second order volterra filtering and its application to nonlinear system identification some recent results on the design and implementation of second order volterra filters are presented the second order volterra filter is a nonlinear filter with the filter structure of second order volterra series a simple minimum mean square error solution for the volterra filter is derived based on the assumption that the filter input is gaussian also we propose an iterative factorization technique to design a subclass of the volterra filters which can alleviate the complexity of the filtering operations considerably furthermore an adaptive algorithm for the volterra filter is investigated along with its mean convergence and asymptotic excess mean square error finally the utility of the volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves

some kinds of view the fuzzy filters of bl algebras the concepts of view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras are introduced and some related properties are investigated some characterizations of these generalized fuzzy filters are derived in particular we describe the relationships among ordinary fuzzy implicative positive implicative and fantastic filters view the mathml source fuzzy implicative positive implicative and fantastic filters and view the mathml source fuzzy implicative positive implicative and fantastic filters of bl algebras finally we prove that a fuzzy set f of a bl algebra l is an view the mathml source fuzzy implicative filter of l if and only if it is both an view the mathml source fuzzy positive implicative filter and an view the mathml source fuzzy fantastic filter

nonlinear digital filter realization by distributed arithmetic it is assumed that a nonlinear shift invariant digital filter is represented by a truncated discrete volterra series a matrix notation based on the properties of the kronecker product of matrices is derived for the nonlinear operator of order k in the volterra expansion the matrix notation shows how the well known distributed arithmetic originally proposed for linear digital filters can be adopted for the realization of nonlinear operators the characteristics of combinatorial and memory oriented structures are compared and the problem of complexity reduction is discussed

adaptive nonlinear system identification in the short time fourier transform domain in this paper we introduce an adaptive algorithm for nonlinear system identification in the short time fourier transform stft domain the adaptive scheme consists of a parallel combination of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we adaptively update the model parameters using the least mean square lms algorithm and derive explicit expressions for the transient and steady state mean square error mse in frequency bins for white gaussian inputs we show that estimation of the nonlinear component improves the mse performance only when the power ratio of nonlinear to linear components is relatively high furthermore as the number of crossband filters increases a lower steady state mse may be obtained at the expense of slower convergence experimental results support the theoretical derivations

modeling and identification of nonlinear systems in the short time fourier transform domain in this paper we introduce a novel approach for improved nonlinear system identification in the short time fourier transform stft domain we first derive explicit representations of discrete time volterra filters in the stft domain based on these representations approximate nonlinear stft models which consist of parallel combinations of linear and nonlinear components are developed the linear components are represented by cross band filters between subbands while the nonlinear components are modeled by multiplicative cross terms we consider the identification of quadratically nonlinear systems and show that a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time domain volterra model particularly when long memory systems are considered experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach

computation tree logic model checking based on possibility measures in order to deal with the systematic verification with uncertain information in possibility theory li and li 2013 introduced model checking of linear time properties in which the uncertainty is modeled by possibility measures xue lei and li 2011 defined computation tree logic ctl based on possibility measures which is called possibilistic ctl poctl this paper is a continuation of the above work first we study the expressiveness of poctl unlike probabilistic ctl it is shown that poctl in particular qualitative poctl is more powerful than ctl with respect to their expressiveness the equivalent expressions of basic ctl formulae using qualitative poctl formulae are presented in detail some poctl formulae that cannot be expressed by any ctl formulae are presented in particular some qualitative properties of repeated reachability and persistence are expressed using poctl formulae next adapting ctl model checking algorithm a method to solve the poctl model checking problem and its time complexity are discussed in detail finally an example is given to illustrate the poctl model checking method

on some logical points of fuzzy conditional decision making abstract the paper deals with some properties of pl probability logic and fl fuzzy logic fl is derived from pl by means of choosing the connectives such that the logical system created is truth functional from many alternatives the usual connectives of fl emerged as is known pl is not truth functional conditionality is considered by means of implication and using a fuzzy counterpart of conditional probability in that way some basic tools are created for bayesian like decision making in a fuzzy environment the analysis shows that the implication and the conditional probability like counterpart are not necessarily the same thing a labelling system is introduced in fuzzy valued fl such that a finite set of non negative integers forms the set of truth values which actually are fuzzy sets of the unit interval 0 1 in this way new quantitative expressions are obtained for each qualitative linguistic variable in doing so the system preserves fuzziness some general rules of inference are also considered

