extending fuzzy logics with many hedges abstract fuzzy logic aims at modeling logical reasoning with vague or imprecise statements which may contain linguistic hedges in fact many hedges e g very highly rather and slightly can be used simultaneously to express different levels of emphasis moreover each hedge might have a dual one e g slightly can be seen as a dual hedge of very thus it is necessary to extend systems of fuzzy logic with multiple hedges this work proposes two axiomatizations for multiple hedges as an expansion of a core fuzzy logic in one axiomatization hedges do not have any dual one while in the other each hedge can have its own dual one it is shown that the proposed logics not only cover a large class of hedge functions but also have all completeness properties as the underlying logic w r t the class of their chains as well as distinguished subclasses of their chains including standard completeness the axiomatizations are also extended to the first order level furthermore we present a method to build linguistic fuzzy logics based on the axiomatizations and a hedge algebra whose corresponding algebras use a linguistic truth domain taken from the hedge algebra for representing and reasoning with linguistically expressed human knowledge where truth values of vague sentences are given in linguistic terms

involutive basic substructural core fuzzy logics involutive mianorm based logics abstract this paper deals with the standard completeness of involutive non associative non commutative substructural fuzzy logics and their axiomatic extensions first fuzzy systems based on involutively residuated mianorms binary monotonic identity aggregation operations on the real unit interval 0 1 their corresponding algebraic structures and their algebraic completeness results are discussed next completeness with respect to algebras whose lattice reduct is 0 1 known as standard completeness is established for these systems via a construction in the style of jenei montagna these standard completeness results resolve a problem left open by cintula horcik and noguera in the recent handbook of mathematical fuzzy logic and review of symbolic logic finally we briefly consider the similarities and differences between constructions of the author and wang s jenei montagna style

which logic is the real fuzzy logic this paper is a contribution to the discussion of the problem whether there is a fuzzy logic that can be considered as the real fuzzy logic we give reasons for taking imtl bl email protected and ev l fuzzy logic with evaluated syntax as those fuzzy logics that should be indeed taken as the real fuzzy logics

fuzzy logics as the logics of chains the paper proposes a formal delimitation of the class of fuzzy logics and answers some objections that can be raised against the definition the focus is put on informal and motivational aspects of the problem

necessary and sufficient conditions for boundedness and oscillation in the retarded lienard equation abstract consider the retarded lienard equation x f x x g x t h 0 where f g r r are continuous and h 0 using liapunov s direct method we give necessary and sufficient conditions to ensure boundedness and oscillation of all solutions and their derivatives

adaptive control of a constrained robot ensuring zero tracking and zero force errors a constrained robot is a mathematical model that describes the interaction between a robot and the environment as the robot moves along a prescribed trajectory the main difficulty in the control of constrained robots is to ensure zero error for the constraint force in addition to accurate trajectory tracking this study extends the result of slotine and li 1991 to design a simple adaptive controller for constrained robots the proposed controller achieves both control objectives in the presence of dynamic parameter uncertainty the overall system is proven to be globally stable in the lyapunov sense simulation results are provided to demonstrate the performance of the proposed method

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

force motion control of constrained robots using sliding mode a sliding mode control algorithm is presented for trajectory tracking of an end effector on a constrained surface with specified constraint forces by using the theory of variable structure systems the development of the algorithm is based on a new formulation of the dynamic model and the expansion of sliding surfaces to include the constraint force error the proposed sliding controller is explicit which ensures the occurrence of the sliding mode on the intersection of the surfaces a detailed numerical example is presented to illustrate the method

on trajectory and force tracking control of constrained mobile manipulators with parameter uncertainty this paper studies the trajectory and force tracking control problem of mobile manipulators subject to holonomic and nonholonomic constraints with unknown inertia parameters adaptive controllers are proposed based on a suitable reduced dynamic model the defined reference signals and the mixed tracking errors the proposed controllers not only ensure the entire state of the system to asymptotically converge to the desired trajectory but also ensure the constraint force to asymptotically converge to the desired force a detailed numerical example is presented to illustrate the developed methods

neighborhood semantics for modal many valued logics abstract the majority of works on modal many valued logics consider kripke style possible worlds frames as the principal semantics despite their well known axiomatizability issues when considering non boolean accessibility relations the present work explores a more general semantical picture namely a many valued version of the classical neighborhood semantics we present it in two levels of generality first we work with modal languages containing only the two usual unary modalities define neighborhood frames over algebras of the logic fl ew with operators and show their relation with the usual kripke semantics this is actually the highest level of generality where one can give a straightforward definition of the kripke style semantics second we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and assuming certain additional conditions axiomatize the logic of all such frames which generalizes the completeness theorem of the classical modal logic e with respect to classical neighborhood frames

