computing with words via turing machines a formal approach computing with words cw as a methodology means computing and reasoning by the use of words in place of numbers or symbols which may conform more to humans perception when describing real world problems in this paper as a continuation of a previous paper we aim to develop and deepen a formal aspect of cw according to the previous paper the basic point of departure is that cw treats certain formal modes of computation with strings of fuzzy subsets instead of symbols as their inputs specifically 1 we elaborate on cw via turing machine tm models showing the time complexity is at least exponential if the inputs are strings of words 2 a negative result of 6 not holding is verified which indicates that the extension principle for cw via tms needs to be re examined 3 we discuss cw via context free grammars and regular grammars and the extension principles for cw via these formal grammars are set up 4 some equivalences between fuzzy pushdown automata respectively fuzzy finite state automata fuzzy context free grammars respectively fuzzy regular grammars are demonstrated in the sense that the inputs are instead strings of words 5 some instances are described in detail summarily formal aspect of cw is more systematically established more deeply dealt with while some new problems also emerge

the generation of dynamically corrected flat plate finite elements and their application to the transverse vibration of flat plates theory is presented together with a computer subroutine which enables the properties of a thin rectangular plate element to be discretized on the basis of dynamic deflection functions the stiffness and frequency dependent inertia properties of a square element given in appendices for both a non conforming and a conforming element are used to predict the vibration frequencies and modal shapes for a square plate subjected to four sets of boundary conditions comparisons made with exact solutions establish the superiority of equivalent mass over consistent mass values in the accuracy with which frequencies are predicted when the conforming element is used the magnitude of individual frequency errors is shown to be associated with the similarity between mode shape and the geometry of the finite element model identification of modal deformation patterns of which 31 are presented for the completely free plate and 21 for the fully clamped plate reveals that the frequencies determined from a particular numerical analysis do not necessarily occur in monotonic sequence frequency comparisons between values determined by alternative methods can only be made with certainty if it has been established that they relate to the same modal pattern two tables embody this correct basis of comparison and reveal that some modes are completely absent from a particular analysis the main findings arise from detailed numerical analysis but are fully supported in the case of the clamped plate by experimental holographic studies

uninorms on bounded lattices we study uninorms on bounded lattices we show the existence of uninorms with the neutral element which is different from the top element and the bottom element using the fact that the t norms and t conorms on arbitrary lattice l always exist as a by product we give a method of constructing uninorms using this method we obtain also the smallest uninorm and the greatest uninorm with a given neutral element e

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

residual operations of left and right uninorms on a complete lattice uninorms are an important generalization of triangular norms and conorms having a neutral element lying anywhere in the unit interval in this paper we introduce the concepts of left and right uninorms on a complete lattice we discuss the residual operations of left and right uninorms and study some basic properties of the residual operations of infinitely distributive left right uninorms and pseudo uninorms

products of mealy type fuzzy finite state machines we introduce seven ways of constructing products for mealy type fuzzy finite state machines as well as the concept of covering the properties of transition functions and output functions are discussed furthermore we investigate the covering properties and mutual relationship with regard to these products we also prove that the covering relationship holds in the product of factor machines

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

the role of am to pm conversion in memoryless nonlinear systems a generalized proof is presented that am to pm conversion can only degrade never improve the intermodulation noise performance of memoryless nonlinear systems with random input signals having even probability density functions and a measure of degradation is defined it is also shown for such signals that am to pm conversion causes a deterministic constant phase shift to be added to the argument of the signal component at the output but has no other effect on its phase this class of inputs includes one or the sum of several psk signals as well as large ensembles that can be modeled as gaussian noise the latter are dealt with by using bussgang s theorem on input output cross correlation in the proof bussgang s theorem is extended to the complex case to include phase as well as amplitude nonlinearities yielding a complex version of the theorem for gaussian inputs it is shown that the undistorted signal and the intermodulation noise at the output of such systems are uncorrelated

on residuation in multilattices filters congruences and homomorphisms continuing with our general study of algebraic hyperstructures we focus on the residuated operation in the framework of multilattices firstly we recall the existing relation between filters homomorphisms and congruences in the framework of multilattices then introduce the notion of residuated multilattice and further study the notion of filter which has to be suitably modified so that the results in the first section are conveniently preserved also in the residuated case

an interval type 2 fuzzy model of computing with words as a methodology computing with words allows the use of words instead of numbers or symbols in the process of computing and reasoning and thus conforms more to humans inference when it is used to describe real world problems motivated by zadeh s paradigm of computing with words the literature has proposed a kind of type 1 fuzzy automata as a formal model of computing with words which takes type 1 fuzzy subsets of symbols as input however type 1 fuzzy representation provides a limited platform for approximating the meaning of words since it is not able to capture linguistic uncertainty in this paper we develop a formal interval type 2 fuzzy model of computing with words by generalizing the existing type 1 fuzzy sets based model to an interval type 2 fuzzy environment concretely we take interval type 2 fuzzy automata i e interval type 2 fuzzy finite automata and interval type 2 fuzzy pushdown automata which combine interval type 2 fuzzy set theory and automaton theory as a computational model of computing with words furthermore we develop the extension principles to extend from computing with values to computing with words and show that computing with words can be implemented with computing with values in the interval type 2 fuzzy setting at an extra computational cost

