a modified orthogonal forward regression least squares algorithm for system modelling from noisy regressors in this paper a modified orthogonal forward regression ofr least squares algorithm is presented for system identification and modelling from noisy regressors under the assumption that the energy and signal to noise ratio snr of the signals are known or can be estimated it is shown that unbiased estimates of the error reduction ratios errs and the parameters can be obtained in each forward regression step examples are provided to illustrate the proposed approach

from canonical tensor operators of su 3 and 3 to bi orthogonal coupling coefficients explicit expansion expansion of the matrix elements of su 3 and canonical tensor operators in terms of the bi orthogonal coupling coefficients and overlaps of the draayer akiyama construction are considered special bi orthogonal extremal isoscalar factors with subscripts as multiplicity labels and proportional to q racah q 6j coefficients or the generalized wilson rahman rational bi orthogonal functions in terms of balanced or hypergeometric series are used as a natural basis for extremal matrix elements of the highest weight component of the canonical tensor operators of su 3 in the generating function approach of biedenharn lohe and louck the expansion that is obtained triple sum together with previously derived asymmetric seed isofactors and elementary overlaps gives the explicit overlap coefficients and can be used to derive su 3 and canonical tensor operators as well as new explicit normalized seed isofactors with regge type symmetry specified for the minimal null space case

axiomatics for fuzzy rough sets abstract a fuzzy t rough set consists of a set x and a t similarity relation r on x where t is a lower semi continuous triangular norm we generalize the farinas prade definition for the upper approximation operator a i x i x of a fuzzy t rough set x r given originally for the special case t min to the case of arbitrary t we propose a new definition for the lower approximation operator a i x i x of x r our definition satisfies the two important identities a a a and a a a as well as a number of other interesting properties we provide axiomatics to fully characterize those upper and lower approximations

two stage orthogonal least squares methods for neural network construction a number of neural networks can be formulated as the linear in the parameters models training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms forward selection methods are popular fast subset selection approaches however they may only produce suboptimal models and can be trapped into a local minimum more recently a two stage fast recursive algorithm tsfra combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model this paper proposes unified two stage orthogonal least squares methods instead of the fast recursive based methods in contrast to the tsfra this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods furthermore a new term exchanging scheme for backward model refinement is introduced to reduce computational demand finally given the error reduction ratio criterion effective and efficient forward and backward subset selection procedures are proposed extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods

new results on granular variable precision fuzzy rough sets based on fuzzy co implications abstract some fuzzy rough sets only consider relative error limit and others are still sensitive to mislabeled samples considering the absolute error limit fang and hu 11 proposed granular variable precision fuzzy rough sets based on fuzzy co implications to remedy these defects which are suitable to the databases with errors in conditional attribute s and decision making however there are some faults in the characterizations of granular variable precision fuzzy rough sets based on fuzzy co implications presented by fang and hu such as false conclusions insufficient and redundant conditions in this paper we further discuss the equivalent expressions of granular variable precision lower and upper approximation operators with the proper semicontinuity of fuzzy co implications based on those new equivalent expressions of granular variable precision lower and upper approximation operators the composition of granular variable precision fuzzy rough sets based on fuzzy co implications is studied with respect to a general fuzzy relation moreover we further study granular variable precision fuzzy rough sets based on fuzzy co implications to rectify those faults mentioned above

on the denominator function for canonical su 3 tensor operators the definition of a canonical unit su 3 tensor operator is given in terms of its characteristic null space as determined by group theoretic properties of the intertwining number this definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique up to phases construction of all su 3 wcg coefficients wigner clebsch gordan using this construction an explicit su 3 invariant denominator function characterizing completely the canonically defined wcg coefficients is obtained it is shown that this denominator function squared is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials these polynomials denoted gtq are defined over three shift parameters and three barycentric coordinates the properties of these polynomials hence of the corresponding invariant denominator function are developed in detail these include a derivation of their degree symmetries and zeros the

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

a comprehensive study of implicator conjunctor based and noise tolerant fuzzy rough sets definitions properties and robustness analysis abstract both rough and fuzzy set theories offer interesting tools for dealing with imperfect data while the former allows us to work with uncertain and incomplete information the latter provides a formal setting for vague concepts the two theories are highly compatible and since the late 1980s many researchers have studied their hybridization in this paper we critically evaluate most relevant fuzzy rough set models proposed in the literature to this end we establish a formally correct and unified mathematical framework for them both implicator conjunctor based definitions and noise tolerant models are studied we evaluate these models on two different fronts firstly we discuss which properties of the original rough set model can be maintained and secondly we examine how robust they are against both class and attribute noise by highlighting the benefits and drawbacks of the different fuzzy rough set models this study appears a necessary first step to propose and develop new models in future research

