realization of input output maps using generalized orthonormal basis functions abstract this paper studies the input output equivalent transformation or hambo transform of linear time invariant systems induced by generalized orthonormal basis functions transformation formulae of the system matrices are derived using the fact that the lifted system associated with the inner function which defines a generalized orthonormal basis is an abstract form of the hambo transform the new formulae are supplements to the results in the literature and they are equally applicable to continuous time and discrete time systems and mimo and siso systems

fuzzy filters of mtl algebras characterizations of fuzzy filters in mtl algebras are given the fuzzy filter generated by a fuzzy set is considered the notion of boolean fuzzy filters and mv fuzzy filters are introduced and related properties are investigated a condition for a fuzzy filter to be boolean is provided a characterization of a boolean fuzzy filter is given a congruence relation on a mtl algebra induced by a fuzzy filter is established and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice

fuzzy filters of bl algebras the aim of this paper is to introduce the notions of fuzzy filters fuzzy prime filters and the cosets of a fuzzy filter in bl algebras and investigate some of their properties the fuzzy filter generated by a fuzzy set is discussed some characterizations of fuzzy filters and fuzzy prime filters are derived the extension theorem of fuzzy prime filters and the fuzzy prime filters theorem are established finally we prove that the algebra l f which is the set of all cosets of f is a bl algebra and is isomorphic to the bl algebra l ff 1 where ff 1 x l f x f 1 moreover each bl algebra l is a subdirect product of linearly ordered bl algebras l fi i where fi i are fuzzy prime filters of l

brief paper stochastic system transformation using generalized orthonormal basis functions with applications to continuous time system identification this paper studies the system transformation using generalized orthonormal basis functions that include the laguerre basis as a special case the transformation of the deterministic systems is studied in the literature which is called the hambo transform the aim of the paper is to develop a transformation theory for stochastic systems the paper establishes the equivalence of continuous and transformed discrete time stochastic systems in terms of solutions the method is applied to the continuous time system identification problem it is shown that using the transformed signals the po moesp subspace identification algorithm yields consistent estimates for system matrices an example is included to illustrate the efficacy of the proposed identification method and to make a comparison with the method using the laguerre filter

fuzzy boolean and positive implicative filters of bl algebras the aim of this paper is to introduce the notions of fuzzy boolean filters and fuzzy positive implicative filters in bl algebras and to investigate their properties several characterizations of fuzzy boolean filters and fuzzy positive implicative filters are derived the extension theorems of fuzzy boolean filters and fuzzy positive implicative filters are obtained the relation between fuzzy boolean filters and fuzzy positive implicative filters is investigated and it is proved that every fuzzy boolean filter is a fuzzy positive implicative filter but the converse may not be true furthermore the conditions under which a fuzzy positive implicative filter is a fuzzy boolean filter are established

triple i method of fuzzy reasoning abstract the theory of the triple i method with total inference rules of fuzzy reasoning is investigated by using zadeh s implication operator rz the computational formulae for both fuzzy modus ponens fmp and fuzzy modus tollens fmt are obtained the reversibility properties for fmp and fmt are analyzed and the reversibility criteria are given we also investigated the generalized problem of the triple i method and obtained the formulae for the triple i fmp and the triple i fmt

boolean products of bl algebras the representation of algebras by boolean products is a very general problem in universal algebra in this paper we shall characterize the boolean products of bl chains the weak boolean products of local bl algebras and the weak boolean products of perfect bl algebras

some weaker versions of topological residuated lattices abstract the aim of this paper is to investigate some weaker versions of topological residuated lattices which are para topological residuated lattices continuous para topological residuated lattices continuous para topological residuated lattices continuous and para topological residuated lattices continuous respectively this paper mainly focuses on the latter two para topological residuated lattices we prove the independence of these para topological residuated lattices by using their algebraic properties moreover we establish the correspondence between algebraic properties and topologies in a residuated lattice l i e there is an injective mapping from m e q l i e q l a e q l c o n l resp to m t r l l i t r l l a t r l l t r l l resp finally some interactions between the topologies and algebraic properties in para semi topological residuated lattices are studied

decision problems under risk and chance constrained programming dilemmas in the transition some important conceptual problems concerning the application of chance constrained programming ccp to risky practical decision problems are discussed by comparing ccp to stochastic programming with recourse spr we expand on garstka s distinction between mathematical equivalence and economic equivalence showing that much of practical usefulness is lost in the transition between spr and ccp by examining the literature on ccp applications we conclude that there is little evidence that ccp is used with the care that is necessary finally we conclude that ccp is seriously deficient as a modeling technique and of limited value as a computational device