on advanced computing with words using the generalized extension principle for type 1 fuzzy sets in this paper we propose and demonstrate an effective methodology for implementing the generalized extension principle to solve advanced computing with words acww problems such problems involve implicit assignments of linguistic truth probability and possibility to begin we establish the vocabularies of the words involved in the problems and then collect data from subjects about the words after which fuzzy set models for the words are obtained by using the interval approach ia or the enhanced interval approach eia next the solutions of the acww problems which involve the fuzzy set models of the words are formulated using the generalized extension principle because the solutions to those problems involve complicated functional optimization problems that cannot be solved analytically we then develop a numerical method for their solution finally the resulting fuzzy set solutions are decoded into natural language words using jaccard s similarity measure we explain how acww problems can solve some potential prototype engineering problems and connect the methodology of this paper with perceptual computing

single symbol ml decoding for orthogonal and quasi orthogonal stbc in clipped mimo ofdm systems using a clipping noise model with gaussian approximation an efficient way to reduce the peak to average power ratio papr in ofdm systems is clipping after the clipping in an mimo ofdm system the additive noise may not be white in this paper we develop fast single symbol ml decoding algorithms for orthogonal space time block codes ostbc and linearly transformed quasi orthogonal space time block codes qostbc in clipped mimo ofdm systems by using a clipping noise model with gaussian approximation by using the statistics of the clipping distortions our newly developed fast ml decoding algorithms improve the performance for clipped mimo ofdm systems with ostbc and qostbc while the decoding complexities are not increased simulation results are presented to illustrate the improvement

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

defending against strategic manipulation in uninorm based multi agent decision making abstract we consider the problem of multi agent group decision making we describe the possible use of the uninorm aggregation operator as a way of combining individual agents preference functions to obtain a group preference function we then discuss the possibility of an agent using a type of strategic manipulation of the preference information it provides in order to get the group to select its most preferred alternative a mechanism is then suggested for modifying the construction of the group decision function to defend against this type of strategic manipulation in addition to considering the case where the preference information is provided numerically we consider the case of ordinal preference information

congruences and homomorphisms of fuzzy automata concepts of congruences and homomorphisms of fuzzy automata are defined and homomorphism theorem is proved lattices of congruences of fuzzy automata are described and an algorithm for computing the greatest congruence contained in an equivalence of a fuzzy automaton is presented it is used for minimization procedures for both fuzzy automata with and without outputs connections with previously known minimization algorithms are discussed

on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations in this paper we study systems of fuzzy relation inequalities and equations of the form u v i v i u i i where u is an unknown and v i i i are given fuzzy relations the dual systems v i u u v i i i their conjunctions the systems of the form u v i v i u i i and certain special types of these systems we call them weakly linear systems for each weakly linear system with a complete residuated lattice as the underlying structure of truth values we prove the existence of the greatest solution and we provide an algorithm for computing the greatest solution which works whenever the underlying complete residuated lattice is locally finite otherwise we determine some sufficient conditions under which the algorithm works the algorithm is iterative and each its single step can be viewed as solving of a particular linear system weakly linear systems emerged from the fuzzy automata theory but we show that they also have important applications in other fields e g in the concurrency theory and social network analysis

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

iterative cancellation of non linear distortion noise in digital communication systems in this paper an iterative receiver that performs non linear distortion noise cancellation is presented the performance is assessed for time division multiple access tdma orthogonal frequency division multiple access ofdma and single carrier frequency division multiple access sc fdma waveforms even though a return link setup is considered the receiver is equally applicable in the forward link taking into account the differences in the data multiplexing and the channel analytical modeling of the received electrical signal to noise ratio snr is carried out for ofdma with one iteration of non linear distortion noise cancellation the performance is assessed in terms of power efficiency and spectral efficiency where the total degradation td of the received snr in a non linear channel is minimized the modulation formats of the dvb rcs2 satellite return link standard and a respective non linear channel have been used ofdma shows the highest power efficiency gain of 1 1 2 5 db with 2 iterations of non linear noise cancellation across the different modulation orders in sc fdma the gain is in the range of 0 3 1 1 db while gains of 0 1 0 8 db and 0 2 1 9 db are presented in tdma with 20 roll off and 5 roll off respectively

theoretical analysis and performance of ofdm signals in nonlinear awgn channels orthogonal frequency division multiplexing ofdm baseband signals may be modeled by complex gaussian processes with rayleigh envelope distribution and uniform phase distribution if the number of carriers is sufficiently large the output correlation function of instantaneous nonlinear amplifiers and the signal to distortion ratio can be derived and expressed in an easy way as a consequence the output spectrum and the bit error rate ber performance of ofdm systems in nonlinear additive white gaussian noise channels are predictable both for uncompensated amplitude modulation amplitude modulation am am and amplitude modulation pulse modulation am pm distortions and for ideal predistortion the aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the ber performance the results in closed form solutions are derived for am am and am pm curves approximated by bessel series expansion and for the ideal predistortion case