sparse kernel regression modeling using combined locally regularized orthogonal least squares and d optimality experimental design the note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares lrols model selection with a d optimality experimental design the proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches the lrols method alone is capable of producing a very parsimonious model with excellent generalization performance the d optimality design criterion further enhances the model efficiency and robustness an added advantage is that the user only needs to specify a weighting for the d optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic the value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values

prepotential formulation of su 3 lattice gauge theory the su 3 lattice gauge theory is reformulated in terms of su 3 prepotential harmonic oscillators this reformulation has enlarged su 3 u 1 u 1 gauge invariance under which the prepotential operators transform like matter fields the hilbert space of su 3 lattice gauge theory is shown to be equivalent to the hilbert space of the prepotential formulation satisfying certain color invariant sp 2 r constraints the su 3 irreducible prepotential operators which solve these sp 2 r constraints are used to construct su 3 gauge invariant hilbert spaces at every lattice site in terms of su 3 gauge invariant vertex operators the electric fields and the link operators are reconstructed in terms of these su 3 irreducible prepotential operators we show that all the su 3 mandelstam constraints become local and take a very simple form within this approach we also discuss the construction of all possible linearly independent su 3 loop states which solve the mandelstam constraints the techniques can be easily generalized to su n

fuzzy adaptive filters with application to nonlinear channel equalization two fuzzy adaptive filters are developed one uses a recursive least squares rls adaptation algorithm and the other uses a least mean square lms adaptation algorithm the rls fuzzy adaptive filter is constructed through the following four steps 1 define fuzzy sets in the filter input space rn whose membership functions cover u 2 construct a set of fuzzy if then rules which either come from human experts or are determined during the adaptation procedure by matching input output data pairs 3 construct a filter based on the set of rules and 4 update the free parameters of the filter using the rls algorithm the design procedure for the lms fuzzy adaptive filter is similar the most important advantage of the fuzzy adaptive filters is that linguistic information in the form of fuzzy if then rules and numerical information in the form of input output pairs can be combined in the filters in a uniform fashion the filters are applied to nonlinear communication channel equalization problems

a branch and bound to minimize the number of late jobs on a single machine with release time constraints this paper presents a branch and bound algorithm for the single machine scheduling problem 1 ri ui where the objective function is to minimize the number of late jobs lower bounds based on a lagrangian relaxation and no reductions to polynomially solvable cases are proposed efficient elimination rules together with strong dominance relations are also used to reduce the search space a branch and bound exploiting these techniques solves to optimality instances with up to 200 jobs improving drastically the size of problems that could be solved by exact methods up to now

nonlinear model structure design and construction using orthogonal least squares and d optimality design a very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy the derived model parameters are estimated via forward orthogonal least squares but the model subset selection cost function includes a d optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness adequacy and parsimony of the final model the proposed approach is based on the forward orthogonal least square ols algorithm such that new d optimality based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward ols approach illustrative examples are included to demonstrate the effectiveness of the new approach

a comparative study of fuzzy sets and rough sets this paper reviews and compares theories of fuzzy sets and rough sets two approaches for the formulation of fuzzy sets are reviewed one is based on many valued logic and the other is based on modal logic two views of rough sets are presented set oriented view and operator oriented view rough sets under set oriented view are closely related to fuzzy sets which leads to non truth functional fuzzy set operators both of them may be considered as deviations of classical set algebra in contrast rough sets under operator oriented view are different from fuzzy sets and may be regarded as an extension of classical set algebra

new realizations of the dual space of su 3 the logic of constructing and interrelating classical realizations of the dual space of so 3 is exhibited analogies with different methods of quantization of gauge theories are pointed out the analysis is applied to su 3 to obtain existing realizations and to construct new ones the gelfand zetlyn basis for the irreducible representations of su 3 is explicitly realized using polynomials in four variables and positive or negative integral powers of a fifth variable another realization uses a spinor of so 6 so 3 1 these are the analogues of schwinger bargmann construction for su 2

a robust nonlinear identification algorithm using press statistic and forward regression this paper introduces a new robust nonlinear identification algorithm using the predicted residual sums of squares press statistic and forward regression the major contribution is to compute the press statistic within a framework of a forward orthogonalization process and hence construct a model with a good generalization property based on the properties of the press statistic the proposed algorithm can achieve a fully automated procedure without resort to any other validation data set for iterative model evaluation

the ϑ lower and t upper fuzzy rough approximation operators on a semigroup in this paper we consider a semigroup as a universal set and investigate the properties of q lower and t upper fuzzy rough approximation operators a new fuzzy algebraic structure called a tl fuzzy rough semigroup is introduced and some related properties are studied finally the homomorphism properties of q lower and t upper fuzzy rough approximation operators are investigated