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

note blau s dilemma revisited the issue of equivalence between chance constrained programming problems ccpp s and bayesian utility maximization problems bump s and the anomalous evaluation of information in ccpp s are re examined in light of a recent paper by jagannathan and the ensuing exchange between jagannathan and lavalle difficulties in explaining value of information within the framework of chance constrained programming are illustrated in a numerical example due to jagannathan

on the logic foundation of fuzzy reasoning abstract fuzzy reasoning and fuzzy formal deduction theory are two closely related subjects and each of them has been investigated by many researchers unfortunately it seems that the two branches have not been successfully connected the aim of this paper is to establish a so called quasi propositional deductive system syntactically as well as semantically and then set a logic foundation for developing the theory of fuzzy reasoning therefrom

system identification using kautz models in this paper the problem of approximating a linear time invariant stable system by a finite weighted sum of given exponentials is considered system identification schemes using laguerre models are extended and generalized to kautz models which correspond to representations using several different possible complex exponentials in particular linear regression methods to estimate this sort of model from measured data are analyzed the advantages of the proposed approach are the simplicity of the resulting identification scheme and the capability of modeling resonant systems using few parameters the subsequent analysis is based on the result that the corresponding linear regression normal equations have a block toeplitz structure several results on transfer function estimation are extended to discrete kautz models for example asymptotic frequency domain variance expressions

rough approximation operators on r0 algebras nilpotent minimum algebras with an application in formal logic l an abstract axiomatization to pawlak rough set theory in the context of r0 algebras equivalently nm algebras has been proposed in the present paper more precisely by employing the conjunction operator and the disjunction operator in r0 algebras the notions of rough upper approximation operator u and rough lower approximation operator l on r0 algebras are proposed respectively owing to the logical properties of and any r0 algebra equipped with l and u forms an abstract approximation space in the sense of g cattaneo a duality relationship between the set of lower crisp elements and the set of upper crisp elements is established and some important properties are examined moreover its connection with tarski closure interior approximation space and halmos closure interior approximation is studied such a pair of rough approximations on r0 algebras can naturally induce a pair of rough upper lower truth degrees for formulae in l some uncertainty measures such as roughness degree and accuracy degree are subsequently presented and two kinds of approximate reasoning methods merging rough approximation and fuzzy logic are eventually established

a generalized orthonormal basis for linear dynamical systems in many areas of signal system and control theory orthogonal functions play an important role in issues of analysis and design in this paper it is shown that there exist orthogonal functions that in a natural way are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l sub 2sup n to this end use is made of balanced realizations of inner transfer functions the orthogonal functions can be considered as generalizations of for example the pulse functions laguerre functions and kautz functions and give rise to an alternative series expansion of rational transfer functions it is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion i e to obtain a good approximation by retaining only a finite number of expansion coefficients consequences for identification of expansion coefficients are analyzed and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

unified forms of fully implicational restriction methods for fuzzy reasoning the goal of this paper is to extend the scope of previously proposed fully implicational restriction methods for fuzzy reasoning and provide a unified form of these methods which can employ diverse implications by means of the residual implications generated by left continuous t norms we obtain the supremum of triple i the abbreviation of triple implications restriction solutions for fuzzy modus ponens and the supremum of multiple i restriction solutions for general fuzzy reasoning respectively furthermore we obtain the infimum of triple i restriction solutions and the supremum of triple i restriction solutions for fuzzy modus tolens finally the optimal i e the largest or smallest depending on context restriction solutions of both basic and general reasoning problems are derived for four specific residual implications

fuzzy set representations of some quantum structures abstract quantum structures are algebraic structures like quantum logics orthomodular posets and lattices orthoalgebras effect algebras d posets which model event structures of quantum mechanics the elements of orthomodular posets can be represented by question observables having their spectrum in 0 1 so they are considered as two valued physical quantities we show that if such a structure possesses an order determining system of states probability measures it can be represented by a system of fuzzy sets and conversely