a novel decomposition analysis of nonlinear distortion in ofdm transmitter systems in orthogonal frequency division multiplexing ofdm transmitter systems nonlinear distortion is a major impairment caused by power amplifier pa the distortion is constituted by numerous noise like inter modulation products imps although the overall behavior of nonlinear imp distortion has been well studied in large multi carrier contexts such as in ofdm the knowledge of individual imps and their quantitative interrelationships together with the derivation of behavioural knowledge and the predictability of consequences arising from such interrelationships is a fairly unexplored topic this is the subject of this paper the powers of the very numerous individual imps generated are analytically derived based on a bessel fourier pa behavioural model and it is proven that these powers have only a small number of distinct powers proven also is that the ratios of these power values are constants and that these constants are invariant with the particular pa s nonlinearity characteristics or operating point further it is proven that specific types of imps dominate nonlinear distortion effects finally it is shown that imp power spectra can be derived from a simple product of two polynomials which are quadrature functions of frequency and pa operating point respectively application possibilities for findings presented in this paper such as their potential to contribute efficiency improvements in ofdm system modulation fidelity calculations over 1100 times faster than conventional methods are also outlined in the conclusions

on the state minimization of fuzzy automata this paper investigates the minimization problem of fuzzy automata aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one the decision version of the minimization problem is as follows given a fuzzy automaton cal a and a natural number k i e a pair langle cal a k rangle is there a k state fuzzy automaton equivalent to cal a we prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton to this end we introduce the concept of systems of fuzzy polynomial equations present a procedure for finding solutions of these systems and finally reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations it is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms the term minimization there did not mean state minimization in our sense since these algorithms did not aim at a minimal fuzzy automaton but found reasonably small fuzzy automata

an analysis of band limited communication systems from amplifier efficiency and distortion perspective considering growing concerns toward green communications not only their bandwidth efficiency but also their power consumption is expected to gain increasing importance for future communication systems a power amplifier pa is one of the most power consuming analog devices at the transmitter in communication systems and a precise estimation of the power consumption at the transmitter circuit requires the knowledge of its efficiency that depends on the distribution of input signal envelope and the amount of input back off in this paper we develop a simple analytical model that can be used for estimating achievable efficiency of a linear pa as well as the amount of resulting nonlinear distortion for a given modulated signal exclusively from its envelope distribution based on this model the trade off relationships between the efficiency and signal to distortion power ratio for several spectrally efficient linear modulations are examined it is also shown that in some special cases of gaussian input and memoryless nonlinearity pa models the results can be represented in simple closed form expressions

frequency independent and frequency dependent nonlinear models of twt amplifiers simple two parameter formulas are presented for the functions involved in the amplitude phase and the quadrature nonlinear models of a twt amplifier and are shown to fit measured data very well also a closed form expression is derived for the output signal of a twt amplifier excited by two phase modulated carriers and an expression containing a single integral is given when more than two such earriers are involved finally a frequencydependent quadrature model is proposed whose parameters are obtainable from single tone measurements

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

optimization of sndr for amplitude limited nonlinearities many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint nonlinearity generates distortions and thus signal to noise and distortion ratio sndr is an appropriate performance measure in this paper we are interested in finding the nonlinear mapping that maximizes the sndr subject to the peak amplitude constraint the answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude we also investigate a bounding relationship between the sndr and capacity of the nonlinear channel the results of this paper can be applied for efficient transmission of high peak to average power ratio signals or for optimal linearization of nonlinear devices

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

performance analysis for ofdm signals with peak cancellation peak cancellation pc is known as one of the simplest peak to average power ratio papr reduction techniques that are applicable to various communications standards the salient advantage of pc is its ease of hardware implementation but it induces in band distortion and out of band radiation in order to restrict the amount of distortion within an acceptable level it is critical to carefully design the cancelling pulses as well as the envelope threshold over which pc is applied in most studies however they are determined empirically through computer simulations this paper thus focuses on a rigorous theoretical analysis of pc applied to band limited orthogonal frequency division multiplexing ofdm signals and discusses its validity and limitation for practical applications based on the level crossing rate approximation of the peak distribution we derive a closed form expression for the achievable signal to distortion power ratio sdr we also analyze the adjacent channel leakage ratio aclr as well as error vector magnitude evm with which the symbol error rate ser over an additive white gaussian noise awgn channel is obtained all the theoretical results developed in this work are compared with those based on the corresponding computer simulations to justify our analytical approach it thus serves as a useful and accurate tool for designing cancelling pulses as well as the threshold level for given specific system requirements such as sdr or evm and aclr

on the use of cascade structure to correct impulsive noise in multicarrier systems we propose a new decoding algorithm based on a cascade structure for impulsive noise correction in multicarrier systems such as orthogonal frequency division multiplexing ofdm based systems this new cascade structure based algorithm has the advantage to lead on one hand to a reduced complexity implementation in an ofdm demodulator and on the other hand to overcome the lacks of other algorithms dedicated for impulsive noise correction to do so we start the derivation by investigating closed form analytical expressions of the a priori probabilities used in hypotheses tests that are necessary for the different steps needed for the execution of the cascade structure based decoding algorithm such closed form expressions for the a priori probabilities result in efficient setups of the threshold values used for the execution of the decoding algorithm furthermore we show that this cascade structure can be applied to efficiently cancel the impulsive noise in ofdm systems as the clipping event present in ofdm systems can be seen as an additive impulsive noise we prove that after introducing some minor modifications we can apply the proposed cascade structure to significantly reduce the peak to average power ratio papr level in such systems simulation results are given to illustrate the usefulness of the proposed algorithm results in practical ofdm based communication systems such as hiperlan 2