on the logic foundation of fuzzy reasoning abstract fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers unfortunately it seems that the two branches have not been successfully connected the aim of this paper is to establish a so called quasi propositional deductive system syntactically as well as semantically and then set a logic foundation for developing the theory of fuzzy reasoning therefrom

adaptive fuzzy control of uncertain stochastic nonlinear systems with unknown dead zone using small gain approach this paper considers the adaptive fuzzy robust control problem for a class of single input and single output siso stochastic nonlinear systems in strict feedback form the systems under study possess unstructured uncertainties unknown dead zone uncertain dynamics and unknown gain functions in the controller design fuzzy logic systems are adopted to approximate the unknown functions and the uncertain nonlinear system is therefore transformed into an uncertain parameterized system with unmodeled dynamics by combining the backstepping technique with the stochastic small gain approach a novel adaptive fuzzy robust control scheme is developed it is shown that the proposed control approach can guarantee that the closed loop system is input state practically stable isps in probability and the output of the system converges to a small neighborhood of the origin by appropriately tuning several design parameters simulation results are provided to illustrate the effectiveness of the proposed control approach

rough set theory for the interval valued fuzzy information systems the notion of a rough set was originally proposed by pawlak z pawlak rough sets international journal of computer and information sciences 11 5 1982 341 356 later on dubois and prade d dubois h prade rough fuzzy sets and fuzzy rough sets international journal of general system 17 2 3 1990 191 209 introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets this paper deals with an interval valued fuzzy information system by means of integrating the classical pawlak rough set theory with the interval valued fuzzy set theory and discusses the basic rough set theory for the interval valued fuzzy information systems in this paper we firstly define the rough approximation of an interval valued fuzzy set on the universe u in the classical pawlak approximation space and the generalized approximation space respectively i e the space on which the interval valued rough fuzzy set model is built secondly several interesting properties of the approximation operators are examined and the interrelationships of the interval valued rough fuzzy set models in the classical pawlak approximation space and the generalized approximation space are investigated thirdly we discuss the attribute reduction of the interval valued fuzzy information systems finally the methods of the knowledge discovery for the interval valued fuzzy information systems are presented with an example

parameter conditions for monotonic takagi sugeno kang fuzzy system this paper presents sufficient conditions on the parameters of the takagi sugeno kang tsk fuzzy system under which the output of the tsk fuzzy system becomes monotonic with respect to its input the output of the tsk fuzzy system is first differentiated with respect to its input and the parameter conditions are derived so as to make the derivative nonnegative the parameter conditions are developed for both single input and multi input tsk fuzzy systems where the involved fuzzy membership functions are differentiable everywhere or bar some finite points the derived monotonicity conditions consist of two parts the conditions on the consequent parts and the conditions on the fuzzy membership functions they are further characterized for the most important types of fuzzy membership functions

multiplicity invariants and tensor product decompositions of compact groups decomposing tensor products of irreducible representations of compact groups almost always involves multiplicity wherein some irreducible representations occur more than once in the direct sum decomposition we show that the multiplicity can always be specified by polynomial group invariants the setting is a bargmann segal fock space in n n complex variables where n is the number of labels needed to specify the tensor product and n is the dimension of the fundamental representation of the compact group both the tensor product and direct sum bases are realized as polynomials in this space and it is shown how clebsch gordan and racah coefficients can be computed by suitably differentiating these polynomials the example of su n is discussed in detail and it is shown that the multiplicity can be computed as the solution of certain diophantine equations arising from powers of group invariants namely minors of determinants

a fast identification algorithm for box cox transformation based radial basis function neural network in this letter a box cox transformation based radial basis function rbf neural network is introduced using the rbf neural network to represent the transformed system output initially a fixed and moderate sized rbf model base is derived based on a rank revealing orthogonal matrix triangularization qr decomposition then a new fast identification algorithm is introduced using gauss newton algorithm to derive the required box cox transformation based on a maximum likelihood estimator the main contribution of this letter is to explore the special structure of the proposed rbf neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma finally the box cox transformation based rbf neural network with good generalization and sparsity is identified based on the derived optimal box cox transformation and a d optimality based orthogonal forward regression algorithm the proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression

robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors this paper describes the design of the robust adaptive fuzzy controller for uncertain single input single output nonlinear dynamical systems with unknown nonlinearities these unknown nonlinearities are approximated by the fuzzy system with a set of fuzzy if then rules whose parameters are adjusted on line according to some adaptive laws for the purpose of controlling the output of the nonlinear system to track a given trajectory the lyapunov synthesis approach is used to develop a state feedback adaptive control algorithm based on the adaptive fuzzy model the key assumption is that the reconstruction errors satisfy certain bounding conditions the control law consists of two terms one is the certainty equivalent control and the other is the bounding control a bounding parameter adaptive law is used to obtain this bounding control the overall control system guarantees that the tracking error converges in the small neighborhood of zero and that all signals involved are uniformly bounded it is also shown that in the special case the tracking error exponentially converges to zero even though the approximation errors exist