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

adjusting estimative prediction limits summary this note presents a direct adjustment of the estimative prediction limit to reduce the coverage error from a target value to third order accuracy the adjustment is asymptotically equivalent to those of barndorff nielsen cox 1994 1996 and vidoni 1998 it has a simpler form with a plug in estimator of the coverage probability of the estimative limit at the target value

nonlinear system identification an effective framework based on the karhunen loeve transform this paper proposes on the basis of a rigorous mathematical formulation a general framework that is able to define a large class of nonlinear system identifiers this framework exploits all those relationships that intrinsically characterize a limited set of realizations obtained by an ensemble of output signals and their parameterized inputs by means of the separation property of the karhunen loeve transform the generality and the flexibility of the approximating mappings ranging from traditional approximation techniques to multiresolution decompositions and neural networks allow the design of a large number of distinct identifiers each displaying a number of properties such as linearity with respect to the parameters noise rejection low computational complexity of the approximation procedure exhaustive experimentation on specific case studies reports high identification performance for four distinct identifiers based on polynomials splines wavelets and radial basis functions several comparisons show how these identifiers almost always have higher performance than that obtained by current best practices as well as very good accuracy optimal noise rejection and fast algorithmic elaboration as an example of a real application the identification of a voice communication channel comprising a digital enhanced cordless telecommunications dect cordless phone for wireless communications and a telephone line is reported and discussed

fuzzy h v ideals in γ h v rings in this paper by means of a kind of new idea we consider the q fuzzy h v ideals of a c h v ring the concept of c h v rings which is a generalization of c rings and h v rings is introduced the notion of q fuzzy h v ideals of a c h v ring is provided and some related properties are investigated the concept of implication based fuzzy h v ideals of a c h v ring is studied in particular the implication operators in the lukasiewicz system of continuous valued logic are discussed finally the homomorphism of q fuzzy h v ideals of a c h v ring is explored

on fuzzy implication in de morgan algebras the behaviour of some fuzzy implications with respect to measure of fuzziness and their deductive power is studied in a lattice framework the point of view of bandler and kohout 1 and willmott 7 is followed

fuzzy sets and toposes towards higher order fuzzy logic abstract a series of paper which have appeared in fuzzy sets and systems over the last three years are reviewed in an expository manner the claims and counter claims made in them are dealt with some of the problems of representing knowledge in the first order predicate calculus are discussed briefly and a case is made for exposing the relationship between topoi and fuzzy mathematics with a view to making a true fuzzy logic both consistent complete and respectable the paper is an attempt to present the controversy to the non specialist and especially to practitioners in expert systems and artificial intelligence

hybrid polynomial filters for gaussian and non gaussian noise environments traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by gaussian and heavy tailed distributions weighted median and weighted myriad filters in contrast are well known for their outlier suppression and detail preservation properties it is shown here that the weighted median and weighted myriad methodologies are naturally extended to the polynomial sample case yielding hybrid filter structures that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers for both gaussian and heavy tailed distributions environments moreover the introduced hybrid polynomial filter classes are well motivated by analysis of cross and square term statistics of gaussian and heavy tailed distributions a presented asymptotic tail mass analysis shows that polynomial terms both under gaussian and heavy tailed noise statistics have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms for the gaussian noise case and weighted median and weighted myriad processing of cross and square terms respectively for the heavy tailed noise case are justified from a maximum likelihood perspective filters parameter optimization procedures are also presented finally the effectiveness of hybrid filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

a new view of fuzzy hypernear rings in this survey article we first introduce the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set this concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we consider the interval valued q fuzzy sub hypernear rings hyperideals of a hypernear ring and hence a generalization of a fuzzy sub near ring ideal is given some related properties of fuzzy hypernear rings are described finally we consider the concept of implication based interval valued fuzzy sub hypernear rings hyperideals in a hypernear ring in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

bayesian prediction with approximate frequentist validity we characterize priors which asymptotically match the posterior coverage probability of a bayesian prediction region with the corresponding frequentist coverage probability this is done considering both posterior quantiles and highest predictive density regions with reference to a future observation the resulting priors are shown to be invariant under reparameterization the role of jeffreys prior in this regard is also investigated it is further shown that for any given prior it may be possible to choose an interval whose bayesian predictive and frequentist coverage probabilities are asymptotically matched

