a generalization of myhill nerode theorem for fuzzy languages the well known myhill nerode theorem provides a necessary and sufficient condition for a language to be regular in the context of fuzzy languages and automata theory myhill nerode type theorems have been proved for fuzzy languages with finite range this paper introduces a new right equivalence relation on the free monoid of an alphabet based on the notion of factorization of fuzzy languages the index of this relation for a fuzzy language with infinite range can be finite this fact allows us to generalize the myhill nerode theorem for any kind of fuzzy languages in this paper is proved that the following two conditions are mutually equivalent for a given fuzzy language x i there exists a factorization such that the right equivalence relation of x defined via the factorization has a finite index ii the fuzzy language x is recognized by a fuzzy deterministic finite automaton

determinization of weighted finite automata over strong bimonoids we consider weighted finite automata over strong bimonoids where these weight structures can be considered as semirings which might lack distributivity then in general the well known run semantics initial algebra semantics and transition semantics of an automaton are different we prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated submonoids moreover for a given weighted finite automaton we construct the nerode automaton and myhill automaton both being crisp deterministic which are equivalent to the original automaton with respect to the initial algebra semantics respectively the transition semantics we prove necessary and sufficient conditions under which the nerode automaton and the myhill automaton are finite and we provide efficient algorithms for their construction also for a given weighted finite automaton we show sufficient conditions under which a given weighted finite automaton can be determinized preserving its run semantics

brzozowski type determinization for fuzzy automata abstract in this paper we adapt the well known brzozowski determinization method to fuzzy automata this method gives better results than all previously known methods for determinization of fuzzy automata developed by b lohlavek 4 li and pedrycz 20 ignjatovic et al 15 and jancic et al 18 namely as in the case of ordinary nondeterministic automata brzozowski type determinization of a fuzzy automaton results in a minimal crisp deterministic fuzzy automaton equivalent to the starting fuzzy automaton and we show that there are cases when all previous methods result in infinite automata while brzozowski type determinization results in a finite one the paper deals with fuzzy automata over complete residuated lattices but identical results can also be obtained in a more general context for fuzzy automata over lattice ordered monoids and even for weighted automata over commutative semirings

fuzzy regular languages over finite and infinite words we consider finite automata over semirings and quemirings accepting finite and infinite words respectively we obtain kleene theorems for fuzzy languages consisting of finite and infinite words furthermore we introduce regular fuzzy grammars and linear fuzzy systems and we show that both of them specify the class of recognizable fuzzy languages consisting of finite and infinite words

determinization of fuzzy automata via factorization of fuzzy states fuzzy finite state automata over the algebra 0 1 max 0 1 in which the monoid 0 1 1 denotes a continuous triangular norm is not locally finite can accept fuzzy languages of infinite range for a given fuzzy finite state automaton which accepts a fuzzy language of infinite range we define the determinization of the fuzzy automaton via factorization of fuzzy states i e the computation of an equivalent deterministic fuzzy automaton whether it is finite this method of determinization is a generalization of the well known accessible subset construction our main contribution is to determine that the representable cycles property is the necessary and sufficient condition for determinization of a fuzzy finite state automaton via a maximal factorization of fuzzy states this property is more general than the twins property adapted for fuzzy automata which is the sufficient condition for weighted automata over the tropical semiring

fuzzy context free languages part 1 generalized fuzzy context free grammars motivated by aspects of robustness in parsing a context free language we study generalized fuzzy context free grammars these fuzzy context free k grammars provide a general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism they model the situation of making a finite choice out of an infinity of possible grammatical errors during each context free derivation step formally a fuzzy context free k grammar is a fuzzy context free grammar with a countable rather than a finite number of rules satisfying the following condition for each symbol the set containing all right hand sides of rules with left hand side equal to forms a fuzzy language that belongs to a given family k of fuzzy languages we investigate the generating power of fuzzy context free k grammars and we show that under minor assumptions on the parameter k the family of languages generated by fuzzy context free k grammars possesses closure properties very similar to those of the family of ordinary context free languages