adaptive control for nonlinear mimo time delay systems based on fuzzy approximation this paper focuses on the problem of adaptive control for a class of nonlinear multi input and multi output mimo systems with time delays a state feedback adaptive controller is constructed by backstepping technique fuzzy logic systems are used to approximate unknown nonlinear functions in the process of the controller design the main advantages of the proposed approach are twofold 1 the controller design is independent of the knowledge of the basis functions of fuzzy logic systems and 2 the suggested approach requires only m adaptive laws to control a nonlinear time delay system with m inputs simulation results illustrate the effectiveness of the proposed approach

the so 6 2 model of su 3 and its generalisation to su n the complementarity relation between the u p q and u n lie groups enables the authors to reformulate the so 6 2 model of su 3 in terms of a u 1 1 group and to outline its generalisation to a family of n 2 models of su n for n or 3 respectively associated with u n 2 1 u n 1 2 and u 1 n 2 groups

regularization in the selection of radial basis function centers subset selection and regularization are two well known techniques that can improve the generalization performance of nonparametric linear regression estimators such as radial basis function networks this paper examines regularized forward selection rfs a combination of forward subset selection and zero order regularization an efficient implementation of rfs into which either delete 1 or generalized cross validation can be incorporated and a reestimation formula for the regularization parameter are also discussed simulation studies are presented that demonstrate improved generalization performance due to regularization in the forward selection of radial basis function centers

generalized neurofuzzy network modeling algorithms using bezier bernstein polynomial functions and additive decomposition this paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are bezier bernstein polynomial functions this paper is generalized in that it copes with n dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n this new construction algorithm also introduces univariate bezier bernstein polynomial functions for the completeness of the generalized procedure like the b spline expansion based neurofuzzy systems bezier bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions unity of support and interpretability of basis function as fuzzy membership functions moreover with the additional advantages of structural parsimony and delaunay input space partition essentially overcoming the curse of dimensionality associated with conventional fuzzy and rbf networks this new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate bezier bernstein polynomial functions used in model construction the overall network weights are then learnt using conventional least squares methods numerical examples are included to demonstrate the effectiveness of this new data based modeling approach

granulation of a fuzzy set nonspecificity granulation decomposition of a fuzzy set a defined on a finite set of objects x is studied two types of decomposition are considered external granulation determined by a given equivalence relation on x and internal granulation created by clusters of elements from x with similar membership grades in a axiomatic definitions of measures of granular nonspecificity and granular specificity are proposed some general approaches to the construction of measures of granular nonspecificity specificity are suggested relationship between granular nonspecificity roughness and nonspecificity of a fuzzy set is discussed

a calculus for su 3 leading to an algebraic formula for the clebsch gordan coefficients we develop a simple computational tool for su 3 analogous to bargmann s calculus for su 2 crucial new inputs are i explicit representation of the gelfand zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable ii an auxiliary gaussian measure with respect to which the gelfand zetlin states are orthogonal but not normalized iii simple generating functions for generating all basis states and also all invariants as an illustration of our techniques an algebraic formula for the clebsch gordan coefficients is obtained for the first time this involves only gaussian integrations thus su 3 is made as accessible for computations as su 2 is

support vector learning for fuzzy rule based classification systems to design a fuzzy rule based classification system fuzzy classifier with good generalization ability in a high dimensional feature space has been an active research topic for a long time as a powerful machine learning approach for pattern recognition problems the support vector machine svm is known to have good generalization ability more importantly an svm can work very well on a high or even infinite dimensional feature space this paper investigates the connection between fuzzy classifiers and kernel machines establishes a link between fuzzy rules and kernels and proposes a learning algorithm for fuzzy classifiers we first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function fuzzy inference on the if part of a fuzzy rule can be viewed as evaluating the kernel function the kernel function is then proven to be a mercer kernel if the reference functions meet a certain spectral requirement the corresponding fuzzy classifier is named positive definite fuzzy classifier pdfc a pdfc can be built from the given training samples based on a support vector learning approach with the if part fuzzy rules given by the support vectors since the learning process minimizes an upper bound on the expected risk expected prediction error instead of the empirical risk training error the resulting pdfc usually has good generalization moreover because of the sparsity properties of the svms the number of fuzzy rules is irrelevant to the dimension of input space in this sense we avoid the curse of dimensionality finally pdfcs with different reference functions are constructed using the support vector learning approach the performance of the pdfcs is illustrated by extensive experimental results comparisons with other methods are also provided

a resolution of the su 3 outer multiplicity problem and computation of wigner coefficients for su 3 a simple algorithm is given for the resolution of the su 3 multiplicity problem and the computation of su 3 wigner coefficients using a complete set of u 2 x u 3 bargmann tensors classified by operator patterns null space properties of these tensors are easily derived their structure is such that a direct one to one correspondence is shown to exist between the bargmann tensors and the terms in the clebsch gordan series for su 3 as derived by o reilly 1982 finally the resolution presented herein is shown to be concordant with an alternative resolution advocated long ago by hecht