nonlinear system identification in impulsive environments nonlinear system identification has been studied under the assumption that the noise has finite second and higher order statistics in many practical applications impulsive measurement noise severely weakens the effectiveness of conventional methods in this paper spl alpha stable noise is used as a noise model in such case the minimum mean square error mmse criterion is no longer an appropriate metric for estimation error due to the lack of finite second order statistics of the noise therefore we adopt minimum dispersion criterion which in turn leads to the adaptive least mean pth power lmp algorithm it is shown that the lmp algorithm under the spl alpha stable noise model converges as long as the step size satisfies certain conditions the effect of p on the performance is also investigated compared with conventional methods the proposed method is more robust to impulsive noise and has better performance

some types of generalized fuzzy filters of bl algebras the aim of this paper is to introduce the notions of interval valued q fuzzy boolean implicative positive implicative and fantastic filters in bl algebras and to investigate some related properties some characterizations of these generalized fuzzy filters are derived finally the relations among these generalized fuzzy filters are discussed it is proved that an interval valued q fuzzy filter in bl algebras is an interval valued q fuzzy boolean implicative filter if and only if it is both an interval valued q fuzzy positive implicative filter and an interval valued q fuzzy fantastic filter

fuzzy logic of lukasiewicz logic a clarification pavelka 10 had shown in 1979 that the only natural way of formalizing fuzzy logic for truth value in the unit interval 0 1 is by using lukasiewicz s implication operator a b min 1 1 a b or some isomorphic form of it a considerable number of other papers around the same time had attempted to formulate alternative definitions for a b by giving intuitive justifications for them there continues to be some confusion however even today about the right notion of fuzzy logic much of this has its origin in the use of improper and or and the not operations and a misunderstanding of some of the key differences between proofs or inferencing in fuzzy logic and those in lukasiewicz s logic we point out the need for defining the strong conjunction operator in connection with fuzzy modus ponens rule and why we do not need the fuzzy syllogism rule we also point out the shortcomings of many of the alternative definitions of a b which indicate further support for pavelka s result we hope that these discussions help to clarify the misconceptions about fuzzy logic

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

formal concept analysis and lattice valued chu systems this paper links formal concept analysis fca both to order theoretic developments in the theory of galois connections and to chu spaces or systems viewed as a common rubric for both topological systems and systems arising from predicate transformers in programming semantics 13 these links are constructed for each of traditional fca and l fca where l is a commutative residuated semiquantale surprising and important consequences include relationships between formal l contexts and l topological systems within the category of l chu systems relationships justifying the categorical study of formal l contexts and linking such study to l chu systems applications and potential applications are primary motivations including several example classes of formal l contexts induced from data mining notions throughout categorical frameworks are given for fca and lattice valued fca in which morphisms preserve the birkhoff operators on which all the structures of fca and lattice valued fca rest and further the results of this paper show that under very general conditions these categorical frameworks are both sufficient and necessary for the interchange or preservation of l concepts and l protoconcepts structures central to fca and lattice valued fca

weighted automata and multi valued logics over arbitrary bounded lattices we show that l weighted automata l rational series and l valued monadic second order logic have the same expressive power for any bounded lattice l and for finite and infinite words we also prove that aperiodicity star freeness and l valued first order and ltl definability coincide this extends classical results of kleene buchi elgot trakhtenbrot and others to arbitrary bounded lattices without any distributivity assumption that is fundamental in the theory of weighted automata over semirings in fact we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices

redefined fuzzy hv submodules and many valued implications this paper considers a relationship between fuzzy sets and algebraic hyperstructures a generalization of ideas presented by davvaz b davvaz fuzzy h v submodules fuzzy sets syst 117 2001 477 484 and bhakat and das s k bhakat p das email protected q fuzzy subgroup fuzzy sets syst 80 1996 359 368 is presented in fact the main purpose of this paper is to introduce and study a new sort of fuzzy h v submodule of an h v module called email protected q fuzzy h v submodules these fuzzy h v submodules are characterized by their level h v submodules the concept of a fuzzy h v submodule with thresholds is introduced and some interesting properties are investigated

after the fuzzy wave reached europe abstract we briefly describe the situation of the fuzzy community in europe before the fuzzy wave we show that there was a lot of expertise in almost all subareas of fuzzy logic then we describe some aspects of the fuzzy wave itself in particular fuzzy control and first generation fuzzy systems that played a role during the time the fuzzy wave reached europe we also make some remarks about european companies and their activities during this time then we discuss the situation after the fuzzy wave some aspects of second generation fuzzy systems the combination of fuzzy logic with other theories and techniques and some new application areas finally we will discuss the chances of fuzzy systems in europe in the future