products of fuzzy finite state machines abstract we introduce the concepts of fuzzy transformation semigroups coverings cascade and wreath products for fuzzy finite state machines in order to overcome some of the difficulties which arise from the fuzzification of these concepts we also introduce the notions of polysemigroups and weak coverings

aggregation of subjective evaluations based on discrete fuzzy numbers in this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail these aggregation functions are constructed from discrete aggregation functions defined on a finite chain and they are applied to the aggregation of subjective evaluations

on factorized l fuzzy automaton and its l fuzzy topological characterization abstract this paper is towards the study of l fuzzy automata via theory of factorizations where l is a complete residuated lattice we study the concept of factorization of l fuzzy sets and factorization of collection of l fuzzy sets such factorizations are used i to study the concept of minimal l fuzzy automaton and ii to introduce l fuzzy topologies for the study of concepts associated with an l fuzzy automaton specifically we introduce the notion of factorized l fuzzy automaton corresponding to a given l fuzzy automaton and study the minimality of such automaton further we associate l fuzzy topologies for factorized l fuzzy automaton and use these to characterize some algebraic concepts

mimo ofdm with nonlinear power amplifiers the influence of nonlinear power amplifiers pas on the performance of multiple input multiple output mimo orthogonal frequency division multiplexing ofdm systems is investigated a full mimo scheme with transmitters tx precoding and receivers rx decoding is considered it is shown under assumption of high order ofdm and frequency selective channel that the ratio between the useful signal and the nonlinear distortions is proportional to the number of tx antennas i e the influence of the nonlinear distortions decreases as the number of tx antennas increases the distortion reduction factor drf is proposed as a performance metric for mimo ofdm systems with nonlinear pas a general formula for signal to distortion and noise ratio is obtained for the nonlinear pa with memory described by the wiener hammerstein wh model special cases of mimo such as maximum ratio transmission mrt and maximum ratio combining mrc are considered a full agreement between the theoretical and simulation results is obtained the main contribution of this paper is in a statement that tx processing reduces the effect of nonlinear distortions this is obtained by novel approach for analysis of the mimo ofdm systems with nonlinear pas with memory

on the optimum multicarrier performance with memoryless nonlinearities it is widely recognized that orthogonal frequency division multiplexing ofdm signals are very prone to nonlinear distortion effects which can lead to significant performance degradation however recent results have showed that nonlinear distortion effects do not necessarily mean performance degradation and can actually lead to performance improvements relative to conventional linear ofdm schemes in this paper we consider the effects of bandpass memoryless nonlinear devices on ofdm signals and study the optimum asymptotic performance for both nondispersive channels and severely time dispersive channels we present analytical methods for obtaining the euclidean distance between two ofdm signals that are subjected to different nonlinear characteristics these results are then employed for obtaining the average asymptotic gain relative to conventional linear ofdm schemes in nondispersive channels and the gain distribution for severely time dispersive channels with rayleigh distributed fading on the different multipath components our analytical results which are shown to be very accurate indicate that the optimum detection of ofdm schemes with strong nonlinear distortion effects allows significant gains when compared with conventional linear ofdm schemes

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

penalizing strategic preference manipulation in multi agent decision making we consider the problem of group decision making where the selection process is based upon a group preference function obtained by an aggregation of the participating agents individual preference functions we describe some methods for formulating the group preference from the individual preference functions we note the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group with this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions this paper presents a kind of controller synthesis method for fuzzy dynamic systems based on a piecewise smooth lyapunov function the basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems it is shown that the control laws can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software an example is given to illustrate the application of the proposed methods

uninorms in fuzzy systems modeling abstract fuzzy systems modeling provides a framework in which input output relationships can be modeled by partitioning the input into fuzzy regions for which we can describe the output the fuzzy modeling inference process the procedure used to obtain the output of a fuzzy systems model for a given input is shown to involve an aggregation step in which the contributions of the different components of the fuzzy systems model are combined it is shown that the uninorm operator provides a general class of operators to implement this step the uninorm it is recalled is an operator that provides a generalization of the t norm and t conorm by allowing the identity element to be any value in the unit interval another step in the inference process is the determination of the contribution of each component of the model based on its relevancy to the current input the performance of this step requires the use of an operator related to the implication operator which we call a relevancy transformation ret operator it is shown that the form of this ret operator is dependent upon the identity value of the uninorm used in the aggregation step we provide some general formulations for this class of operators we show how the well known forms of fuzzy inference are special cases of our uninorm based approach

pseudo uninorms and coimplications on a complete lattice pseudo uninorms are a generalization of uninorms by removing the commutativity from the axioms of the uninorms in this paper we further study pseudo uninorms and coimplications on a complete lattice firstly we discuss the residual coimplications of pseudo uninorms and give equivalent conditions for left right infinitely distributive pseudo uninorms then we study some properties of u n coimplications generated from a pseudo uninorm and a strong negation finally we investigate the pseudo uninorms induced by coimplications present equivalent conditions for right infinitely distributive coimplications and provide some conditions such that the operators induced by coimplications are uninorms