θ t fuzzy rough approximation operators and the tl fuzzy rough ideals on a ring in this paper we consider a ring as a universal set and study t fuzzy rough approximation operators with respect to a tl fuzzy ideal of a ring first some new properties of generalized t fuzzy rough approximation operators are obtained then a new fuzzy algebraic structure tl fuzzy rough ideal is defined and its properties investigated and finally the homomorphism of t fuzzy rough approximation operators is studied

a class of fuzzy rough expected value multi objective decision making model and its application to inventory problems in this paper we concentrate on developing a fuzzy rough multi objective decision making model according to fuzzy rough theory then we prove the existence of a solution of the fuzzy rough multi objective decision making model formulated next we develop an effective algorithm to solve the fuzzy rough expected value multi objective decision making model concerning the inventory problem and prove the convergence of the proposed algorithm finally these are applied to practical inventory problem in which all inventory costs purchasing and selling prices in the objectives and constraints are assumed to be fuzzy rough in nature comparing the results with those from the fuzzy multi objective decision making model we reach that the proposed fuzzy rough multi objective decision making model and algorithm which will be of much use to management and provide significant solutions to construct other inventory models with fuzzy rough variables in real life

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

constructive and algebraic methods of the theory of rough sets this paper reviews and compares constructive and algebraic approaches in the study of rough sets in the constructive approach one starts from a binary relation and defines a pair of lower and upper approximation operators using the binary relation different classes of rough set algebras are obtained from different types of binary relations in the algebraic approach one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators various classes of rough set algebras are characterized by different sets of axioms axioms of approximation operators guarantee the existence of certain types of binary relations producing the same operators

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

fuzzy reasoning based on a new fuzzy rough set and its application to scheduling problems in this paper we study the fuzzy reasoning based on a new fuzzy rough set first we define a broad family of new lower and upper approximation operators of fuzzy sets between different universes using a set of axioms then based on the approximation operators above we propose the fuzzy reasoning based on the new fuzzy rough set by means of the above fuzzy reasoning based on the new fuzzy rough set for a given premise we can obtain the fuzzy reasoning consequence expressed by the fuzzy interval constructed by the above two approximations of fuzzy sets furthermore through the defuzzification of the lower and upper approximations we can get the corresponding two values constructing the interval used as the fuzzy reasoning consequence after defuzzification then from the above interval a suitable value can be selected as the final reasoning consequence so that some special constraints are satisfied as possibly at last we apply the fuzzy reasoning based on the new fuzzy rough set to the scheduling problems and numerical computational results show that the fuzzy reasoning based on the new fuzzy rough set is more suitable for the scheduling problems compared with the fuzzy reasoning based on the cri method and the iii method

a fuzzy rule based approach for screening international distribution centres in practical situations a decision maker often has to deal with numerous alternatives in evaluating and selecting the most suitable international distribution centre idc location for enhancing the organizational competitiveness to improve the effectiveness of the decision making process it is critical to reduce the number of alternatives through screening so that the decision maker can focus on the most attractive alternatives for further consideration this paper presents a fuzzy rule based approach to effectively screen decision alternatives in adequately solving the problem of evaluating and selecting idc locations case based reasoning with the use of fuzzy production rules is adopted to screen out unattractive alternatives based on past experience in a specific decision making situation a decision support system based on the proposed approach is presented to improve the effectiveness of the screening process an example is given to demonstrate the applicability of the proposed approach in improving the effectiveness of the decision making process in multicriteria decision making

adaptive control of a class of nonlinear pure feedback systems using fuzzy backstepping approach a controller is proposed for the robust backstepping control of a class of nonlinear pure feedback systems using fuzzy logic the proposed control scheme utilizes fuzzy logic systems to learn the behavior of the unknown plant dynamics filtered signals are employed to circumvent algebraic loop problems encountered in the implementation of the usual controllers and the approximation errors can be efficiently counteracted by employing smooth robust compensators most importantly the uniform ultimate boundedness of all signals in the closed loop system can be guaranteed and a priori knowledge of the plant dynamics is no longer required furthermore the proposed method can be used for adaptive control of a large class of single input single output nonlinear systems in both strict feedback and pure feedback forms and has great potential in many diverse applications the performance of the proposed approach is demonstrated through three simulation examples including one nonlinear pure feedback and two nonlinear strict feedback systems