new types of fuzzy ideals in bck bci algebras a generalization of an email protected q fuzzy ideal of a bck bci algebra is discussed characterizations of an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are provided conditions for an email protected q k fuzzy ideal resp email protected email protected email protected q email protected fuzzy ideal to be a fuzzy ideal are provided using the notion of a fuzzy ideal with thresholds characterizations of a fuzzy ideal an email protected q k fuzzy ideal and an email protected email protected email protected q email protected fuzzy ideal are discussed

on standard models of fuzzy modal logics abstract we improve the valuations of modal sentences of schotch 7 and build a more reasonable kind of standard models so some important results about d t b 4 5 are generalized into fuzzy situation

blind identifiability of a quadratic stochastic system quadratic systems appear in various fields of signal processing in particular in detection and estimation in this paper we establish some conditions to determine the order and identify the coefficients of any discrete and finite extent quadratic system driven by a sequence of independent and identically distributed random variables the input sequence is assumed unobservable and the conditions are based on some properties of the output cumulant functions up to the third order necessary and sufficient conditions ensuring the determination of the order are given a sufficient condition of uniqueness to recover the parameters is presented lastly some examples are given

frequentist prediction intervals and predictive distributions summary we consider parametric frameworks for the prediction of future values of a random variable y based on previously observed data x simple pivotal methods for obtaining calibrated prediction intervals are presented and illustrated frequentist predictive distri butions are defined as confidence distributions and their utility is demonstrated a simple pivotal based approach that produces prediction intervals and predictive distributions with well calibrated frequentist probability interpretations is introduced and efficient simulation methods for producing predictive distributions are considered properties related to an average kullback leibler measure of goodness for predictive or estimated distributions are given the predictive distributions here are shown to be optimal in certain settings with invariance structure and to dominate plug in distributions under certain conditions

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

a resolution like strategy based on a lattice valued logic as the use of nonclassical logics becomes increasingly important in computer science artificial intelligence and logic programming the development of efficient automated theorem proving based on nonclassical logic is currently an active area of research this paper aims at the resolution principle for the pavelka type fuzzy logic 1979 pavelka showed that the only natural way of formalizing fuzzy logic for truth values in the unit interval 0 1 is by using the lukasiewicz s implication operator a spl rarr b min 1 1 a b or some isomorphic forms of it hence we first focus on the resolution principle for the lukasiewicz logic l sub spl aleph with 0 1 as the truth valued set some limitations of classical resolution and resolution procedures for fuzzy logic with kleene implication are analyzed then some preliminary ideals about combining resolution procedure with the implication connectives in l sub spl aleph are given moreover a resolution like principle in l sub spl aleph is proposed and the soundness theorem of this resolution procedure is also proved second we use this resolution like principle to horn clauses with truth values in an enriched residuated lattice and consider the l type fuzzy prolog

multiary α resolution principle for a lattice valued logic this paper focuses on resolution based automated reasoning theory in a lattice valued logic system with truth values that are defined in a lattice valued logical algebraic structure lattice implication algebras lias which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment concretely we investigate a generalization of the known conjunctive normal form cnf in the classical logic representation that we call the generalized conjunctive normal form gcnf which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic we then extend the established resolution principle at a certain truth value level called resolution in this lattice valued logic to a more general form i e from binary resolution to multiary resolution the extension to multiary resolution starts from lattice valued propositional logic lp x while its theorems of both soundness and completeness are proved multiary resolution principle is then further established in the corresponding lattice valued first order logic lf x along with its soundness theorem lifting lemma and completeness theorem meanwhile an important result that multiary resolution principle in lf x can be equivalently transformed into that in lp x to some extent is obtained all these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision making problems under uncertainty

a new approach for fuzzy topology ii abstract we point out a new approach for fuzzy topology with fuzzy logic and discuss the neighborhood structure of a point and the convergence of nets and filters in this new framework

applications of likelihood asymptotics for nonlinear regression in herbicide bioassays dose response models are intensively used in herbicide bioassays despite recent advancements in the development of new herbicides statistical analyses are commonly based on asymptotic approximations that are sometimes poor this paper presents the use of recent results in higher order asymptotics for likelihood based inference in nonlinear regression the methods presented provide accurate approximation for the distribution of test statistics and for prediction limits analyses of the fit and measures of detection limits of the bioassays are considered and the potential of the methods is illustrated by examples with real data

a representation of exponential form on fuzzy logic abstract this paper proposes a representation of exponential form ef in fuzzy logic by ef any fuzzy value a in fuzzy valued logic or fuzzy linguistic valued logic can be represented as b c where b is called the truth base and c the confidence exponent the basic idea of this form and its properties are discussed by using a different truth base the exponential form can be applied to represent positive and negative logic in fuzzy valued logic as well as fuzzy linguistic valued logic some applications of ef for approximate reasoning and fuzzy neural networks are also introduced in this paper