a formal power series approach to the construction of minimal fuzzy automata abstract a new approach to the problem of construction of minimal fuzzy automata using formal power series representation is presented the proceduie involves automated inference of regular fuzzy grammar from a set of sample strings the technique yields a minimal fuzzy automaton that recognizes the positive samples of the language the desired automata are inferred from a finite submatrix of the fuzzy hankel matrix of the coefficients of formal power series representing the set of strings of the given language an application in pattern recognition is shown for the inference of fuzzy grammar

power calculations for general linear multivariate models including repeated measures applications abstract recently developed methods for power analysis expand the options available for study design we demonstrate how easily the methods can be applied by 1 reviewing their formulation and 2 describing their application in the preparation of a particular grant proposal the focus is a complex but ubiquitous setting repeated measures in a longitudinal study describing the development of the research proposal allows demonstrating the steps needed to conduct an effective power analysis discussion of the example also highlights issues that typically must be considered in designing a study first we discuss the motivation for using detailed power calculations focusing on multivariate methods in particular second we survey available methods for the general linear multivariate model glmm with gaussian errors and recommend those based on f approximations the treatment includes coverage of the multivariate and univariate approaches to repeated measures manova anova multivariate regression and

fuzzy languages with infinite range accepted by fuzzy automata pumping lemma and determinization procedure abstract the formulation of fuzzy automata allows us to select a great variety of triangular norms depending on the selected triangular norm a fuzzy automaton can accept a fuzzy language fa language with infinite range these fuzzy automata are not equivalent to the so called deterministic fuzzy automata deterministic automata with a fuzzy subset of final states which only accept fuzzy languages with finite range in this paper we study fa languages with infinite range and a determinization procedure in order to obtain an equivalent fuzzy deterministic automaton for a given fuzzy automaton a fuzzy deterministic automaton is a fuzzy automaton which satisfies the deterministic condition in its state transition function the main contributions of our paper are 1 a pumping lemma of fa languages with infinite range 2 the formulation of fuzzy deterministic automata and a pumping lemma of fda languages 3 the necessary conditions for the determinization of fuzzy automata under continuous triangular norms which accept fuzzy languages of infinite range and 4 a determinization algorithm for fuzzy automata its correctness proof and performance

characterizations of complete residuated lattice valued finite tree automata this paper deals with the concept of complete residuated lattice valued referred to as l valued finite tree automata in this regard we first define an l valued regular tree language and then we prove a necessary and sufficient condition for the regularity of an l valued tree language furthermore we generalize the pumping lemma for l valued finite tree automata l fta afterwards the behavior of l fta is addressed and some theorems are provided moreover the existence of the minimal form of an l fta is considered finally a minimization algorithm of the l fta is presented and its time complexity is analyzed

canonization of max min fuzzy automata abstract in this paper we propose a canonization method for fuzzy automata i e a determinization method that is able to return a minimal fuzzy deterministic automaton equivalent to the original fuzzy automaton the canonization method is derived from the well known brzozowski s algorithm for ordinary nondeterministic automata for a given fuzzy automaton a we prove that the construction m r n r a returns a minimal fuzzy deterministic automaton equivalent to a in that construction r represents the reversal of a fuzzy automaton n is the determinization of a fuzzy automaton based on fuzzy accessible subset construction and m is the determinization of a fuzzy automaton via factorization of fuzzy states which also includes a simple reduction of a particular case of proportional fuzzy states the method is accomplished for fuzzy automata with membership values over the godel structure also called max min fuzzy automata these fuzzy automata are always determinizable and have been proved useful in practical applications

approximation of fuzzy context free grammars fuzzy context free max grammar or fcfg for short as a straightforward extension of context free grammar has been introduced to express uncertainty imprecision and vagueness in natural language fragments li recently proposed the approximation of fuzzy finite automata which may effectively deal with the practical problems of fuzziness impreciseness and vagueness in this paper we further develop the approximation of fuzzy context free grammars in particular we show that a fuzzy context free grammar under max compositional inference can be approximated by some fuzzy context free grammar under max min compositional inference with any given accuracy in addition some related properties of fuzzy context free grammars and fuzzy languages generated by them are studied finally the sensitivity of fuzzy context free grammars is also discussed

stochastic random walk summability on etudie les proprietes limites des sommes partielles ponderees lorsque les poids sont donnes par une procedure de sommation en marche aleatoire