design of an adaptive fuzzy model based controller for chaotic dynamics in lorenz systems with uncertainty this paper presents the control methodology for uncertain chaotic dynamics of lorenz systems an adaptive fuzzy control afc scheme based on well known takagi sugeno t s fuzzy models for the mimo plants is constructed the developed control law and adaptive law guarantee the boundedness of all signals in the closed loop system in addition the chaotic state tracks the state of the stable reference model srm asymptotically with time for any bounded reference input signal the proposed control is applied to control of an uncertain lorenz system such as stabilization synchronization and chaotic model following control cmfc

point set morphological filtering and semantic spatial configuration modeling application to microscopic image and bio structure analysis high level spatial relation and configuration modeling issues are gaining momentum in the image analysis and pattern recognition fields in particular it is deemed important whenever one needs to mine high content images or large scale image databases in a more expressive way than a purely statistically one continuing previous efforts to incorporate structural analysis by developing specific efficient morphological tools performing on mesh representations like delaunay triangulations we propose to formalize spatial relation modeling techniques dedicated to unorganized point sets we provide an original mesh lattice framework which is more convenient for structural representations of large image data by means of interest point sets and their morphological analysis the set of designed numerical operators is based on a specific dilation operator that makes it possible to handle concepts like between or left of over sparse representations of image data such as graphs based on this new theoretical framework for reasoning about images we are able to process high level queries over large histopathological images knowing that digitized histopathology is a new challenge in the field of bio imaging due to the high content nature and large size of these images

on the accuracy of the gaussian approximation for the evaluation of nonlinear effects in ofdm signals the almost gaussian nature of ofdm orthogonal frequency division multiplexing signals with high number of subcarriers n is widely employed to characterize nonlinearly distorted ofdm signals and to evaluate the corresponding performance in this paper we study the accuracy of the gaussian approach when evaluating nonlinear effects in ofdm signals with finite number of subcarriers showing the strengths and limitations of this approach it is shown that the decomposition in useful and self interference components is valid even for a reduced number of subcarriers the gaussian approximation of the nonlinear self interference at the subcarrier level is very accurate provided that n2 is high however the nonlinear distortion levels slightly lower than the ones obtained with the gaussian approximation with relative errors dropping with 1 n leading to somewhat pessimistic sir levels signal to interference ratio

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

minimization algorithm of fuzzy finite automata in this paper a class of fuzzy finite automata corresponding to the mealy type of ordinary automata is formulated and also two types of statewise equivalence relations are introduced from the equivalence relations a minimal form is defined and a minimization algorithm of the mealy type of fuzzy finite automata is obtained

a frequency dependent rectangular plate finite dynamic element for high precision transverse vibration analysis of simply supported plates the inclusion of the twist parameter is shown to be essential using a rational choice of parameters to form the deflection functions a constant term sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling

a practical analysis of performance optimization in ostbc based nonlinear mimo ofdm systems this paper presents a practical performance analysis of an orthogonal space time block code ostbc based multiple input multiple output mimo orthogonal frequency division multiplexing ofdm system in the presence of nonlinear power amplifiers pas the equivalent single input single output siso scalar model is introduced and this then is used to construct a model for the nonlinear mimo ofdm system based on an unique inter modulation product imp analysis it is shown how the receiver signal to noise ratio snr may be derived to a polynomial based function of the system operating point it is also shown that expressions for the asymptotical behavior of this snr when the linear and highly nonlinear pa operations are applied may also be derived based on these derivations it is further shown that the optimal system operating point which corresponds to the maximum receiver snr and sep lower bound can be identified and be derived to a polynomial based expression additionally a general expression for the different integral expressions of sep for the phase shift keying psk and quadrature amplitude modulation qam signals is found by means of these analytical results it was found possible to advance analytical explanations of observed behaviour in simulations and also to provide a practical analysis of performance optimization of nonlinear mimo ofdm systems

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

ranks of fuzzy matrices applications in state reduction of fuzzy automata abstract in this paper we consider different types of ranks of fuzzy matrices over residuated lattices we investigate relations between ranks and prove that row rank column rank and schein rank of idempotent fuzzy matrices are equal in particular ranks and corresponding decompositions of fuzzy matrices representing fuzzy quasi orders are studied in detail we show that fuzzy matrix decomposition by ranks can be used in the state reduction of fuzzy automata moreover we prove that using rank decomposition of fuzzy matrices improves results of any state reduction method based on merging indistinguishable states of fuzzy automata

nondeterministic fuzzy automata to handle fuzzy uncertainty in system modeling nondeterministic finite automata have been generalized into fuzzy automata after a reexamination of the notions of fuzzy automata in the literature we ascertain that the fundamental property nondeterminism in nondeterministic finite automata has not been well embodied in the generalization in order to reflect nondeterminism in fuzzy automata we introduce nondeterministic fuzzy automata with or without e moves and fuzzy languages recognized by them like nondeterministic finite automata nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems moreover we show that deterministic fuzzy automata nondeterministic fuzzy automata and nondeterministic fuzzy automata with e moves are all equivalent in the sense that they recognize the same class of fuzzy languages which is an extension of the well known equivalence among finite automata nondeterministic finite automata and nondeterministic finite automata with e moves

