products of lattice valued fuzzy transition systems and induced fuzzy transformation semigroups in this study several products of fuzzy transformation semigroups are generalized to the case where their truth structure is a complete lattice we show that the direct product of two such fuzzy transformation semigroups is again a fuzzy transformation semigroup if and only if the lattice is distributive in addition after extending the cascade product we introduce a novel way of building a fuzzy transformation semigroup starting from a unique automaton the particular case of the lattice comprising all the closed subintervals contained in 0 1 is analyzed

stability of square root domains associated with elliptic systems of pdes on nonsmooth domains abstract we discuss stability of square root domains for uniformly elliptic partial differential operators l a a in l 2 with mixed boundary conditions on with respect to additive perturbations we consider open bounded and connected sets r n n n 1 that satisfy the interior corkscrew condition and prove stability of square root domains of the operator l a with respect to additive potential perturbations v l p l p n 2 special emphasis is put on the case of uniformly elliptic systems with mixed boundary conditions

a kato s second type representation theorem for solvable sesquilinear forms abstract kato s second representation theorem is generalized to solvable sesquilinear forms these forms need not be non negative nor symmetric the representation considered holds for a subclass of solvable forms called hyper solvable precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator this condition always holds for closed semibounded forms and it is also considered by several authors for symmetric sign indefinite forms as a consequence a one to one correspondence between hyper solvable forms and operators which generalizes those already known is established

algorithmic and logical characterizations of bisimulations for non deterministic fuzzy transition systems abstract bisimulation is a well known behavioral equivalence for discrete event systems and has been developed in fuzzy systems quickly in this paper we adopt an approach of the relational lifting that is one of the most used methods in the field of bisimulation research to define it for a non deterministic fuzzy transition system an o s 4 2 algorithm is given for testing bisimulation where s is the number of states and the number of transitions in the underlying transition systems two different modal logics are presented one is two valued and indicates whether a state satisfies a formula which is an extension of hennessy milner logic the other is real valued and shows to what extent a state satisfies a formula they both characterize bisimilarity soundly and completely interestingly the second characterization holds under a class of fuzzy logics in addition this real valued logic allows us to conveniently define a logical metric that captures the similarity between states or systems that is the smaller distance the more states alike although the work is inspired by the corresponding work in probabilistic systems it is obviously different in particular the real valued logic in this paper remains unexplored in fuzzy systems even in probabilistic systems

distribution based behavioral distance for nondeterministic fuzzy transition systems modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems in this paper we first present a new notion of bisimulation for nondeterministic fuzzy transition systems which is distribution based and coarser than state based bisimulation appeared in the literature then we define a distribution based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations we also propose an on the fly algorithm for computing the bisimilarity metric moreover we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric interestingly this characterization holds for a class of fuzzy modal logics in addition we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric which makes compositional verification possible

information retrieval from interval valued fuzzy automata through k α operators abstract in this paper fuzzy finite transition systems and fuzzy transformation semigroups are analyzed when the truth structure is the set of all the closed real subintervals contained in 0 1 our approach involves the application of interval valued fuzzy sets techniques in order to retrieve the information given by the transition functions of the considered automata in particular a characterization of those atanassov s k operators which provide a fuzzy transformation semigroup starting from an interval valued fuzzy automaton is achieved conversely different ways of getting an interval valued fuzzy transformation semigroup starting from two real fuzzy automata are compared

quadratic estimates and functional calculi of perturbed dirac operators we prove quadratic estimates for complex perturbations of dirac type operators and thereby show that such operators have a bounded functional calculus as an application we show that spectral projections of the hodge dirac operator on compact manifolds depend analytically on l changes in the metric we also recover a unified proof of many results in the calderon program including the kato square root problem and the boundedness of the cauchy operator on lipschitz curves and surfaces