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

a note on cut worthiness of recognizable tree series the topic of this short note is tree series over semirings with partially ordered carrier set thus tree series become poset valued fuzzy sets starting with a collection of recognizable tree languages we construct a tree series recognizable over any semiring such that the carrier set is a poset generated by the collection in the framework of fuzzy structures the starting collection becomes a subset of the collection of the corresponding cut sets under some stricter conditions it is even equal to this collection we also partially solve an open problem which was posed in borchardt et al cut sets as recognizable tree languages fuzzy sets and systems 157 2006 1560 1571 namely we show that if f is a given tree series over a partially ordered locally finite semiring a then f is recognizable if and only if there are finitely many cut sets of f and every cut set is a recognizable tree language

a tableau like proof procedure for normal modal logics abstract in this paper a new proof procedure for some propositional and first order normal modal logics is given it combines a tableau like approach and a resolution like inference completeness and decidability for some propositional logics are proved an extension for the first order case is presented

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

algebras of fuzzy sets in this paper we investigate two kinds of algebras of fuzzy sets which are obtained by using zadeh s extension principle we give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets we prove that if the structure of truth values is a complete residuated lattice the induced algebra of a subalgebra of an algebra a can be embedded into the induced algebra of fuzzy sets of a for direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product in the case of homomorphisms and direct products the two kinds of algebras of fuzzy sets behave in different ways

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

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

adjusting power for a baseline covariate in linear models the analysis of covariance provides a common approach to adjusting for a baseline covariate in medical research with gaussian errors adding random covariates does not change either the theory or the computations of general linear model data analysis however adding random covariates does change the theory and computation of power analysis many data analysts fail to fully account for this complication in planning a study we present our results in five parts i a review of published results helps document the importance of the problem and the limitations of available methods ii a taxonomy for general linear multivariate models and hypotheses allows identifying a particular problem iii we describe how random covariates introduce the need to consider quantiles and conditional values of power iv we provide new exact and approximate methods for power analysis of a range of multivariate models with a gaussian baseline covariate for both small and large samples the new results apply to the hotelling lawley test and the four tests in the univariate approach to repeated measures unadjusted huynh feldt geisser greenhouse box the techniques allow rapid calculation and an interactive graphical approach to sample size choice v calculating power for a clinical trial of a treatment for increasing bone density illustrates the new methods we particularly recommend using quantile power with a new satterthwaite style approximation

on closure properties of l valued linear languages abstract in 2001 and 2002 daowen qiu has established a new theory of l valued automata which is based on complete residuated lattices moreover besides the finite automata several other classes of machines grammars and languages have been generalized using the ideas introduced by qiu this paper generalizes the concept of linear grammars and linear languages in this context moreover it presents some operations for l valued languages and some closure properties for the l valued linear languages

fuzzy tree language recognizability a fuzzy tree language with membership grades in an arbitrary set is syntactically recognizable s recognizable if its syntactic algebra is finite the equality problem for such languages is decidable and their syntactic algebra can be effectively constructed provided that they are s recognizable linear but non arbitrary tree homomorphisms preserve s recognizability tree automata whose transitions are weighted over the unit interval and whose behavior is computed with respect to a pair made of a t norm distributive over a t conorm have the syntactic recognition power and thus their equivalence problem is decidable however s recognizability is more powerful when dealing with non distributive pairs of such operations

algebraic aspects of families of fuzzy languages we study operations on fuzzy languages such as union concatenation kleene intersection with regular fuzzy languages and several kinds of iterated fuzzy substitution then we consider families of fuzzy languages closed under a fixed collection of these operations which results in the concept of full abstract family of fuzzy languages or full affl this algebraic structure is the fuzzy counterpart of the notion of full abstract family of languages that has been encountered frequently in investigating families of crisp i e non fuzzy languages some simpler and more complicated algebraic structures such as full substitution closed affl full super affl full hyper affl will be considered as well in the second part of the paper we focus our attention to full affls closed under iterated parallel fuzzy substitution where the iterating process is prescribed by given crisp control languages proceeding inductively over the family of these control languages yields an infinite sequence of full affl structures with increasingly stronger closure properties