on the boundedness of the solutions of the nonlinear oscillating equation abstract we consider the nonlinear oscillating equation x f x h x x g x k x 0 without the common conditions a f x 0 for all x r b xg x 0 for all x 0 and give a set of necessary and sufficient conditions for the boundedness of all solutions of this equation and their derivatives

on the generalized lienard equation without the signum condition abstract we consider the generalized lienard equation x x h x x g x k x 0 without the signum condition xg x 0 for all x 0 and give a necessary and sufficient condition for the boundedness of all solutions of this equation and their derivatives

weakening free non associative fuzzy logics this paper deals with standard completeness for weakening free non associative substructural fuzzy logics first fuzzy systems which are based on micanorms binary monotonic identity commutative aggregation operations on the real unit interval 0 1 their corresponding algebraic structures and algebraic completeness results are discussed next completeness with respect to algebras whose lattice reduct is 0 1 so called standard completeness is established for these systems using construction in the style of jenei montagna in particular standard completeness results for the involutive logics which was a problem left open by horcik in the recent handbook of mathematical fuzzy logic are provided finally we briefly consider the similarities and differences between constructions of the author and wang s jenei montagna style

boundedness and convergence of solutions of a second order nonlinear differential system abstract consider the second order nonlinear differential system x 1 a x h y f x y a x g x e t where a is a positive and continuous function on r h f and g are continuous functions on r and e t is a continuous function on i 0 we obtain sufficient and necessary conditions for all solutions to be bounded and to converge to zero our results can be applied to the well known equation x f 1 x x f 2 x x 2 g x e t which substantially extends and improves important results in the literature

robust adaptive motion force tracking control design for uncertain constrained robot manipulators in the presence of uncertain constraint and robot model an adaptive controller with robust motion force tracking performance for constrained robot manipulators is proposed first robust motion and force tracking is considered where a performance criterion containing disturbance and estimated parameter attenuations is presented then the proposed controller utilizes an adaptive scheme and an auxiliary control law to deal with the uncertain environmental constraint disturbances and robotic modeling uncertainties after solving a simple linear matrix inequality for gain conditions the effect from disturbance and estimated parameter errors to motion force errors is attenuated to an arbitrary prescribed level moreover if the disturbance and estimated parameter errors are square integrable then an asymptotic motion tracking is achieved while the force error is as small as the inversion of control gain finally numerical simulation results for a constrained planar robot illustrate the expected performance

boundedness of solutions for a class of retarded lienard equation consider the retarded lienard equation x f1 x x f2 x x2 gx t h e t where h is a nonnegative constant f1 f2 and g are continuous functions on r and e t is a continuous function on r 0 we obtain some new sufficient conditions as well as some new necessary and sufficient conditions for all solutions and their derivatives to be bounded which substantially extend and improve some important results in the literature

boundedness theorems by two liapunov functions on considere le systeme d equations differentielles dx dt f t x y dy dt g t x y avec x r n y r m et f g des fonctions continues sur r r n r m on demontre un theoreme qui donne des criteres pour que des solutions soient uniformement bornees en se servant de deux fonctions de lyapunov et du theoreme de comparaison

trilateral teleoperation of adaptive fuzzy force motion control for nonlinear teleoperators with communication random delays in this paper an adaptive fuzzy control scheme is proposed for hybrid motion force of trilateral teleoperation systems with a dual master single slave configuration under stochastic time varying delays in communication channels different from previous works on bilateral teleoperation systems this paper addresses dual master trilateral control of a single holonomic constrained robotic manipulator where the communication delays are modeled as multiple markov chains and the motion force controls are investigated under consideration of unsymmetric stochastic time varying delays and system dynamical uncertainties using partial feedback linearization the whole trilateral teleoperation system which consists of both master and slave manipulator dynamics is transformed into three subsystems by integrating markov jump systems to handle random delays adaptive fuzzy control strategies are developed for the nonlinear teleoperators with modeling uncertainties and external disturbances by using the approximation property of the fuzzy logic systems flss it is proven that the trilateral teleoperation system is stochastically stable in mean square under specific linear matrix inequality lmi conditions and all the signals of the resulting closed loop system are uniformly bounded the proposed scheme is validated by extensive simulations

on the boundedness of solution of the generalized lie nard equation without the signum condition on presente des criteres de limitation pour l equation de lienard generalisee x f x x g x 0 ou un systeme equivalent x y f x y g x ou f g r r sont continues et f x 0 x f d

control of nonlinear systems with partial state constraints using a barrier lyapunov function this article addresses the problem of control design for strict feedback systems with constraints on the states to prevent the states from violating the constraints we employ a barrier lyapunov function blf which grows to infinity whenever its arguments approaches some finite limits based on blf based backstepping we show that asymptotic output tracking is achieved without violation of any constraint provided that the initial states and control parameters are feasible we also establish sufficient conditions to ensure feasibility which can be checked offline without precise knowledge of the initial states the feasibility conditions are relaxed when handling the partial state constraint problem as compared to the full state constraint problem in the presence of parametric uncertainties blf based adaptive backstepping is useful in preventing the states from transgressing the constrained region during the transient stages of online parameter adaptation to relax the feasibility conditions asymme