logic based fuzzy neurocomputing with unineurons in this paper we introduce a new category of logic neurons unineurons that are based on the concept of uninorms as uninorms form a certain generalization of the generic categories of fuzzy set operators such as t norms and t conorms the proposed unineurons inherit their logic processing capabilities which make them flexible and logically appealing we discuss several fundamental categories of uninorms such as uni or uni and and alike in particular we focus on the interpretability of networks composed of unineurons leading to several categories of rules to be exploited in rule based systems the learning aspects of the unineurons are presented along with detailed optimization schemes experimental results tackle two categories of problems such as a a logic approximation of fuzzy sets and b a design of associations between information granules where the ensuing development schemes directly relate to the fundamentals of granular fuzzy modeling

adaptive control of a class of nonlinear systems with fuzzy logic an adaptive tracking control architecture is proposed for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture employs fuzzy systems which are expressed as a series expansion of basis functions to adaptively compensate for the plant nonlinearities global asymptotic stability of the algorithm is established in the lyapunov sense with tracking errors converging to a neighborhood of zero simulation results for an unstable nonlinear plant are included to demonstrate that incorporating the linguistic fuzzy information from human experts results in superior tracking performance

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

perspectives of fuzzy systems and control although fuzzy control was initially introduced as a model free control design method based on the knowledge of a human operator current research is almost exclusively devoted to model based fuzzy control methods that can guarantee stability and robustness of the closed loop system state of the art techniques for identifying fuzzy models and designing model based controllers are reviewed in this article attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy such as expert control supervision and diagnostic systems open issues are highlighted and an attempt is made to give some directions for future research

fuzzy control with fuzzy inputs this paper is concerned with the use of fuzzy inputs in fuzzy logic controllers a precise representation of fuzzy logic controllers by means of mappings is used to introduce different ways for dealing with fuzzy inputs two types of fuzzy inputs are presented and their potential use in fuzzy control is discussed the proposed concepts are applied to control a first order process with a pi controller this simple process is chosen to clearly illustrate the behavior of the closed loop system using fuzzy inputs for fuzzy reference and fuzzy measurement finally a nonlinear process is used to illustrate the effects of fuzzy inputs on a more complex system although it is sometimes speculated that fuzzy inputs may improve the behavior of fuzzy controllers experiments developed in this paper show this point is not straightforward and that the relevance of fuzzy inputs should be questioned in closed loop fuzzy control

fuzzy control of a benchmark problem a computing with words approach the rotational translational proof mass actuator rtac system is a well known benchmark for nonlinear control for which a number of controllers were designed in this paper we apply fuzzy lyapunov synthesis which is a computing with words version of classical lyapunov synthesis to design fuzzy controllers for the rtac system this allows us to systematically design state feedback and output feedback controllers using only a linguistic description of the rtac system the designed fuzzy controllers yield a globally asymptotically stable closed loop system we demonstrate their advantages in comparison with a previously designed linear controller for the rtac system

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

a formal model of computing with words classical automata are formal models of computing with values fuzzy automata are generalizations of classical automata where the knowledge about the system s next state is vague or uncertain it is worth noting that like classical automata fuzzy automata can only process strings of input symbols therefore such fuzzy automata are still abstract devices for computing with values although a certain vagueness or uncertainty are involved in the process of computation we introduce a new kind of fuzzy automata whose inputs are instead strings of fuzzy subsets of the input alphabet these new fuzzy automata may serve as formal models of computing with words we establish an extension principle from computing with values to computing with words this principle indicates that computing with words can be implemented with computing with values with the price of a big amount of extra computations

determinism and fuzzy automata the concept of a fuzzy automaton as studied in the literature is a direct generalization of the classical concept of a non deterministic automaton in this paper we consider the question of whether there is a deterministic counterpart to the notion of a fuzzy automaton we propose a definition of deterministic fuzzy automata and show that they are equally powerful as fuzzy automata compared to the classical notion of a deterministic automaton the deterministic fuzzy automaton defined in our paper differs essentially only in that the final states form a fuzzy set moreover we show that deterministic fuzzy automata are equally powerful as nested systems of deterministic automata

passive detection of correlated subspace signals in two mimo channels in this paper we consider a two channel multiple input multiple output passive detection problem in which there is a surveillance array and a reference array the reference array is known to carry a linear combination of broadband noise and a subspace signal of known dimension but unknown basis the question is whether the surveillance channel carries a linear combination of broadband noise and a subspace signal of the same dimension but unknown basis which is correlated with the subspace signal in the reference channel we consider a second order detection problem where these subspace signals are structured by an unknown but common p dimensional random vector of symbols transmitted from sources of opportunity and then received through unknown m times p matrices at each of the m element arrays the noises in each channel have spatial correlation models ranging from arbitrarily correlated to independent with identical variances we provide a unified framework to derive the generalized likelihood ratio test for these different noise models in the most general case of arbitrary noise covariance matrices the test statistic is a monotone function of canonical correlations between the reference and surveillance channels