mapping abelian l groups with strong unit one one into mv algebras abstract we exhibit a functor from lattice ordered abelian groups with strong unit l fuchs partially ordered algebraic systems pergamon new york 1963 to c c chang s mv algebras trans amer math soc 88 1958 467 490 in such a way that every mv algebra is the image of at most one such group

a generalization of median filtering using linear combinations of order statistics we consider a class of nonlinear filters whose output is given by a linear combination of the order statistics of the input sequence assuming a constant signal in white noise the coefficients in the linear combination are chosen to minimize the output mse for several noise distributions it is shown that the optimal order statistic filter osf tends toward the median filter as the noise becomes more impulsive the optimal osf is applied to an actual noisy image and is shown to perform well combining properties of both the averaging and median filters a more general design scheme for applications involving nonconstant signals is also given

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

on the definition of a fuzzy subgroup abstract using the idea of quasi coincidence of a fuzzy point with a fuzzy set some new concepts of a fuzzy subgroup are introduced and their acceptibility is investigated some fundamental properties of one such viable fuzzy subgroup are obtained

a small set of axioms for residuated logic we show that a set of three axioms together with modus ponens suffices to build up a formal system for the class r of all quadruples l t j in which l is a partially ordered set with a top element and t is a triangular norm on l that has a residuated implication j we show that this r is not a variety

a fuzzy inverse relation based on godelian logic and its applications abstract fuzzy logic applicable to decision making processes such as diagnostic expert systems and fuzzy controllers is the prime concern of this paper in these applications an inverse operation or backward inference plays an important role in the current paper a new backward inference technique based on godelian logic is proposed the relation between the forward and backward inferences is established by introducing fuzzy joint and conditional relations

generalized fuzzy groups and many valued implications in this paper we give the definition of a fuzzy subgroup with thresholds which is a generalization of rosenfeld s fuzzy subgroup and bhakat and das s fuzzy subgroup we also give the definition of an implication based fuzzy subgroup and discuss relations between two fuzzy subgroups

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

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

an axiomatizable logical foundation for lattice ordered qualitative linguistic approach for reasoning with words it is commonsense that people do express think reason and make decision directly using linguistic terms in natural language rather than using numerical quantification how to establish the formalized approach imitating the common way of human being s to manipulate directly linguistic terms without numerical approximation to provide the rational decision is still an open research area investigations on the algebraic structure of linguistic term set for varied decision making applications especially in social science still lack a formalism for development of strict linguistic valued logic system as a theoretical foundation and its approximate reasoning scheme in practice to attain this goal we characterize and construct a typical structure of commonly used linguistic term sets in natural language by a lattice ordered algebra structure lattice implication algebra lia where lukasiewicz implication algebra as a special case of lia plays a substantial role by using lukasiewicz logic s axiomatizability in terms of pavelka type fuzzy logic we propose a new axiomatizable lattice ordered qualitative linguistic truth valued logic system based on lia to place an important foundation for further establishing formal linguistic truth valued logic based approximate reasoning and decision making with applications this proposed logic system has a distinct feature of handling comparable or incomparable linguistic terms directly without numerical quantification will be especially beneficial for perception based decision making processes it attempts to enhance the quantitative theory of decision science with qualitative algebraic and logic oriented approaches to achieve reasoning with words

geometric symmetry in the quadratic fisher discriminant operating on image pixels this correspondence examines the design of quadratic fisher discriminants qfds that operate directly on image pixels when image ensembles are taken to comprise all rotated and reflected versions of distinct sample images a procedure based on group theory is devised to identify and discard qfd coefficients made redundant by symmetry for arbitrary sampling lattices this procedure introduces the concept of a degeneracy matrix tensor representations are established for the square lattice point group 8 fold symmetry and hexagonal lattice point group 12 fold symmetry the analysis is largely applicable to the symmetrization of any quadratic filter and generalizes to higher order polynomial volterra filters experiments on square lattice sampled synthetic aperture radar sar imagery verify that symmetrization of qfds can improve their generalization and discrimination ability

predictive fit for natural exponential families summary the paper examines predictive distributions concentrating on measuring their fit to the true distribution by average kullback leibler divergence the notion of an averaged bootstrap predictive distribution is introduced this predictive distribution is shown to be asymptotically superior to the estimative distribution in terms of average kullbackleibler divergence when the true distribution is in a natural exponential family smallsample results are presented for the poisson and binomial distributions which suggest that the bootstrap distribution performs well in these cases