triangle algebras a formal logic approach to interval valued residuated lattices in this paper we introduce triangle algebras a variety of residuated lattices equipped with approximation operators and with a third angular point u different from 0 and 1 we show that these algebras serve as an equational representation of interval valued residuated lattices ivrls furthermore we present triangle logic tl a system of many valued logic capturing the tautologies of ivrls triangle algebras are used to cast the essence of using closed intervals of l as truth values into a set of appropriate logical axioms our results constitute a crucial first step towards solving an important research challenge the axiomatic formalization of residuated t norm based logics on l i the lattice of closed intervals of 0 1 in a similar way as was done for formal fuzzy logics on the unit interval

a combined direct indirect and variable structure method for robust adaptive control direct methods and indirect methods for the adaptive control of linear plants with unknown parameters are currently well known methods for combining direct and indirect methods have also been suggested in the paper the latter method is combined with the variable structure method new adaptive laws are suggested which overcome the principal drawbacks of the variable structure method while the direct and indirect components of the new method assure stability the variable structure component improves the transient response of the system simulation results are presented to show that the overall system is asymptotically stable in the ideal case and exhibits robustness and improved performance in the presence of perturbations

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

basic substructural core fuzzy logics and their extensions mianorm based logics abstract this paper addresses standard completeness for non associative non commutative substructural fuzzy logics and their axiomatic extensions first fuzzy systems which are based on mianorms binary monotonic identity aggregation operations on the real unit interval 0 1 their corresponding algebraic structures and algebraic completeness results are discussed next completeness with respect to algebras whose lattice reduct is 0 1 so called standard completeness is established for these systems using construction in the style of jenei montagna finally some axiomatic extensions of the non associative non commutative core fuzzy logics having axioms corresponding to the structural rule s of exchange and or associativity are considered

reasoning about mathematical fuzzy logic and its future this paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author our goal is to think of the state of the art in mathematical fuzzy logic mfl and to outline some of the tasks on which in the author s opinion mfl should focus in the future in our discussion we will mention not only the basic theory but also its extension called fuzzy logic in broader sense flb the paradigm of the latter is to be the logic of natural human reasoning whose most essential characteristic is the use of natural language besides brief description of flb we will also mention some of its applications on the basis of that we will ponder on other possible directions for research namely the possibility of using fln as a metatheory of fuzzy mathematics as a proper tool for modeling of the main manifestations of the phenomenon of vagueness and as a reasonable tool for developing models of linguistic semantics

brief paper control of nonlinear systems with time varying output constraints this paper presents control design for strict feedback nonlinear systems with time varying output constraints an asymmetric time varying barrier lyapunov function blf is employed to ensure constraint satisfaction by allowing the barriers to vary with the desired trajectory in time the initial condition requirements are relaxed through a change of tracking error coordinates we eliminate the explicit dependence of the blf on time thereby simplifying the analysis of constraint satisfaction we show that asymptotic output tracking is achieved without violation of the output constraint and also quantify the transient performance bound as a function of time that converges to zero to handle parametric model uncertainty we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation the performance of the proposed control is illustrated through a simulation example

combined adaptive and variable structure control for constrained robots abstract this paper addresses the problem of controller design for constrained robots a control algorithm described as a combination of the direct adaptive and the variable structure method is presented for the trajectory tracking of an end effector on a constrained surface with specified constraint forces this scheme has certain advantages both with respect to computational efficiency and with respect to design with respect to computational efficiency the calculation of the regressor is avoided with respect to design since the number of parameter update laws required in the adaptation is independent of the number of links of the robot the difficulty of tuning numerous adaptation gains is avoided

the logic of the strongest and the weakest t norms it is well known that the strongest t norm that is the largest with respect to the pointwise order is the minimum in 2001 the logic mtl was introduced as the base of a framework of many valued logics and in 2002 it was shown that it is the logic of all left continuous t norms and their residua within this family of logics the many valued logic associated with the minimum t norm is the godel one whilst there is no logic associated to the drastic product t norm indeed the drastic product is not left continuous and hence it does not have a residuum however in a recent paper the logic dp has been studied by showing that the monoidal operation of every dp chain is like the drastic product t norm in this paper we present the logic emtl whose algebraic variety is the smallest to contain the ones of godel and dp algebras we show that the chains in this algebraic variety are exactly all the godel and dp chains we classify and axiomatize all the subvarieties and we show some limitative results concerning the amalgamation property