logic based fuzzy networks a study in system modeling with triangular norms and uninorms the ultimate challenges of system modeling concern designing accurate yet highly transparent and user centric models we have witnessed a plethora of neurofuzzy architectures which are aimed at addressing these two highly conflicting requirements this study is concerned with the design and the development of transparent logic networks realized with the aid of fuzzy neurons and fuzzy unineurons the construction of networks of this form requires a formation of efficient interfaces that constitute a conceptually appealing bridge between the model and the real world experimental environment in which the model is to be used in general the interfaces are constructed by invoking some form of granulation of information and binary boolean discretization in particular we introduce a new discretization environment that is realized by means of particle swarm optimization pso and data clustering implemented by the k means algorithm the underlying structure of the network is optimized by invoking a combination of the pso and the mechanisms of conventional gradient based learning we discuss various optimization strategies by considering boolean as well as fuzzy data coming as the result of discretization of original experimental data and then involving several learning strategies we elaborate on the interpretation aspects of the network and show how those could be strengthened through efficient pruning we also show how the interpreted network leads to a simpler and more accurate logic description of the experimental data a number of experimental studies are included

a categorical approach to minimal realization for a fuzzy language abstract in this study we provide a general theory of minimal realization for a given fuzzy language in a category theory setting we introduce categorical characterizations of a run map reachability map and observability map for a crisp deterministic fuzzy automaton finally we show that all minimal realizations for a given fuzzy language are isomorphic to the nerode realization for the same case

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

the extended sequentially drilled joint congruence transformation and its application in gaussian independent vector analysis independent vector analysis iva has emerged in recent years as an extension of independent component analysis ica into multiple sets of mixtures where the sources in each set are independent but may depend on sources in the other sets in a semiblind iva framework information regarding the probability distributions of the sources may be available giving rise to maximum likelihood ml separation in recent work we have shown that under the multivariate gaussian model with arbitrary temporal covariance matrices stationary or non stationary of the sources ml separation requires the solution of a sequentially drilled joint congruence sedjoco transformation of a set of matrices which is reminiscent of but different from classical joint diagonalization in this paper we extend our results to the iva problem showing how the ml solution for the gaussian model with arbitrary covariance and cross covariance matrices takes the form of an extended sedjoco solution we formulate the extended problem derive a condition for the existence of a solution and propose two iterative solution algorithms additionally we derive the induced cramer rao lower bound icrlb on the resulting interference to source ratios isr and demonstrate by simulation how the ml separation obtained by solving the extended sedjoco problem attains the icrlb asymptotically as opposed to other separation approaches which cannot exploit prior knowledge regarding the sources distributions

the universal fuzzy automaton abstract in this paper we introduce the notion of universal fuzzy automaton with membership values in a complete residuated lattice whose states are the factorizations of this fuzzy language and transition function is defined using the inclusion degree of related fuzzy languages next we define the homomorphism of fuzzy automata prove that every automaton accepting a fuzzy language can canonically map into the universal fuzzy automaton of this language which is called the universal property for a fuzzy language the connections between the universal fuzzy automaton and fuzzy minimal automata of the given fuzzy language are exploited finally we give a method to construct the universal fuzzy automaton by a deterministic fuzzy automaton accepting the given fuzzy language which is effective in the case that this deterministic fuzzy automaton is finite

connecting the linguistic hierarchy and the numerical scale for the 2 tuple linguistic model and its use to deal with hesitant unbalanced linguistic information the 2 tuple linguistic representation model is widely used as a basis for computing with words cw in linguistic decision making problems two different models based on linguistic 2 tuples i e the model of the use of a linguistic hierarchy and the numerical scale model have been developed to address term sets that are not uniformly and symmetrically distributed i e unbalanced linguistic term sets ultss in this study we provide a connection between these two different models and prove the equivalence of the linguistic computational models to handle ultss further we propose a novel cw methodology where the hesitant fuzzy linguistic term sets hfltss can be constructed based on ultss using a numerical scale in the proposed cw methodology we present several novel possibility degree formulas for comparing hfltss and define novel operators based on the mixed 0 1 linear programming model to aggregate the hesitant unbalanced linguistic information

performance analysis of deliberately clipped ofdm signals we analyze the performance of the clipped orthogonal frequency division multiplexing ofdm system in terms of peak power reduction capability and degradation of channel capacity the clipping is performed on the baseband ofdm signals with and without oversampling followed by the ideal low pass filter first the effect of the envelope clipping on the peak to average power ratio papr and the instantaneous power of the band limited ofdm signal is studied we then discuss the channel capacity of the oversampled and clipped ofdm signals over the additive white gaussian noise and ideally interleaved rayleigh fading channels the capacity is calculated based on the assumption that the distortion terms caused by the clipping are gaussian it is shown that the snr penalty due to the clipping can be considerably alleviated by using optimal coding and reducing the information data rate the results are justified by the simulation results using near optimal turbo codes

uninorms on bounded lattices constructed by t norms and t subconorms abstract the construction of uninorms on bounded lattices has been a attractive research area in this paper we introduce some new classes of uninorms on bounded lattices via t subnorms and t subconorms with a neutral element e under some constraints we also give some illustrative examples to help understand the structure of these new uninorms moreover we provide an answer to the open problem raised by cayli in 2019 finally the differences between our methods and existing approaches are assessed