a function space approach to sampled data control systems and tracking problems this paper presents a new framework for hybrid sampled data control systems instead of considering the state only at sampling instants this paper introduces a function piece during the sampling period as the state and gives an infinite dimensional model with such a state space this gives the advantage that sampled data systems with built in intersample behavior can be regarded as linear time invariant discrete time systems as a result the approach makes it possible to introduce such time invariant concepts as transfer functions poles and zeros to the sampled data systems even with the presence of the intersample behavior in particular tracking problems can be studied in this setting in a simple and unified way and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions this leads to the internal model principle for sampled data systems

three and two valued łukasiewicz theories in the formal deductive system l nm logic in order to offer a logic foundation for fuzzy reasoning and to reduce the gap between fuzzy reasoning and artificial intelligence a new formal deductive system l was introduced in 1996 it was proved that the prominent nilpotent minimum logic is a logic system equivalent to l as is well known in classical propositional logic there is a one to one correspondence between deductively closed theories and topologically closed subsets of the stone space of all maximally consistent theories recently by means of the strong completeness of l we obtained the structural and topological characterizations of maximally consistent theories in this logic it was proved that the set of all maximally consistent theories over l with an induced topology is a cantor space in order to establish a similar connection between theories over l and closed subsets of this topological space to the classical case we introduce in this paper the notion of three valued lukasiewicz theory and the notion of two valued lukasiewicz boolean theory we prove that there is also a one to one correspondence between deductively closed three valued lukasiewicz theories and closed subsets of the space and boolean theories correspond to the closed subsets of the subspace of all maximally consistent boolean theories lastly we give an alternative proof for the structural characterization of the maximality of consistent theories over l by induction on the complexity of formulas which is independent of the strong completeness of l and also independent of the perfectness of the standard r 0 algebra

simplification and independence of axioms of fuzzy logic systems imtl and nm monoidal t norm based logic mtl is the common formalization of all fuzzy logic of left continuous t norms and their residua this system has two important schematic extensions involutive monoidal t norm based logic imtl and nilpotent minimum logic nm in this paper we discuss simplification and independence of axioms of imtl and nm the shorter axioms of both logics and an independent axioms of the system imtl are given

characterizations of maximal consistent theories in the formal deductive system l nm logic and cantor space a maximal consistent theory is a maximal theory with respect to its consistency the present paper is divided into two parts the first one is devoted to characterize the maximality of a consistent theory in the formal deductive system l which is a logic system equivalent to the nilpotent minimum logic it is proved that each maximal consistent theory in this logic must be the deductive closure of a collection of simple compound formulas hence it follows that there is a one to one correspondence between the set of all maximal consistent theories and the set of evaluations e assigning to each propositional variable p its truth degree e p 0 12 1 the satisfiability theorem and compactness theorem of l are obtained the second part is to investigate the topological structure of the set of all maximal consistent theories over l and the results show that this topological space is a cantor space

approximation of stable systems by laguerre filters laguerre methods are used to develop concrete techniques and results for approximating stable infinite dimensional systems both hankel norm and l approximation by laguerre filters are studied the infimum of the hankel norm approximation error when the system is approximated by laguerre filters of given maximum order is given by the norm of a certain shifted hankel operator and the best laguerre filter to approximate the system is obtained essentially from the associated eigenproblem for the shifted hankel operator hankel optimal laguerre filters are here called cf laguerre filters as there is a certain connection to the caratheodory fejer interpolation problem and typically provide near best solutions to related l approximation problems a time domain compressed laguerre shift method for solving certain nehari problems for delay systems is used to determine analytically the achievable hankel error norms and thus also to obtain bounds for the achievable l error norm for delay systems a result on a laguerre filter approximation problem in the hilbert schmidt norm is given as well

laguerre series approximation of infinite dimensional systems laguerre fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems specifically time domain supremum and l1 norm convergence results and frequency domain h norm convergence results are given for laguerre fourier approximations it is also shown that the theory of laguerre polynomials solves explicitly the problem of determining laguerre fourier approximations for a large class of delay systems furthermore it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems

note response to use of sample information in stochastic recourse and chance constrained programming models on the bayesability of ccp s jagannathan s jagannathan r 1985 use of sample information in stochastic recourse and chance constrained programming models management sci 31 96 108 invocation of a utility function for a chance constrained programming problem ccpp produces a bayesian utility maximation problem bump which is not equivalent to the given ccpp therefore the nonanomalous behavior shown to characterize information value in the bump does not refute examples such as blau s blau r a 1974 stochastic programming and decision analysis an apparent dilemma management sci 21 271 276