fuzzy turing machines variants and universality in this paper we study some variants of fuzzy turing machines ftms and universal ftm first we give several formulations of ftms including in particular deterministic ftms dftms and nondeterministic ftms nftms we then show that dftms and nftms are not equivalent as far as the power of recognizing fuzzy languages is concerned this contrasts sharply with classical tms second we show that there is no universal ftm that can exactly simulate any ftm on it but if the membership degrees of fuzzy sets are restricted to a fixed finite subset a of 0 1 such a universal machine exists we also show that a universal ftm exists in some approximate sense this means for any prescribed accuracy that we can construct a universal machine that simulates any ftm with the given accuracy finally we introduce the notions of fuzzy polynomial time bounded computation and nondeterministic fuzzy polynomial time bounded computation and investigate their connections with polynomial time bounded computation and nondeterministic polynomial time bounded computation

bisimulation for probabilistic transition systems a coalgebraic approach the notion of bisimulation as proposed by larsen and skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of aczel and mendier in terms of a set functor this coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving borel probability measures under reasonable conditions generalized probabilistic bisimilarity can be characterized categorically application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation

polynomial time algorithms for computing distances of fuzzy transition systems behaviour distances to measure the resemblance of two states in a nondeterministic fuzzy transition system have been proposed recently in literature such a distance defined as a pseudo ultrametric over the state space of the model provides a quantitative analogue of bisimilarity in this paper we focus on the problem of computing these distances we first extend the definition of the pseudo ultrametric by introducing discount such that the discounting factor being equal to 1 captures the original definition we then provide polynomial time algorithms to calculate the behavioural distances in both the non discounted and the discounted setting the algorithm is strongly polynomial in the former case

approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures abstract for the purpose of reducing the number of states of fuzzy automata we study approximate bisimulations of fuzzy automata under fuzzy similarity measures which are induced by residuums of left continuous t norms for a real number 0 1 and a fuzzy similarity measure s we define approximate bisimulation under s between two fuzzy automata and prove that the degree of similarity between them is more than or equal to if there exists an approximate bisimulation between them furthermore we put forward the notion of surjective functional approximate bisimulations between two fuzzy automata under s using the notion of surjective functional approximate bisimulations under s the approximate bisimulations for a fuzzy automaton under s is defined as an equivalence relation with two additional properties according to an approximate bisimulation for a fuzzy automaton an aggregated fuzzy automaton has been constructed and the degree of similarity between them is also more than or equal to it is significant for us to find that there might not possess the greatest approximate bisimulation for a fuzzy automaton and we provide a polynomial time algorithm for computing all maximal approximate bisimulations finally we provide the conditions of the existence of the greatest approximate bisimulation

weak bisimulations for fuzzy automata abstract forward and backward bisimulations have been introduced recently by ciric et al 2012 9 as a means for modeling the equivalence between states of fuzzy automata and approximating the language equivalence as well as for use in the state reduction of fuzzy automata the main aim of the present paper is to introduce two new kinds of bisimulations weak forward and backward bisimulations which provide better approximations of the language equivalence than forward and backward bisimulations and when employed in the state reduction they provide better reductions we give procedures for deciding whether there exist weak forward and backward simulations and bisimulations and for computing the greatest ones whenever they exist using weak bisimulations in conjunction with the concept of a uniform fuzzy relation we determine necessary and sufficient conditions under which two fuzzy automata are weak bisimulation equivalent we also characterize uniform weak backward and forward bisimulations between two fuzzy automata in terms of isomorphisms between their nerode and reverse nerode automata

fuzzy automata with fuzzy relief this paper shows a definition of a fuzzy automaton which has the state input and output sets as fuzzy sets the state transition function is defined as moving on a fuzzy relief with fuzzy peak states and boundaries between different membership functions after the definition of fuzzy automaton with fuzzy relief the paper deals with a generalization simulation and realization of such a fuzzy automaton the paper links the defined fuzzy automaton to an existing fuzzy jk memory cell and to well known fuzzy automata defined on the basis of crisp sets