numerical formulation for a higher order plane finite dynamic element the paper describes the development of an eight node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices numerical test results of free vibration analyses are presented in detail for the newly developed eight node element and also the corresponding four node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures such results indicate a superior pattern of solution convergence of the presently developed dynamic element

retraction and generalized extension of computing with words fuzzy automata whose input alphabet is a set of numbers or symbols are a formal model of computing with values motivated by zadeh s paradigm of computing with words rather than numbers ying proposed a kind of fuzzy automata whose input alphabet consists of all fuzzy subsets of a set of symbols as a formal model of computing with all words in this paper we introduce a somewhat general formal model of computing with some special words the new features of the model are that the input alphabet only comprises some not necessarily all fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily by employing the methodology of fuzzy control we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs these principles show that computing with values and computing with all words can be respectively implemented by computing with words some algebraic properties of retractions and generalized extensions are addressed as well

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

aggregation functions on the set of discrete fuzzy numbers defined from a pair of discrete aggregations abstract in this paper we propose a method to construct aggregation functions on the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers from a couple of discrete aggregation functions the interest on these discrete fuzzy numbers lies on the fact that they can be interpreted as linguistic expert valuations that increase the flexibility of the elicitation of qualitative information based on linguistic terms finally a linguistic decision making model based on a pair of aggregation functions defined on discrete fuzzy numbers is given

stable multi input multi output adaptive fuzzy neural control in this letter stable direct and indirect adaptive controllers are presented that use takagi sugeno t s fuzzy systems 1985 conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal vector for a class of continuous time multi input multi output mimo square nonlinear plants with poorly understood dynamics the direct adaptive scheme allows for the inclusion of a priori knowledge about the control input in terms of exact mathematical equations or linguistics while the indirect adaptive controller permits the explicit use of equations to represent portions of the plant dynamics we prove that with or without such knowledge the adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of the reference inputs we do not impose any initialization conditions on the controllers and guarantee convergence of the tracking error to zero

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

bisimulations for fuzzy automata bisimulations have been widely used in many areas of computer science to model equivalence between various systems and to reduce the number of states of these systems whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata we prove that a uniform fuzzy relation between fuzzy automata a and b is a forward bisimulation if and only if its kernel and co kernel are forward bisimulation fuzzy equivalence relations on a and b and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations as a consequence we get that fuzzy automata a and b are ufb equivalent i e there is a uniform forward bisimulation between them if and only if there is a special isomorphism between the factor fuzzy automata of a and b with respect to their greatest forward bisimulation fuzzy equivalence relations this result reduces the problem of testing ufb equivalence to the problem of testing isomorphism of fuzzy automata which is closely related to the well known graph isomorphism problem we prove some similar results for backward forward bisimulations and we point to fundamental differences because of the duality with the studied concepts backward and forward backward bisimulations are not considered separately finally we give a comprehensive overview of various concepts on deterministic nondeterministic fuzzy and weighted automata which are related to bisimulations

deformed fuzzy automata for correcting imperfect strings of fuzzy symbols presents a fuzzy method for the recognition of strings of fuzzy symbols containing substitution deletion and insertion errors as a preliminary step we propose a fuzzy automaton to calculate a similarity value between strings the adequate selection of fuzzy operations for computing the transitions of the fuzzy automaton allows us to obtain different string similarity definitions including the levenshtein distance a deformed fuzzy automaton based on this fuzzy automaton is then introduced in order to handle strings of fuzzy symbols the deformed fuzzy automaton enables the classification of such strings having an undetermined number of insertion deletion and substitution errors the selection of the parameters determining the deformed fuzzy automaton behavior would allow to implement recognizers adapted to different problems the paper also presents algorithms that implement the deformed fuzzy automaton experimental results show good performance in correcting these kinds of errors

characterization of uninorms on bounded lattices in this paper we propose a characterization of uninorms on a general bounded lattice l by means of a sextuple of a triangular norm a triangular conorm and four aggregation functions on l observe that in the case when l is a chain it is enough to consider a triple consisting of a t norm a t conorm and an averaging aggregation function an example of a proper uninorm which has an absorbing element differing from both 0 and 1 is also shown note that this cannot happen if we consider uninorms acting on a chain two general constructions of uninorms on l are added letting a t norm a t conorm linked to a fixed neutral element e of the constructed uninorm to be free and fixing the remaining functions

on quotient machines of a fuzzy automaton and the minimal machine in this paper the concept of substitution property sp partition for a finite fuzzy automaton is formulated and the quotient automaton with respect to an sp partition is defined the state minimization problem for such automata by using the method of quotient machines is solved

observability and decentralized control of fuzzy discrete event systems fuzzy discrete event systems as a generalization of crisp discrete event systems have been introduced in order that it is possible to effectively represent uncertainty imprecision and vagueness arising from the dynamic of systems a fuzzy discrete event system has been modeled by a fuzzy automaton its behavior is described in terms of the fuzzy language generated by the automaton in this paper we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation observability normality and co observability of crisp languages are extended to fuzzy languages it is shown that the observability together with controllability of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor when a decentralized solution is desired it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co observable moreover the infimal controllable and observable fuzzy superlanguage and the supremal controllable and normal fuzzy sublanguage are also discussed simple examples are provided to illustrate the theoretical development