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

on some types of fuzzy covering based rough sets fuzzy coverings are a natural extension of the coverings by replacing crisp sets with fuzzy sets recently an excellent introduction to the definition of a fuzzy covering is due to ma and two fuzzy covering based rough set models are presented in this paper by introducing some new definitions of fuzzy covering approximation spaces the properties of fuzzy covering approximation spaces and ma s fuzzy covering based rough set models are studied furthermore three new types of fuzzy covering based rough set models as generalizations of ma s models are first proposed in this paper first some properties of fuzzy covering and its fuzzy neighborhood family are proposed we present a necessary and sufficient condition for fuzzy neighborhood family induced by a fuzzy covering to be equal to the fuzzy covering itself then we study the characterizations of ma s fuzzy covering based rough set models and give a necessary and sufficient condition for two fuzzy coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation finally this paper proposes three new types of fuzzy covering based rough set models by introducing a new notion of a fuzzy complementary neighborhood

textures and fuzzy unit operations in rough set theory an approach to fuzzy rough set models abstract in this paper an approach for the fuzzy rough set models is presented using textures and a fuzzy version of the unit operations of wybraniec skardowska first a fuzzy unit operation and fuzzy unit co operation on fuzzy lattices are defined it is proved that the well known fuzzy rough set upper approximations as the approximation of dubois and prade are fuzzy unit operation using fuzzy direlations an axiomatic system for fuzzy unit operations is studied and it is shown that fuzzy rough set systems obtained by different fuzzy logical connectives as kleene dienes and godel implicators can be generated by the same textural fuzzy direlation finally it is observed that the approximations of two different fuzzy rough set models together constitute two different galois connections

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

a comparative study of variable precision fuzzy rough sets based on residuated lattices abstract although qiao and hu intended to propose granular variable precision l fuzzy rough sets based on residuated lattices l actually denotes a doubly residuated lattice with an involutive negation however there exist doubly residuated lattices without involutive negations this paper presents a comparative study of variable precision fuzzy rough sets based on residuated lattices in which we compare variable precision l fuzzy rough sets with the preexisting models a variable precision upper l fuzzy rough approximation operator is proposed with l fuzzy granules based on l fuzzy implication on a residuated lattice l instead of a doubly residuated lattice the variable precision upper l fuzzy rough approximation operator is investigated with respect to different l fuzzy relations regardless of proposing an involutive negation on a residuated lattice

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

a comprehensive study of fuzzy covering based rough set models definitions properties and interrelationships abstract fuzzy covering based rough set models are hybrid models using both rough set and fuzzy set theory the former is often used to deal with uncertain and incomplete information while the latter is used to describe vague concepts the study of fuzzy rough set models has provided very good tools for machine learning algorithms such as feature and instance selection in this article we discuss different types of dual fuzzy rough set models which all consider fuzzy coverings in particular we study two models using non nested level based representation of fuzziness in addition to the study of the theoretical properties for each model interrelationships between the different models are discussed resulting in a hasse diagram of fuzzy covering based rough set models for a finite fuzzy covering an imtl t norm and its residual implicator

observer based control of systems with slope restricted nonlinearities an observer design is presented which makes use of bounds on the slope of system nonlinearities necessary and sufficient conditions are derived for the feasibility of the design a class of state feedback control laws are characterized which when implemented with the observer states ensure global asymptotic stability one such certainty equivalence design is illustrated on an active magnetic bearing example

a theorem on global stabilization of nonlinear systems by linear feedback abstract in this paper we investigate the global stabilizability problem for a wide class of single input nonlinear systems whose the linearization at the equilirrium is controllable we show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium the proof of our main theorem is based on some ideas from a previous paper we use the theorem to recover a recent result of gauthier et al concerning the observer design problem

granular variable precision l fuzzy rough sets based on residuated lattices abstract firstly as for the beginning of this paper we introduce the granular variable precision l fuzzy rough sets based on residuated lattices with arbitrary l fuzzy relations and then the equivalent expressions for the lower and upper approximation operators are given with l fuzzy implications and l fuzzy coimplications on arbitrary l fuzzy relations which can calculate the lower and upper approximation operators efficiently finally some basic properties of the granular variable precision l fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices

exact computation of the infimum in h sub infinity optimization via output feedback the authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard h sub infinity optimal control with output feedback the problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables the method is applicable to systems that satisfy the following conditions 1 the transfer function from the control input to the controlled output is right invertible and has no invariant zeros on the j omega axis and 2 the transfer function from the disturbance to the measurement output is left invertible and has no invariant zeros on the j omega axis

nearly optimal control laws for nonlinear systems with saturating actuators using a neural network hjb approach the hamilton jacobi bellman hjb equation corresponding to constrained control is formulated using a suitable nonquadratic functional it is shown that the constrained optimal control law has the largest region of asymptotic stability ras the value function of this hjb equation is solved for by solving for a sequence of cost functions satisfying a sequence of lyapunov equations le a neural network is used to approximate the cost function associated with each le using the method of least squares on a well defined region of attraction of an initial stabilizing controller as the order of the neural network is increased the least squares solution of the hjb equation converges uniformly to the exact solution of the inherently nonlinear hjb equation associated with the saturating control inputs the result is a nearly optimal constrained state feedback controller that has been tuned a priori off line

notes on a comprehensive study of implicator conjunctor based and noise tolerant fuzzy rough sets definitions properties and robustness analysis abstract d eer et al evaluated the implicator conjunctor based fuzzy rough set model or shortly ic model and different noise tolerant fuzzy rough set models however neither ic model nor fuzzy variable precision rough set fvprs model satisfies id property without the reflexivity of fuzzy relation upper approximation operator in ic model cannot necessarily be expressed by fuzzy granules moreover a fuzzy t similarity relation is equivalent to a fuzzy relation that is reflexive and t euclidean where t denotes a t norm therefore t euclidean condition is redundant for ic model satisfying all properties listed in the work of d eer et al

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

dynamic output feedback linearization and global stabilization abstract we present a class of single input single output nonlinear systems which are globally transformable by a dynamic output feedback control and a time varying state space transformation into a linear observable and minimum phase system we then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

nonlinear h almost disturbance decoupling the l2 gain almost disturbance decoupling problem for siso nonlinear systems is formulated sufficient conditions are identified for the existence of a parametrized state feedback controller such that the l2 gain from disturbances to output can be made arbitrarily small by increasing its gain the controller is explicity constructed using a lyapunov based recursive scheme sufficient conditions for the solvability of the h almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems

granular variable precision fuzzy rough sets with general fuzzy relations the variable precision fuzzy rough sets were proposed to remedy the defects of preexisting fuzzy rough set models however the variable precision fuzzy rough sets were only defined and investigated on fuzzy similarity relations in this paper the granular variable precision fuzzy rough sets with general fuzzy relations are proposed on arbitrary fuzzy relations the equivalent expressions of the approximation operators are given with fuzzy co implications on arbitrary fuzzy relations which can calculate efficiently the approximation operators the granular variable precision fuzzy rough sets are characterized from the constructive approach which are investigated on different fuzzy relations the conclusions on the variable precision fuzzy rough sets are generalized into the granular variable precision fuzzy rough sets

global almost disturbance decoupling with stability for non minimum phase single input single output nonlinear systems the so called problem of almost disturbance decoupling with internal stability addps is the following one given a system and an arbitrarily small number 0 find a feedback law yielding a closed loop system which is stable and in which the gain in the l2 sense between the exogenous input and the regulated output is less than or equal to the complete solution of this problem has been known since a long time in the case of linear systems in the case of nonlinear systems the only global results available so far in the literature were about siso systems having an asymptotically stable zero dynamics in this paper a new set of results are presented dealing with nonlinear siso systems having a possibly unstable zero dynamics which include the general class of linear siso systems as a special case

nonlinear h control and estimation of optimal h gain abstract the structure of nonlinear h controller and the estimation of optimal h gain are investigated in this paper the essential problem boils down to the existence of semipositive solution to the hamilton jacobi isaacs inequality further the solvability of this first order fully nonlinear differential inequality is discussed we look for one kind of special semipositive radial solution to the hamilton jacobi isaacs inequality an explicit estimation of optimal h gain and explicit formulas of semipositive radial solutions to the hamilton jacobi isaacs inequality are obtained the results are quite simple and intuitive they even shed a new insight on the linear h theory

almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance affected unstable zero dynamics the problem of global almost disturbance decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by disturbance this result complements some recent work on the topic where unstable zero dynamics is not allowed to be affected by the disturbances