reactive generative and stratified models of probabilistic processes abstract we introduce three models of probabilistic processes namely reactive generative and stratified these models are investigated within the context of pccs an extension of milner s sccs in which each summand of a process summation expression is guarded by a probability and the sum of these probabilities is 1 for each model we present a structural operational semantics of pccs and a notion of bisimulation equivalence which we prove to be a congruence we also show that the models form a hierarchy the reactive model is derivable from the generative model by abstraction from the relative probabilities of different actions and the generative model is derivable from the stratified model by abstraction from the purely probabilistic branching structure moreover the classical nonprobabilistic model is derivable from each of these models by abstraction from all probabilities

a belief evolution based approach for online control of fuzzy discrete event systems under partial observation in this paper we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete event systems dess the goal is to synthesize a fuzzy supervisor such that the behavior of the closed loop system is within a given fuzzy language a new approach for solving this problem is proposed based on the idea of belief evolution specifically we propose an algorithm that can be implemented in an online manner we show that the proposed algorithm is both sound and complete i e it effectively solves the supervisor synthesis problem to the best of our knowledge this is the first algorithm with such a property for fuzzy dess as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem

theory of extended fuzzy discrete event systems for handling ranges of knowledge uncertainties and subjectivity in 2001 we originated a theory of fuzzy discrete event systems fdess that generalized the conventional crisp discrete event systems dess vagueness and imprecision concerning states and event transitions of dess were represented by membership grades and computed via fuzzy logic our application of the fdes theory to computerized human immunodeficiency virus acquired immune deficiency syndrome treatment regimen selection although preliminarily successful suggests that a more comprehensive fdes theory is needed to address two general issues critically important not only to biomedical applications but also to real world problems in other industries first domain experts should have means other than point estimates and type 1 fuzzy sets mandated in the current framework to describe uncertainties subjectivity and imprecision in their complex knowledge and experience second when a group of experts with distinct opinions is involved they should not be forced to reach consensus for the sake of system development this is because collective consensus may not be achievable which is often the case in medicine where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time the theory of extended fdes presented in this paper addresses both the problems and contains the fdes theory as a special case experts are now allowed to use interval numbers and type 1 and type 2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices accordingly we have established mathematical operations that cover the computations of fuzzy states fuzzy event transitions and parallel composition numerical examples are provided

multilinear littlewood paley estimates with applications to partial differential equations abstract we obtain a collection of multilinear littlewood paley estimates which we then apply to two problems in partial differential equations the first problem is the estimation of the square root of an elliptic operator in divergence form and the second is the estimation of solutions to the cauchy problem for nondivergence form parabolic equations

fuzzy bisimulation for godel modal logic bisimulation is a central concept in the model theory of modal logic with extensive computational applications it is a relation between two models in which related states have identical atomic properties and matching transition possibilities bisimulation captures the expressive power of propositional modal logic in the sense that bisimilar states are not distinguishable by any propositional modal formula in recent years fuzzy modal logic has received much attention because of the connection between uncertainty measures and fuzzy modalities in this paper we define the notion of fuzzy bisimulation and prove that in a fuzzified version it bears the same relationship to fuzzy modal logic that bisimulation bears to propositional modal logic

epsilon bisimulation relations for fuzzy automata this paper investigates the approximate bisimulation relations for fuzzy automata in order to study the approximate minimization problem of fuzzy automata for a small positive real number epsilon we introduce the notion of epsilon bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton a differs by epsilon from the behavior of a fuzzy automaton b under a epsilon bisimulation relation between them also the notion of surjective functional epsilon bisimulation relations between two fuzzy automata is defined according to surjective functional epsilon bisimulation relations we discuss epsilon bisimulation relations for a fuzzy automaton a construction of aggregated fuzzy automaton by the given epsilon bisimulation for a fuzzy automaton is given furthermore we find that there might not exist the greatest epsilon bisimulation relation for a fuzzy automaton and we novelly give an effective algorithm to construct all maximal epsilon bisimulation relations for the given fuzzy automaton finally we point out that bisimulation relations for a fuzzy automaton are also epsilon bisimulation relations the conditions for the real number epsilon to ensure the existence of the greatest epsilon bisimulation are also discussed

a limit theorem in some dynamic fuzzy systems abstract in this paper using a fuzzy relation we define a dynamic fuzzy system with a compact state space by introducing a contraction property we study the limit of a sequence of fuzzy states and obtain a theorem for the existence and uniqueness of the solution of a fuzzy relational equation as an application we deal with a dynamic fuzzy system with a terminal fuzzy gain and give some characterizations for the fuzzy expected gain a numerical example is given to comprehend our idea in this paper