formalized theory of general fuzzy reasoning first a rigorous mathematical theory for calculating the conclusion of general fuzzy reasoning is proposed second a formalized non fuzzy version of the theory of general fuzzy reasoning is founded in classical logics

the search for information a patient perspective on multiple opinions abstract this paper describes the first dynamic formulation of the optimal strategy from a patient perspective for the search for additional information in the form of multiple opinions the mehrez and gafni framework for choosing an optimal treatment from a patient perspective is employed to study the optimal search strategy for a representative individual who is an expected utility maximizer two different processes for gathering information regarding the probability of treatment success p are studied in the first physicians provide information in a yes or no treatment type of recommendation in the second physicians provide probabilistic information about the likelihood of success in the treatment for the first system the optimal strategy is derived using an algorithm of an order o n n is the number of opinions to be purchased from expert doctors for a prior beta probability density function of p and a bernoulli process of information gathering evsi expected value of sample information measures are incorporated into the bayesian analysis to study this case and to obtain an upper bound on n the optimal number of opinions to be purchased the approach developed here is different than the well known one provided by raiffa and schlaifer in 1961 and it enables us to present additional results regarding the optimal search strategy and how to identify it for example if i the process of information gathering is generated by a bernoulli process ii the natural conjurate prior distribution is beta and iii the utility functions are linear functions of the probability of treatment success then for each n there exists at most one value of x the number of experts recommending treatment for which a search should continue at this value the incremental increase of the individual s lifetime expected utility stemming from the decision to seek additional expert s opinion is positive this observation might explain a reality where the likelihood of seeking a large number of opinions is very low furthermore sufficient conditions for not initiating the information search process and on the range of n are provided in addition an analysis of the second process is provided and properties of the optimal strategy are studied it is shown that the formulations of the two processes are equivalent and that they can be further analyzed through the two action space project selection problem studied by mehrez and stulman and others a numerical comparison and a sensitivity analysis between the two processes for gathering information is presented it is illustrated that for similar cost figures the probability estimation procedure provides more information than the yes no type recommendation to the patient

generalized bosbach and riecan states based on relative negations in residuated lattices bosbach and riecan states on residuated lattices both are generalizations of probability measures on boolean algebras recently two types of generalized bosbach states on residuated lattices were introduced by georgescu and muresan through replacing the standard mv algebra in the original definition with arbitrary residuated lattices as codomains however several interesting problems there remain still open the first part of the present paper gives positive answers to these open problems it is proved that every generalized bosbach state of type ii is of type i and the similarity cauchy completion of a residuated lattice endowed with an order preserving generalized bosbach state of type i is unique up to homomorphisms preserving similarities where the codomain of the type i state is assumed to be cauchy complete consequently many existing results about generalized bosbach states can be further strengthened the second part of the paper introduces the notion of relative negation with respect to a given element called relative element in residuated lattices and then many issues with the canonical negation such as glivenko property semi divisibility generalized riecan state of residuated lattices can be extended to the context of such relative negations in particular several necessary and sufficient conditions for the set of all relatively regular elements of a residuated lattice to be special residuated lattices are given of which one extends the well known glivenko theorem and it is also proved that relatively generalized riecan states vanishing at the relative element are uniquely determined by their restrictions on the mv algebra consisting of all relatively regular elements when the domain of the states is relatively semi divisible and the codomain is involutive

use of sample information in stochastic recourse and chance constrained programming models in probabilistic linear programming models the decision maker is typically assumed to know the probability distribution of the random parameters here it is assumed that the distribution functions of the parameters have a specified functional form f t where is an unknown real vector parameter we suppose that the decision maker has the opportunity of observing a random sample drawn from f t for a two stage stochastic programming with recourse model the deterministic equivalent model is found using a bayesian approach properties are presented for the deterministic equivalents in general and in the special case of the simple recourse model expressions for expected value of sample information evsi and expected net gain from sampling engs are also derived in the final section similar results are obtained for chance constrained programming models

brief paper a new expression for the h2 performance limit based on state space representation this paper aims to clarify the performance limit via state space representation in order to handle multiple input multiple output systems in a transparent way to this end by applying some results on infinite dimensional control theory a closed formula for the h 2 performance limit is derived for systems with a special structure described in terms of a rational transfer matrix and a scalar inner function this formulation is capable of dealing with various control problems including h 2 control of a class of infinite dimensional systems the resulting formula given as a functional of the inner function helps us to understand how achievable h 2 performance deteriorates due to non minimum phase properties or unstable modes of plants