infinite fuzzy computations we consider buchi automata weighted over the fuzzy semiring f 0 1 max min 0 1 a buchi theorem for the class of w recognizable series with coefficients in f i e for behaviors of buchi automata over f is established furthermore we show that an infinitary language is buchi recognizable iff its characteristic series is w recognizable

model checking of linear time properties in multi valued systems abstract in this paper we study the model checking problem of linear time properties in multi valued systems safety properties invariant properties liveness properties persistence and dual persistence properties in multi valued logic systems are introduced some algorithms related to the above multi valued linear time properties are discussed the verification of multi valued regular safety properties and multi valued regular properties using lattice valued automata are thoroughly studied since the law of non contradiction i e a a 0 and the law of excluded middle i e a a 1 do not hold in multi valued logic the linear time properties introduced in this paper have new forms compared to those in classical logic compared to those classical model checking methods our methods to multi valued model checking are accordingly more direct we give an algorithm for showing ts p for a model ts and a linear time property p which proceeds by directly checking the inclusion traces ts p instead of t r a c e s t s p a new form of multi valued model checking with membership degree is also introduced in particular we show that multi valued model checking can be reduced to classical model checking the related verification algorithms are also presented some illustrative examples and a case study are also provided

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

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

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

a unified approach to power calculation and sample size determination for random regression models the underlying statistical models for multiple regression analysis are typically attributed to two types of modeling fixed and random the procedures for calculating power and sample size under the fixed regression models are well known however the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution this paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables numerical examples are provided to illustrate the usefulness of the proposed method and monte carlo simulation studies are also conducted to assess the accuracy the results show that the proposed method performs well for various model specifications and explanatory variable distributions

fuzzy tree automata in this paper we map an arbitrary algebra to a completely distributive lattice and define algebras of fuzzy sets when the algebra is a term algebra we obtain fuzzy tree languages after defining fuzzy equational sets fuzzy rational sets and fuzzy recognizable tree languages we derive a kleene theorem for fuzzy tree languages

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

finite automata theory with membership values in lattices in this paper we study finite automata with membership values in a lattice which are called lattice valued finite automata the extended subset construction of lattice valued finite automata is introduced then the equivalences between lattice valued finite automata lattice valued deterministic finite automata and lattice valued finite automata with e moves are proved a simple characterization of lattice valued languages recognized by lattice valued finite automata is given then it is proved that the kleene theorem holds in the frame of lattice setting a minimization algorithm of lattice valued deterministic finite automata is presented in particular the role of the distributive law for the truth valued domain of finite automata is analyzed the distributive law is not necessary to many constructions of lattice valued finite automata but it indeed provides some convenience in simply processing lattice valued finite automata

on the recognizability of fuzzy languages ii it is shown that a fuzzy language is recognized by a finite monoid iff it has finitely many right derivatives iff it has finitely many left derivatives finally we show that the behaviors of lukasiewicz automata have the above properties

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

fuzzy ω automata abstract in this paper we introduce the notion of fuzzy automata as an accepting device for fuzzy languages we define fuzzy finite state automata which accept fuzzy regular languages with different acceptance criteria we also define distributed fuzzy finite state automata which are a group of fuzzy finite state automata working in unison to accept a language with different modes of acceptance like the t mode mode k mode k mode and k mode we prove that distributed fuzzy finite state automata accept the same set of languages as fuzzy finite state automata analogously we define fuzzy pushdown automata and distributed fuzzy pushdown automata along with the different acceptance criteria and modes of acceptance for the distributed case the class of languages accepted by fuzzy pushdown automata is fuzzy cfl while the class of languages accepted by distributed fuzzy pushdown automata contains cfl we give proofs to show that all modes of acceptance are equal in the case of distributed fuzzy pushdown automata we also define l fuzzy automata and give some examples to show how it can be used to accept some non fuzzy languages which are not accepted by their classical counterparts