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

square roots of elliptic operators consider an elliptic sesquilinear form defined on v v by j u v ajk u xk t6v xj ak u xkv ju t6v xj auvdx where v is a closed subspace of h1 which contains c0 is a bounded lipschitz domain in rn ajk ak j a l and re ajk k j 0 for all cn with 1 let l be the operator with largest domain satisfying j u v lu v for all v then l i is a maximal accretive operator in l2 for a sufficiently large real number it is proved that l i 12 is a bounded operator from v to l2 provided mild regularity of the coefficients is assumed in addition it is shown that if the coefficients depend differentiably on a parameter t in an appropriate sense then the corresponding square root operators also depend differentiably on t the latter result is new even when the forms j are hermitian

logical characterizations of simulation and bisimulation for fuzzy transition systems simulations and bisimulations are known to be useful for abstracting and comparing formal systems and they have recently been introduced into fuzzy systems in this study we provide sound and complete logical characterizations for simulation and bisimulation which are defined over fuzzy labeled transition systems via two variants of the hennessy milner logic the logic for characterizing fuzzy simulation has neither negation nor disjunction which is very different from the well known logical characterizations of probabilistic simulations although the completeness proofs of our characterization results are inspired by relevant research in probabilistic concurrency theory the logic for characterizing fuzzy bisimulation also deviates from that for probabilistic bisimulations

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

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

heat kernels of second order complex elliptic operators and applications we study the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on rn we obtain gaussian bounds without further assumption ifn 2 and when the principal part has holder continuous coefficients ifn 3 a thorough study of the boundedness properties of the green operator is made in dimension 1 we construct the fundamental solution of these operators in dimension 2 boundedness results of the maximal accretive square roots onlpsobolev spaces and holder spaces are obtained whenn 2 under holder continuity assumption on the coefficients boundedh functional calculi onlp 1 p are also discussed

model checking fuzzy computation tree logic traditional temporal logics such as linear temporal logic and computation tree logic are widely used to specify properties of reactive systems model checking is a well established technique for verifying if a desired property described as a temporal logic formula holds over a reactive system model this paper presents fuzzy computation tree logic fctl a fuzzy extension of temporal logics by combining general fuzzy logic with computation tree logic and discusses its model checking problem first the notion of fuzzy kripke structures fkss and the syntax and semantics of their specification language fctl are introduced then we give a direct model checking algorithm for fctl over fks on the other hand we study when fctl model checking problem can be reduced to classical model checking ones and give a reduction method for an important fragment of fctl

square roots of elliptic second order divergence operators on strongly lipschitz domains l p theory we study l p estimates for square roots of second order elliptic non necessarily selfadjoint operators in divergence form l mathrm div a nabla on lipschitz domains subject to dirichlet or to neumann boundary conditions pursuing our work 4 where we considered operators on mathbb r n we obtain among other things l 1 2 f p le c nabla f p for all 1 p infty if l is real symmetric and the domain bounded which is new for 1 p 2 we also obtain similar results for perturbations of constant coefficients operators our methods rely on a singular integral representation calderon zygmund theory and quadratic estimates a feature of this study is the use of a commutator between the resolvent of the laplacian dirichlet and neumann and partial derivatives which carries the geometry of the boundary

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

weakly linear systems of fuzzy relation inequalities the heterogeneous case new types of systems of fuzzy relation inequalities and equations called weakly linear have been recently introduced in j ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 the mentioned paper dealt with homogeneous weakly linear systems composed of fuzzy relations on a single set and a method for computing their greatest solutions has been provided this method is based on the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems where the unknown fuzzy relation relates two possibly different sets we also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems besides we point out to applications of the obtained results in the state reduction of fuzzy automata and computing the greatest simulations and bisimulations between fuzzy automata as well as in the positional analysis of fuzzy social networks