minimal partial realization from generalized orthonormal basis function expansions a solution is presented for the problem of realizing a discrete time lti state space model of minimal mcmillan degree such that its first n expansion coefficients in terms of generalized orthonormal basis match a given sequence the basis considered also known as the hambo basis can be viewed as a generalization of the more familiar laguerre and two parameter kautz constructions allowing general dynamic information to be incorporated in the basis for the solution of the problem use is made of the properties of the hambo operator transform theory that underlies the basis function expansion as corollary results compact expressions are found by which the hambo transform and its inverse can be computed efficiently the resulting realization algorithms can be applied in an approximative sense for instance for computing a low order model from a large basis function expansion that is obtained in an identification experiment

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

system identification using laguerre models the traditional approach of expanding transfer functions and noise models in the delay operator to obtain linear in the parameters predictor models leads to approximations of very high order in cases of rapid sampling and or dispersion in time constants by using prior information about the time constants of the system more appropriate expansions related to laguerre networks are introduced and analyzed it is shown that the model order can be reduced compared to arx fir ar modeling by using laguerre models furthermore the numerical accuracy of the corresponding linear regression estimation problem is improved by a suitable choice of the laguerre parameter consistency error bounds persistence of excitation conditions and asymptotic statistical properties are investigated this analysis is based on the result that the covariance matrix of the regression vector of a laguerre model has a toeplitz structure

nuclei and conuclei on residuated lattices in this paper we investigate some properties of nuclei and conuclei on residuated lattices and their concrete structures by means of nuclei and conuclei we give the respective characterizations for a residuated lattice reducing to a generalized mv algebra and a generalized bl algebra based on studying regular commutative bounded integral residuated lattices we introduce the concept of a pseudo dual quantale and investigate some properties of it and prove that the set of fuzzy sets of a nonempty set equipped with multiplication and negation operations is a commutative girard quantale finally we discuss the relationship between quantic nuclei and quantic conuclei on a pseudo dual quantale and show that the quantic nuclei and the ideal conuclei on a pseudo girard quantale are in one to one correspondence

l fuzzy version of stone s representation theorem for distributive lattices abstract in this paper the category of l fuzzy locales is introduced which is proved to play the same role with respect to stratified l fuzzy topological spaces as the locales play for topological spaces secondly stone s representation theorem for distributive lattices is generalized to the l fuzzy case and the notion of l fuzzy spectrum of distributive lattices is introduced and its properties are systematically studied moreover the harmony between the localic version of stone s representation theorem and spectral spaces of distributive lattices is also valid in the l fuzzy case

orthonormal basis functions in time and frequency domain hambo transform theory the class of finite impulse response fir laguerre and kautz functions can be generalized to a family of rational orthonormal basis functions for the hardy space h2 of stable linear dynamical systems these basis functions are useful for constructing efficient parameterizations and coding of linear systems and signals as required in e g system identification system approximation and adaptive filtering in this paper the basis functions are derived from a transfer function perspective as well as in a state space setting it is shown how this approach leads to alternative series expansions of systems and signals in time and frequency domain the generalized basis functions induce signal and system transforms hambo transforms which have proved to be useful analysis tools in various modelling problems these transforms are analyzed in detail in this paper and a large number of their properties are derived principally it is shown how minimal state space realizations of the system transform can be obtained from minimal state space realizations of the original system and vice versa

on equivalent forms of fuzzy logic systems nm and imtl the nilpotent minima are important t norms in fuzzy logic and fuzzy reasoning two interesting formal systems nilpotent minimum logic nm and l based on nilpotent minima have been proposed and have been intensively studied in this paper their equivalence is pointed out moreover coincidence of two related algebraic structures nm and r0 algebras is also proved in addition we give an equivalent form of involutive monoidal t norm based logic imtl

a triangular norm based propositional fuzzy logic in 1997 wang introduced the formal system l for a type of fuzzy propositional calculus given by a particular t norm different from the three famous ones lukasiewicz godel product recently pei proved the completeness theorem for l with respect to w semantic by developing a theory of algebraic systems in this paper we aim to prove it by essentially metamathematical method furthermore we discussed originally the completeness for the schematic extension l n of l with respect to w n semantic