brief paper explicit construction of h control law for a class of nonminimum phase nonlinear systems this paper addresses a nonlinear h control problem for a class of nonminimum phase nonlinear systems the given system is first transformed into a special coordinate basis in which the system zero dynamics is divided into a stable part and an unstable part a sufficient solvability condition is then established for solving the nonlinear h control problem moreover based on the sufficient solvability condition an upper bound of the best achievable l 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear h control problem the proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear h control problem in particular the solution to the nonlinear h control problem does not require solving any hamilton jacobi equations finally the obtained results are utilized to solve a benchmark problem on a rotational translational actuator rtac system

neighborhood operators for covering based rough sets covering based rough sets are important generalizations of the classical rough sets of pawlak a common way to shape lower and upper approximations within this framework is by means of a neighborhood operator in this article we study 24 such neighborhood operators that can be derived from a single covering we verify equalities between them reducing the original collection to 13 different neighborhood operators for the latter we establish a partial order showing which operators yield smaller or greater neighborhoods than others six of the considered neighborhood operators result in new covering based rough set approximation operators we study how these new approximation operators relate to existing ones in terms of partial order relations i e whether the generated approximations are in general greater smaller or incomparable finally we discuss the connection between the covering based approximation operators and relation based approximation operators another prominent generalization of pawlak s rough sets

stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix this paper presents a procedure for stabilizing a class of uncertain linear systems the uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters this matrix of uncertain parameters may be time varying however it is constrained by a bound on its induced norm the stabilization procedure presented involves the repeated solution of an algebraic riccati equation when a positive definite solution to this riccati equation is obtained this solution is used to construct a stabilizing linear control law another important result contained in this paper can be stated roughly as follows for the class of uncertain systems under consideration if a system can be stabilized via nonlinear control then it is also possible to stabilize the system via linear control

a note on almost disturbance decoupling for nonlinear minimum phase systems this note discusses a recent paper by marino et al nonlinear h almost disturbance decoupling systems control lett 23 1994 159 168 who have presented a series of interesting results about the problem of almost disturbance decoupling with internal stability for nonlinear systems

on a state space approach to nonlinear h control we study the standard h optimal control problem using state feedback for smooth nonlinear control systems the main theorem obtained roughly states that the l2 induced norm from disturbances to inputs and outputs can be made smaller than a constant 0 if the corresponding h norm for the system linearized at the equilibrium can be made smaller than by linear state feedback necessary and sufficient conditions for the latter problem are by now well known e g from the state space approach to linear h optimal control our approach to the nonlinear h optimal control problem generalizes the state space approach to the linear h problem by replacing the hamiltonian matrix and corresponding riccati equation as used in the linear context by a hamiltonian vector field together with a hamiltonian jacobi equation corresponding to its stable invariant manifold

semiglobal l sub 2 performance bounds for disturbance attenuation in nonlinear systems this paper addresses the problem of disturbance attenuation in the sense of l sub 2 gain with internal stability and no cost on the control input for nonlinear systems when the problem of almost disturbance decoupling is not solvable i e when the least achievable attenuation level between disturbance and regulated output is nonzero two different approaches are provided which facilitate the estimation of an upper bound for such a value

the model of fuzzy variable precision rough sets the fuzzy rough set frs model has been introduced to handle databases with real values however frs was sensitive to misclassification and perturbation here misclassification means error or missing values in classification and perturbation means small changes of numerical data the variable precision rough sets vprss model was introduced to handle databases with misclassification however it could not effectively handle the real valued datasets now it is valuable from theoretical and practical aspects to combine frs and vprs so that a powerful tool which not only can handle numerical data but also is less sensitive to misclassification and perturbation can be developed in this paper we set up a model named fuzzy vprss fvprss by combining frs and vprs with the goal of making frs a special case first we study the knowledge representation ways of frs and vprs and then propose the set approximation operators of fvprs second we employ the discernibility matrix approach to investigate the structure of attribute reductions in fvprs and develop an algorithm to find all reductions third in order to overcome the np complete problem of finding all reductions we develop some fast heuristic algorithms to obtain one near optimal attribute reduction finally we compare fvprs with rs frs and several flexible rs based approaches with respect to misclassification and perturbation the experimental comparisons show the feasibility and effectiveness of fvprs