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

recognizable formal power series on trees trees are a very basic object in computer science they intervene in nearly a ly domain and they are studied for their own or used to represent conveniently a given situation there are at least three directions where investigations on trees themselves are motivated and this for different reasons first the notion of tree is the basis of algebraic semantics nivat 19 rosen 2 2 etc in this context the study of special languages of trees i e forests their classification and their behaviour under various types of transformations are of great importance arnold fl dauchet 8 j l ilin 1161 mongy 18 by essence work in this area is an extension of the algebraic theory of languages trees and ianguages are in fact directly related via the derivation trees of an algebraic grammar thatcher 25 a second topic heavily related to trees concerns dzra structures trees mainly binary trees and its variants constitute one of the most widely known data structures see e g hlnuth 15 the analysis of the worst cale expected or average running time t ehzvgrr nfi certain algorithms requires sometimes long and delicate computations flajolet lo kemp 14 flajolet and steyaert 12 finally trees occupy a distinguished place in the enumeration of graphs and maps both because of the simplicity of their structure and for the relationship between their el lcodings and aigebraic languages the nature of the enumerating series and especially the question whether they are algebraic or not is one of the central problems in this domain cori 7 chottin 4 we propose here a theory of formal power series on trees and present some of their basic properties together with various examples of applications which as we hope will show the interest of its development within the framework we just sketched a formal power series on trees is a function which gssociates a number to esch tree thus we could also have called them tree functions ii in analogy with the term word function used by several authors paz and salomaa zo cobham 5 as an equivalent denomination for formal power series on words the main goal of a formal power series is to count or to represent the result of some computation on

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

quantitative model checking of linear time properties based on generalized possibility measures abstract model checking of linear time properties based on possibility measures was studied in previous work li and li 2013 however the linear time properties considered in the previous work was qualitative and was based on boolean logic the linear time properties containing possibility information we call it fuzzy linear time properties here which is based on fuzzy logic of system could not be represented and tackled using the previous methods we shall study quantitative model checking of fuzzy linear time properties based on generalized possibility measures in the paper both the model of the system as well as the properties the system needs to adhere to are described using possibility information to identify the uncertainty in the model properties the systems are modeled by generalized possibilistic kripke structures gpks in short and the properties are described by fuzzy linear time properties concretely fuzzy linear time properties about reachability always reachability constrain reachability repeated reachability and persistence in gpkss are introduced and studied fuzzy regular safety properties and fuzzy regular properties in gpkss are introduced the verification of fuzzy regular safety properties and fuzzy regular properties using fuzzy finite automata are thoroughly studied it has been shown that the verification of fuzzy regular safety properties and fuzzy regular properties in a finite gpks can be transformed into the verification of always reachability properties and repeated reachability persistence properties in the product gpks introduced in this paper several examples are given to illustrate the methods presented in the paper

power and sample size calculations for multivariate linear models with random explanatory variables this article considers the problem of power and sample size calculations for normal outcomes within the framework of multivariate linear models the emphasis is placed on the practical situation that not only the values of response variables for each subject are just available after the observations are made but also the levels of explanatory variables cannot be predetermined before data collection using analytic justification it is shown that the proposed methods extend the existing approaches to accommodate the extra variability and arbitrary configurations of the explanatory variables the major modification involves the noncentrality parameters associated with the f approximations to the transformations of wilks likelihood ratio pillai trace and hotelling lawley trace statistics a treatment of multivariate analysis of covariance models is employed to demonstrate the distinct features of the proposed extension monte carlo simulation studies are conducted to assess the accuracy using a child s intellectual development model the results update and expand upon current work in the literature

principal abstract families of weighted tree languages abstract we introduce semiring weighted regular tree grammars with storage where the semiring is complete we show that the class of weighted tree languages generated by them is a principal abstract family of weighted tree languages provided that the semiring is commutative the rank of symbols occurring in trees is bounded by a global parameter and that the storage is finitely encoded and contains a reset instruction moreover we prove the same statement for the iterated pushdown instead of finitely encoded storage containing a reset instruction