fuzzy implicative and boolean filters of r 0 algebras the notions of fuzzy filters fuzzy implicative filters and fuzzy boolean filters are introduced in r0 algebras respectively some of their properties are investigated the relations between fuzzy implicative filters and fuzzy boolean filters are discussed the characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent 1 a fuzzy filter f is implicative 2 f is a fuzzy boolean filter 3 x y z l f x z f x z y f y z 4 x y l f x y f x y y 5 x l n 1 f nx f x

undefinability of min conjunction in mtl firstly a sufficient and necessary condition is given to decide whether the lattice operations of a wnm chain can be definable from its other operations secondly we show that it is indeed necessary to introduce the min conjunction into mtl as a primitive connective by constructing a left continuous t norm such that in the propositional calculus defined by this t norm the min conjunction and max disjunction are not definable from the strong conjunction implication and truth constant email protected

fuzzy positive implicative and fuzzy associative filters of lattice implication algebras we fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras we prove that i every fuzzy positive implicative filter is a fuzzy implicative filter and ii every fuzzy associative filter is a fuzzy filter we provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter

characterizations and new subclasses of i filters in residuated lattices abstract filters play an important role in studying logical systems and the related algebraic structures various filters have been proposed in the literature in this paper we aim to develop a unifying definition for some specific filters called i filters which provide us with a meaningful method to study these filters and corresponding logical algebras in particular trivial characterizations of i filters non trivial characterizations of classes of i filters such as implicative fantastic and boolean filters and characterizations of homologous logical algebras are obtained next three new types of i filters named divisible filters strong and n contractive filters in residuated lattices are introduced particularly it is verified that n fold implicative bl algebras and n contractive bl algebras coincide finally we investigate the relationships between these specific i filters it is shown that a filter is a fantastic filter if and only if it is both a divisible filter and a regular filter

unified forms of triple i method first the present paper provides unified forms of triple i method for fuzzy modus ponens and fuzzy modus tollens of which diverse implication operators can be employed second it is clarified that in a sense zadeh s cri method for fuzzy modus ponens can be brought into line with the unified form of the triple i method lastly a unified form of a triple i method is established as well and a duality result concerning a triple i solutions of fuzzy modus ponens and fuzzy modus tollens is obtained

boolean filters and positive implicative filters of residuated lattices the aim of this paper is to introduce the notions of boolean filters and positive implicative filters in residuated lattices and to investigate their properties several characterizations of boolean filters and positive implicative filters are derived the extension theorems of implicative filters and positive implicative filters are obtained the relations among boolean filters implicative filters and positive implicative filters are investigated and it is proved that boolean filters are equivalent to implicative filters and that every boolean filter is a positive implicative filter but the converse may not be true furthermore the conditions under which a positive implicative filter is a boolean filter are established

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

stone like representation theorems and three valued filters in r0 algebras nilpotent minimum algebras nilpotent minimum algebras nm algebras are algebraic counterpart of a formal deductive system where conjunction is modeled by the nilpotent minimum t norm a logic also independently introduced by guo jun wang in the mid 1990s such algebras are to this logic just what boolean algebras are to the classical propositional logic in this paper by introducing respectively the stone topology and a three valued fuzzy stone topology on the set of all maximal filters in an nm algebra we first establish two analogues for an nm algebra of the well known stone representation theorem for a boolean algebra which state that the boolean skeleton of an nm algebra is isomorphic to the algebra of all clopen subsets of its stone space and the three valued skeleton is isomorphic to the algebra of all clopen fuzzy subsets of its three valued fuzzy stone space respectively then we introduce the notions of boolean filter and of three valued filter in an nm algebra and finally we prove that three valued filters and closed subsets of the stone space of an nm algebra are in one to one correspondence and boolean filters uniquely correspond to closed subsets of the subspace consisting of all ultrafilters

the lattice of prefilters of an eq algebra in this paper the notion of a prefilter generated by a nonempty subset of an eq algebra is introduced and a characterization of it is obtained it is proved that the set of all prefilters of an eq algebra is an algebraic lattice and it is a brouwerian lattice for an eq algebra furthermore it is shown that the set of all principal prefilters of an eq algebra is a sublattice of the lattice of prefilters then by defining an implication between two prefilters it is determined that the lattice of prefilters is a heyting algebra for an eq algebra finally the eq algebras for which the lattice of prefilters is a boolean algebra are given

a characterization of truth functions in the nilpotent minimum logic abstract by introducing a new family of partitions into the n cube 0 1 n the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented so far only this kind of fuzzy truth functions have normal forms among all fuzzy propositional calculi which are based on left continuous but discontinuous t norm