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

on characterizations of i t fuzzy rough approximation operators in rough set theory the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties various fuzzy generalizations of rough approximations have been made in the literature this paper proposes a general framework for the study of i t fuzzy rough approximation operators within which both constructive and axiomatic approaches are used in the constructive approach a pair of lower and upper generalized fuzzy rough approximation operators determined by an implicator i and a triangular norm t is first defined basic properties of i t fuzzy rough approximation operators are investigated the connections between fuzzy relations and fuzzy rough approximation operators are further established in the axiomatic approach an operator oriented characterization of rough sets is proposed that is i t fuzzy approximation operators are defined by axioms different axiom sets of t upper and i lower fuzzy set theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators finally an open problem proposed by radzikowska and kerre in fuzzy sets and systems 126 2002 137 is solved

postbuckling of laminated cylindrical shells in different formulations the sensitivity of laminated cylindrical shells to imperfection is investigated throughout their entire nonlinear behavior the study has two objectives 1 comparison of the simplest formulation using the airy stress function called the wf formulation with the more accurate one using the three displacement components called the uvw formulation and 2 examining the correlation between the sensitivity to imperfection according to this nonlinear analysis and that of koiter s process for the initial postbuckling behavior for laminated cylindrical shells in contrast to isotropic shells significant differences are observed between the two formulations wf and uvw and koiter s theory does not always represent the actual sensitivity behavior a general symbolic code using maple was programmed to create the differential operators then the code used the galerkin procedure the newton raphson procedure and a finite difference scheme for automatic development of an efficient fortran code which was used for the parametric study

attributes reduction using fuzzy rough sets fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data the existing researches on fuzzy rough sets are mainly concentrated on the construction of approximation operators less effort has been put on the attributes reduction of databases with fuzzy rough sets this paper mainly focuses on the attributes reduction with fuzzy rough sets after analyzing the previous works on attributes reduction with fuzzy rough sets we introduce formal concepts of attributes reduction with fuzzy rough sets and completely study the structure of attributes reduction an algorithm using discernibility matrix to compute all the attributes reductions is developed based on these lines of thought we set up a solid mathematical foundation for attributes reduction with fuzzy rough sets the experimental results show that the idea in this paper is feasible and valid

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

generalized fuzzy rough sets determined by a triangular norm the theory of rough sets has become well established as an approach for uncertainty management in a wide variety of applications various fuzzy generalizations of rough approximations have been made over the years this paper presents a general framework for the study of t fuzzy rough approximation operators in which both the constructive and axiomatic approaches are used by using a pair of dual triangular norms in the constructive approach some definitions of the upper and lower approximation operators of fuzzy sets are proposed and analyzed by means of arbitrary fuzzy relations the connections between special fuzzy relations and the t upper and t lower approximation operators of fuzzy sets are also examined in the axiomatic approach an operator oriented characterization of rough sets is proposed that is t fuzzy approximation operators are defined by axioms different axiom sets of t upper and t lower fuzzy set theoretic operators guarantee the existence of different types of fuzzy relations producing the same operators the independence of axioms characterizing the t fuzzy rough approximation operators is examined then the minimal sets of axioms for the characterization of the t fuzzy approximation operators are presented based on information theory the entropy of the generalized fuzzy approximation space which is similar to shannon s entropy is formulated to measure uncertainty in t generalized fuzzy rough sets a notion of fuzziness is introduced some basic properties of this measure are examined for a special triangular norm t min it is proved that the measure of fuzziness of the generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable

some properties of viscosity solutions of hamilton jacobi equations abstract recently m g crandall and p l lions introduced the notion of viscosity solutions of scalar nonlinear first order partial differential equations viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics the value of this concept is established by the fact that very general existence uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application the notion of a viscosity solution admits several equivalent formulations here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner moreover by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper author

h control by state feedback for plants with zeros on the imaginary axis algebraic tests are derived for the suboptimality of some parameter in the h infty optimization problem by state feedback where the finite zero structure of the plant is not restricted as an application of these characterizations a quadratically convergent algorithm for the computation of the optimal value is presented the suboptimality tests are based on new solvability criteria for general algebraic riccati inequalities that are of independent interest

passivity and disturbance attenuation via output feedback for uncertain nonlinear systems the authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties the problem is approached by means of adaptive output feedback control which does not require any state observer the results obtained extend an earlier result of steinberg and corless 1985 sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example