su n irreducible schwinger bosons we construct su n irreducible schwinger bosons satisfying certain u n 1 constraints which implement the symmetries of su n young tableaues as a result all su n irreducible representations are simple monomials of n 1 types of su n irreducible schwinger bosons further we show that these representations are free of multiplicity problems thus all su n representations are made as simple as su 2

combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks presents a two level learning method for radial basis function rbf networks a regularized orthogonal least squares rols algorithm is employed at the lower level to construct rbf networks while the two key learning parameters the regularization parameter and the rbf width are optimized using a genetic algorithm ga at the upper level nonlinear time series modeling and prediction is used as an example to demonstrate the effectiveness of this hierarchical learning approach

fuzzy basis functions universal approximation and orthogonal least squares learning fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions using the stone weierstrass theorem it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy based on the fuzzy basis function representations an orthogonal least squares ols learning algorithm is developed for designing fuzzy systems based on given input output pairs then the ols algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system the fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system and the simulation results show that the control performance is improved by incorporating some common sense fuzzy control rules

complementary group resolution of the su n outer multiplicity problem ii recoupling approach for su 3 u 2 reduced wigner coefficients a general procedure for the derivation of su 3 u 2 reduced wigner coefficients rwcs for the coupling 1 1 2 2 where is the outer multiplicity label required in the decomposition is proposed based on a recoupling approach that follows the complementary group technique for a resolution of the outer multiplicity of su n introduced in part i of this series rwcs of su n are not unique under a canonical resolution of the outer multiplicity the transformation from one set to another are elements of so m where m is the number of occurrences of the irrep in the decomposition 1 1 2 2 a special resolution of the multiplicity is identified that leads to a recursive procedure for the determination of rwcs new features of these special rwcs and differences from those obtained with other choices are discussed the method can be applied to the derivation of general su n wigner or rwcs algebraic expressions for another kind of rwcs the so called reduced auxiliary wigner coef

models for su 3 in terms of so n 2 and so 2n algebras mathematical and physical models for su 3 are given in terms of unirreps of the so n 2 and so 2n algebras vector coherent state representations are given for all the discrete series unirreps of so n 2 and so 2n traceless bosons are shown to arise naturally in these representations a new and elegant realisation of the so 8 approximately so 6 2 model for su 3 is given and it is shown how to perform calculations in the so 8 model using the powerful vector coherent state representations formalism

a new boson calculus for su 3 it is shown that the gelfand weyl pattern for su 3 can be uniquely expressed in terms of four non negative and one positive or negative free integers this provides an optimal albeit non linear boson calculus for su 3 in terms of four harmonic oscillators and one planar rotor by optimal it is meant that every irreducible representation is obtained once and once only our techniques can be generalized to other groups

nonlinear model structure detection using optimum experimental design and orthogonal least squares a very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy the derived model parameters are estimated via forward orthogonal least squares but the subset selection cost function includes an a optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model an illustrative example is included to demonstrate the effectiveness of the new approach

necessary conditions for some typical fuzzy systems as universal approximators abstract we investigate necessary conditions for general single input single output fuzzy systems and a class of typical multiple input single output fuzzy systems as universal approximators for continuous functions defined on compact domains with arbitrarily small uniform approximation error bounds considering the case where the only available data about the continuous function to be approximated are a finite set of its extrema we have established some necessary conditions for the fuzzy systems to be universal approximators of the function the conditions can be used practically to determine input fuzzy sets output fuzzy sets and fuzzy rules of the fuzzy systems furthermore these necessary conditions provide a basis for insightful analysis of the strengths as well as the limitations of the fuzzy systems the main strength is that only a small number of fuzzy rules may be needed to uniformly approximate continuous functions that have a complicated formulation but a relatively small number of extrema the limitation is that in order to approximate highly oscillatory continuous functions the number of fuzzy rules must be large 1997 elsevier science ltd

a simplified so 6 2 model of su 3 a new realization is obtained of the representation of so 6 2 which has been shown recently by flath and biedenharn and also by bracken and macgibbon to define a model of su 3 in contrast to the realization in terms of six pairs of boson operators used previously which involved cubic expressions the new realization involves only quadratic expressions in eight pairs of boson operators and is manifestly hermitian properties of this new oscillator realization and in particular its advantages over the old realization are discussed briefly it is deduced that the representation of so 6 2 is integrable to a unitary group representation