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

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

fuzzy ϵ approximate regular languages and minimal deterministic fuzzy automata ϵ accepting them abstract in this paper for a real number 0 1 we put forward the notion of fuzzy approximate regular languages and study their properties especially the pumping lemma in the context of this kind of languages by comparing sets of fuzzy approximate regular languages under the order of set inclusion we get an infinite hierarchy of fuzzy languages the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages and the sets of approximate regular languages are different for different 0 1 2 we also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy approximate regular languages furthermore for a fuzzy approximate regular language f approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata accepting f if a fuzzy approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton a then we give a polynomial time algorithm to construct at least one minimal deterministic fuzzy automaton accepting f by means of a finally we point out that the number of states of minimal deterministic fuzzy automata accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language

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

bisimulation relations for weighted automata bisimulation is a well known equivalence relation for discrete event systems and has been extended to probabilistic and stochastic systems this paper introduces a general definition of bisimulation which can be applied to finite automata where weights and labels are assigned to transitions it is shown that this general view contains several known bisimulations as special cases and defines naturally equivalences for different classes of models apart from the well known forward bisimulation also backward bisimulation is introduced and it is shown that both types of bisimulation preserve different types of results furthermore it is shown that forward and backward bisimulation are congruences according to commonly known composition operations for automata

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

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

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

bisimulation and bisimilarity for fuzzy description logics under the godel semantics abstract description logics dls are a suitable formalism for representing knowledge about domains in which objects are described not only by attributes but also by binary relations between objects fuzzy extensions of dls can be used for such domains when data and knowledge about them are vague and imprecise one of the possible ways to specify classes of objects in such domains is to use concepts in fuzzy dls as dls are variants of modal logics indiscernibility in dls is characterized by bisimilarity the bisimilarity relation of an interpretation is the largest auto bisimulation of that interpretation in dls and their fuzzy extensions such equivalence relations can be used for concept learning in this paper we define and study fuzzy bisimulation and bisimilarity for fuzzy dls under the godel semantics as well as crisp bisimulation and strong bisimilarity for such logics extended with involutive negation the considered logics are fuzzy extensions of the dl alc r e g a variant of pdl with additional features among inverse roles nominals qualified or unqualified number restrictions the universal role local reflexivity of a role and involutive negation we formulate and prove results on invariance of concepts under fuzzy resp crisp bisimulation conditional invariance of fuzzy tboxes aboxes under bisimilarity resp strong bisimilarity and the hennessy milner property of fuzzy resp crisp bisimulation for fuzzy dls without resp with involutive negation under the godel semantics apart from these fundamental results we also provide results on using fuzzy bisimulation to separate the expressive powers of fuzzy dls as well as results on using strong bisimilarity to minimize fuzzy interpretations

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

exact performance equivalence an equivalence relation for stochastic automata stochastic automata are an established formalism to describe and analyse systems according to their qualitative and quantitative behaviour equivalence is a basic concept for the analysis comparison and reduction of untimed automata whereas equivalence of stochastic automata is less established this paper introduces a new equivalence relation for stochastic automata denoted as exact performance equivalence it is shown that this equivalence relation preserves several important qualitative properties and also quantitative results exact performance equivalence is a congruence according to the synchronised product of stochastic automata the smallest exactly equivalent automaton exists for a stochastic automaton and can be generated by a partition refinement algorithm

applications of the purely imaginary powers of operators in hilbert spaces in c r acad sci paris299 1984 173 176 we discussed purely imaginary powers aiy y of linear operators a in hilbert spaces here we utilize the results to consider the various problems generation of cosine families in hilbert spaces coincidence of the definition domains of the fractional powers of operators differentiability of the functions of the form a 0 0 1 where a is an operator valued function defined on an interval 0 t and so forth