved in the paper we give a global optimization condition on a class of multiplicative programming problems and prove that the proposed algorithm is finite terminative and gain a global optimal solution of the former problem when it stops it can be shown by the numerical results that the proposed algorithm is effective and the computational results can be gained in short time

linear quadratic and bilinear programming approaches to the linear complementarity problem abstract traditional pivoting procedures for solving the linear complementarity problem can only guarantee convergence for problems having well defined structures recently optimization procedures based on linear quadratic and bilinear programming have been developed to extend the class of problems that can be solved efficiently these latter approaches are the focus of this paper the strengths and weaknesses of each of the approaches are discussed the linear programming approach advanced by mangasarian is the most efficient once an appropriate objective function is found this requires the solution of a system of linear and bilinear equations that is easily solvable only in some cases extensions to this approach due to shiau show some promise but are still limited to special cases of the general problem the quadratic programming approaches discussed here are restricted to specialized procedures for the complementarity problem one proposed by cheng is based on the levitin poljak gradient projection method and the other due to cirina is based on karush kuhn tucker theory both are only successful on some problems the two bilinear programming algorithms discussed are the most general for any problem they are guaranteed to find at least one solution or conclude that none exist one is a specialization of the recent biconvex programming algorithm of al khayyal and falk and the other is an entirely new implicit enumeration procedure

special cases of the quadratic assignment problem abstract this paper presents a result of transforming a class of non convex programs into parametric programs parametric linear programming algorithms are then developed to solve several special cases of the quadratic assignment problem qap lower and upper bounds of the parameters are derived to further accelerate the parameter search numerical experiments are conducted to show the efficiency of the algorithm

internal direct product of integral ν distributive binary aggregation functions and the classification of all integral ν distributive binary aggregation functions of length 3 we present some relations between an external direct product and an internal direct product of a family of integral distributive binary aggregation functions relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral distributive binary aggregation function are investigated using these results the classification of all integral distributive binary aggregation functions on a lattice of length 3 and a description of all lattices of length 3 with an integral distributive binary aggregation function are given

problems of classification in a fuzzy environment this paper presents a classification model in a fuzzy environment by using possibility distributions and fuzzy measures optimal in bayes sense membership functions are induced these functions are similar to decision rules used in classical discriminant analysis the relations between fuzzy measures and possibility measures are also discussed to formulate a classification model where sugeno s fuzzy measures and integrals are used

a practicable branch and bound algorithm for sum of linear ratios problem abstract this article presents a practicable algorithm for globally solving sum of linear ratios problem slr the algorithm works by globally solving a bilinear programming problem eq that is equivalent to the problem slr in the algorithm by utilizing convex envelope and concave envelope of bilinear function the initial nonconvex programming problem is reduced to a sequence of linear relaxation programming problems in order to improve the computational efficiency of the algorithm a new accelerating technique is introduced which provides a theoretical possibility to delete a large part of the investigated region in which there exists no global optimal solution of the eq by combining this innovative technique with branch and bound operations a global optimization algorithm is designed for solving the problem slr finally numerical experimental results show the feasibility and efficiency of the proposed algorithm

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

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

generalized fuzzy integrals of set valued functions in this paper based on wu s generalized fuzzy integrals of point valued function c wu et al fuzzy sets and systems 70 1995 75 a theory of generalized fuzzy integrals of fuzzy valued functions will be investigated it includes definitions properties and various kinds of convergence theorems these are extensions of results in c wu et al fuzzy sets and systems 70 1995 75 d zhang and z wang fuzzy sets and systems 54 1993 63

a duality bounds algorithm for non convex quadratic programs with additional multiplicative constraints this article presents a duality bounds algorithm for globally solving a non convex quadratic programming problem p that contains several additional multiterm multiplicative constraints to our knowledge little progress has been made so far for globally solving p the algorithm uses a branch and bound scheme where lagrange duality theory is used to obtain the lower bounds as a result the lower bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently convergence of the algorithm is proved and a solved sample problem is given to show the feasibility of the proposed algorithm

λ generalized sugeno integral and its application sugeno integral is a useful tool for many problems in several domains especially in game theory measure theory decision making probability image processing and finance in this paper we introduce the concept of generalized sugeno integral then we establish general versions of chebyshev type inequality for this kind of sugeno integral by using a monotone measure our results generalize and improve the corresponding ones in the literature finally some conclusions and problems for further investigations are given

cutting planes for low rank like concave minimization problems concavity cuts play an important role in several algorithms for concave minimization such as pure cutting plane algorithms conical algorithms and branch and bound algorithms for concave quadratic minimization problems konno et al 1998 have demonstrated that the lower the rank of the problem i e the smaller the number of nonlinear variables the deeper the concavity cuts usually turn out to be in this paper we examine the case where the number of nonlinear variables of a concave minimization problem is large but most of the objective value of a good solution is determined by a small number of variables only we will discuss ways to exploit such a situation to derive deep cutting planes to this end we apply concepts usually applied for efficiently solving low rank concave minimization problems

the spectrum of a family of circulant preconditioned toeplitz systems the solutions of symmetric positive definite toeplitz systems ax b are studied by the preconditioned conjugate gradient method the preconditioner is the circulant matrix c that minimizes the frobenius norm c a f t chan an optimal circulant preconditioner for toeplitz systems ucla department of mathematics cam report 87 06 june 1987 the convergence rate of these iterative methods is known to depend on the distribution of the eigenvalues of c 1 a for toeplitz matrix a with entries which are fourier coefficients of a positive function in the wiener class this paper establishes the invertibility of c finds the asymptotic behaviour of the eigenvalues of the preconditioned matrix c 1 a as the dimension increases and proves that they are clustered around 1

a concept of duality for multivariate exchangeable survival models in some past works by the author and collaborators the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed generally the ageing function turns out to be a semi copula here we focus attention on the special class of survival models whose ageing function is actually a copula for pairs of models in this class we define a notion of duality such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula the formulation of the notion of duality presented here came out some years ago in the frame of research activity in collaboration with bruno bassan

linear multiplicative programming an algorithm for solving a linear multiplicative programming problem referred to as lmp is proposed lmp minimizes the product of two linear functions subject to general linear constraints the product of two linear functions is a typical non convex function so that it can have multiple local minima it is shown however that lmp can be solved efficiently by the combination of the parametric simplex method and any standard convex minimization procedure the computational results indicate that the amount of computation is not much different from that of solving linear programs of the same size in addition the method proposed for lmp can be extended to a convex multiplicative programming problem cmp which minimizes the product of two convex functions under convex constraints