coherent states for su 3 we define coherent states for su 3 using six bosonic creation and annihilation operators these coherent states are explicitly characterized by six complex numbers with constraints for the completely symmetric representations n 0 and 0 m only three of the bosonic operators are required for mixed representations n m all six operators are required the coherent states provide a resolution of identity satisfy the continuity property and possess a variety of group theoretic properties we introduce an explicit parametrization of the group su 3 and the corresponding integration measure finally we discuss the path integral formalism for a problem in which the hamiltonian is a function of su 3 operators at each site

further remarks on the relation between rough and fuzzy sets abstract based on results of pawlak and wygralak some remarks on the relation between rough sets and fuzzy sets are given an improved definition of rough set is also proposed

an interval type 2 fuzzy rough set model for attribute reduction rough set theory is a very useful tool for describing and modeling vagueness in ill defined environments traditional rough set theory is restricted to crisp environments however nowadays it has been extended to fuzzy environments resulting in the development of the so called fuzzy rough sets type 2 fuzzy sets possess many advantages over type 1 fuzzy sets but for the general type 2 fuzzy sets the computational complexity is severe on the other hand set theoretic and arithmetic computations for the interval type 2 fuzzy sets are very simple motivated by the aforementioned accomplishments in this paper the concept of fuzzy rough sets is generalized to interval type 2 fuzzy environments subsequently a method of attribute reduction within the interval type 2 fuzzy rough set framework is proposed lastly the properties of the interval type 2 fuzzy rough sets are presented

orthogonal least squares learning algorithm for radial basis function networks the radial basis function network offers a viable alternative to the two layer neural network in many applications of signal processing a common learning algorithm for radial basis function networks is based on first choosing randomly some data points as radial basis function centers and then using singular value decomposition to solve for the weights of the network such a procedure has several drawbacks and in particular an arbitrary selection of centers is clearly unsatisfactory the authors propose an alternative learning procedure based on the orthogonal least squares method the procedure chooses radial basis function centers one by one in a rational way until an adequate network has been constructed in the algorithm each selected center maximizes the increment to the explained variance or energy of the desired output and does not suffer numerical ill conditioning problems the orthogonal least squares learning strategy provides a simple and efficient means for fitting radial basis function networks this is illustrated using examples taken from two different signal processing applications

on the structure of tensor operators in su3 a global algebraic formulation of su3 tensor operator structure is achieved a single irreducible unitary representation irrep v ofso 6 2 is constructed which contains every su3 irrep precisely once an algebra of polynomial differential operatorsa acting onv is given the algebraa is shown to consist of linear combinations of all su3 tensor operators with polynomial invariant operators as coefficients by carrying out an analysis ofa the multiplicity problem for su3 tensor operators is resolved

an extended orthogonal forward regression algorithm for system identification using entropy in this paper a fast identification algorithm for non linear dynamic stochastic system identification is presented the algorithm extends the classical orthogonal forward regression ofr algorithm so that instead of using the error reduction ratio err for term selection a new optimality criterion shannon s entropy power reduction ratio eprr is introduced to deal with both gaussian and non gaussian signals it is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach

complementary group resolution of the su n outer multiplicity problem i the littlewood rules and a complementary u 2n 2 group structure a complementary group to su n is found that realizes all features of the littlewood rules for kronecker products of su n representations this is accomplished by considering a state of su n to be a special gel fand state of the complementary group u 2n 2 with labels of the latter used to distinguish multiple occurrences of irreducible representations of su n irreps in the su n su n su n decomposition that is obtained from the littlewood rules furthermore this realization also helps us to determine su n su n 1 u 1 reduced wigner coefficients rwcs frequently called isoscalar factors and clebsch gordan coefficients cgcs or full nonreduced wigner coefficients of su n using algebraic or numeric methods in either the canonical or a noncanonical basis new explicit formulas for the su 3 and su 4 multiplicities are obtained by using this technique

creation and annihilation operators for su 3 in an so 6 2 model creation and annihilation operators are defined which are wigner operators tensor shift operators for su 3 while the annihilation operators are simply boson operators the creation operators are cubic polynomials in boson operators together they generate under commutation the lie algebra of so 6 2 the vector space generated from a vacuum vector by repeated application of the creation operators carries an irreducible representation of the so 6 2 algebra equivalent to an hermitian representation and also carries in direct sum every different irreducible representation of su 3 so 6 2 exactly once a model for su 3 in the sense of bernstein gel fand and gel fand is therefore defined the different su 3 irreducible representations appear explicitly as manifestly covariant irreducible tensors whose orthogonality and normalisation properties are examined other wigner operators for su 3 can be constructed simply as products of the new creation and annihilation operators or sums of such products

a closed formula for the product of irreducible representations of su 3 we determine a closed formula in terms of p q r and s for the decomposition of the product p q r s of finite dimensional irreducible representations of su 3 we also determine in terms of p q r s m and n necessary and sufficient conditions that a term m n appears in this decomposition and its multiplicity

frsvms fuzzy rough set based support vector machines this paper aims to improve hard margin support vector machines svms by considering the membership of every training sample in constraints the membership is computed by employing the technique of fuzzy rough sets so that hard margin svms can be combined with fuzzy rough sets and the inconsistence between conditional features and decision labels can be taken into account at the same time in this paper we first propose fuzzy transitive kernel based fuzzy rough sets for binary classification we use a lower approximation operator in fuzzy transitive kernel based fuzzy rough sets to compute the membership for every training input and then we reformulate hard margin support vector machines into fuzzy rough set based svms frsvms with new constraints in which the membership is taken into account finally comparisons with soft margin svms and fuzzy svms are made the experimental results show that the proposed approach is feasible and valid it significantly improved the performance of the hard margin svms

calculation of clebsch gordan and racah coefficients using symbolic manipulatio n programs a procedure for calculating clebsch gordan and racah coefficients arising from the decomposition of n fold tensor products of the u n groups using symbolic manipulation programs is given basic states are realized as polynomials in a space equipped with a differentiation inner product the desired coefficients are then obtained by differentiating the relevant polynomials examples from su 2 and su 3 are given copyright 1989 academic press inc

advanced fuzzy inference engines in situation aware computing we focus on the very important family of context aware applications context aware computing relies on tasks like capturing sensing environmental parameters e g lightness location classifying context and inferring further knowledge about that context determine the situation the user is currently in however the relevant applications have to deal with the inherent imperfection of context sensing for decision making we propose an extension of context representation and inference for situation aware applications our model relies on fuzzy set theory to accommodate the imperfection of sensed context based on this model we have developed three fuzzy inference engines which rely on advanced semantics specialization mereological and compatibility relations we have evaluated the proposed engines through a series of experiments involving real users our findings indicate the strong points of the proposed context classification and inference processes

su n coherent states we generalize schwinger boson representation of su 2 algebra to su n and define coherent states of su n using 2 2n 1 1 bosonic harmonic oscillator creation and annihilation operators we give an explicit construction of all n 1 casimirs of su n in terms of these creation and annihilation operators the su n coherent states belonging to any irreducible representations of su n are labeled by the eigenvalues of the casimir operators and are characterized by n 1 complex orthonormal vectors describing the su n manifold the coherent states provide a resolution of identity satisfy the continuity property and possess a variety of group theoretic properties

the missing link operators for labelling multiplicity in the clebsch gordan series it is indicated that there are invariant operators on the direct product space of irreducible representations of lie groups which distinguish between repeating representations they complete the labelling of the clebsch gordan series

a fuzzy variable structure approach to feedback regulation of uncertain dynamical systems with application to robotics this paper develops a fuzzy logic based control design methodology for a large class of nonlinear uncertain dynamical systems the proposed control design approach combines the powerful tools of fuzzy logic and approximate reasoning with the advanced mathematical synthesis techniques used in variable structure control systems theory the rationale for the proposed control design approach is motivated by the results of a recent study that has rigorously established some connections between fuzzy logic and variable structure control systems the results of this paper represent a step in the right direction for systematic design of a less expert dependent fuzzy logic control to illustrate the merits of the new control approach the latter is applied to a 2 degree of freedom robot manipulator preliminary simulation results suggest that the proposed control design deals effectively with the chattering problem encountered when the classical variable structure control is used alone

a kernel based two class classifier for imbalanced data sets many kernel classifier construction algorithms adopt classification accuracy as performance metrics in model evaluation moreover equal weighting is often applied to each data sample in parameter estimation these modeling practices often become problematic if the data sets are imbalanced we present a kernel classifier construction algorithm using orthogonal forward selection ofs in order to optimize the model generalization for imbalanced two class data sets this kernel classifier identification algorithm is based on a new regularized orthogonal weighted least squares rowls estimator and the model selection criterion of maximal leave one out area under curve loo auc of the receiver operating characteristics rocs it is shown that owing to the orthogonalization procedure the loo auc can be calculated via an analytic formula based on the new regularized orthogonal weighted least squares parameter estimator without actually splitting the estimation data set the proposed algorithm can achieve minimal computational expense via a set of forward recursive updating formula in searching model terms with maximal incremental loo auc value numerical examples are used to demonstrate the efficacy of the algorithm

e factor of representations of classical groups abstract we let g be the isometry group of a nondegenerate symmetric or skew symmetric form h on a space v over some local or global field k i e g u v h we let lg be the l group of go the identity component of g and r be the natural representation of this group we develop here a theory of l functions and e factors attached to this r in particular we develop a theory of local and global zeta integrals for such g we use very special intertwining operators therein we require an analysis of the proper normalization of such operators with such techniques we determine the correct e factors associated to local representations the issue of the correct local l factor is discussed