bootstrap calibrated interval estimates for latent variable scores in item response theory in most item response theory applications model parameters need to be first calibrated from sample data latent variable lv scores calculated using estimated parameters are thus subject to sampling error inherited from the calibration stage in this article we propose a resampling based method namely bootstrap calibration bc to reduce the impact of the carryover sampling error on the interval estimates of lv scores bc modifies the quantile of the plug in posterior i e the posterior distribution of the lv evaluated at the estimated model parameters to better match the corresponding quantile of the true posterior i e the posterior distribution evaluated at the true model parameters over repeated sampling of calibration data furthermore to achieve better coverage of the fixed true lv score we explore the use of bc in conjunction with jeffreys prior we investigate the finite sample performance of bc via monte carlo simulations and apply it to two empirical data examples

undermodeling error quantification for quadratically nonlinear system identification in the short time fourier transform domain in this paper we introduce an estimation error analysis for quadratically nonlinear system identification in the short time fourier transform stft domain the identification scheme consists of a parallel connection of a linear component represented by crossband filters between subbands and a quadratic component which is modeled by multiplicative cross terms we mainly concentrate on two types of undermodeling errors the first is caused by employing a purely linear model in the estimation process i e nonlinear undermodeling and the second is a consequence of restricting the number of estimated crossband filters in the linear component we derive analytical relations between the noise level nonlinearity strength and the obtainable mean square error mse in subbands we show that for low signal to noise ratio snr conditions a lower mse is achieved by allowing for nonlinear undermodeling and utilizing a purely linear model however as the snr increases the performance can be generally improved by incorporating a nonlinear component into the model we further show that as the snr increases a larger number of crossband filters should be estimated to attain a lower mse whether a linear or nonlinear model is employed experimental results support the theoretical derivations

quadratic digital filters for image processing a class of nonlinear two dimensional filters is presented a matrix description is developed for such operators and some symmetry conditions are imposed which simplify and render more effective the filter structure a strategy for the design of filters capable of enhancing images having reduced contrast and degraded by noise is proposed

theory of expertons and fuzzy logic abstract since 1965 when l a zadeh presented the concept of fuzzy sets various types of extensions have been proposed the treatment of subjectivity knowledge and uncertain data from one or several experts is now an important field in computer science in this paper a general concept the experton is described it is especially adapted for the case where several experts and or users are concerned the properties of expertons give also a monoid and a distributive lattice with the norms min and max then every process used with fuzzy sets stays available for expertons with a constraint of monotonicity expertons are based on probabilistic sets when intervals of probabilities are considered

on asymptotic properties of predictive distributions summary second order asymptotic theory of predictive distributions is investigated it is shown that estimative distributions with asymptotically efficient estimators can be improved to predictive distributions that do not belong to the model the model is assumed to be a multidimensional curved exponential family predictive distributions can be constructed by shifting estimative distributions in a direction orthogonal to the model the average kullback leibler divergence from the true distribution to a predictive distribution is represented as the sum of two components one of them depends on the choice of the estimative distribution and the other depends on the shift orthogonal to the model the optimal shift orthogonal to the model is obtained a quantity that can be regarded as the mixture mean curvature of the model in the space of all probability distributions is introduced the difference in average kullback leibler divergence between an estimative distribution and the optimal predictive distribution obtained by shifting it can be regarded as the mixture mean curvature of the model an asymptotic expression for bayesian predictive distributions is also obtained

polynomial weighted median filtering this paper extends weighted median wm filters to the class of polynomial weighted median pwm filters traditional polynomial filtering theory based on linear combinations of polynomial terms is able to approximate important classes of nonlinear systems the linear combination of polynomial terms however yields poor performance in environments characterized by heavy tailed distributions weighted median filters in contrast are well known for their outlier suppression and detail preservation properties the weighted median sample selection methodology is naturally extended to the polynomial sample case yielding a filter structure that exploits the higher order statistics of the observed samples while simultaneously being robust to outliers moreover the pwm filter class is well motivated by an analysis of cross and square term statistics a presented probability density function analysis shows that these terms have heavier tails than the observed samples indicating that robust combination methods should be utilized to avoid undue influence of outliers further analysis shows weighted median processing of polynomial terms is justified from a maximum likelihood perspective the established pwm filter class is statistically analyzed through the determination of the filter output distribution and breakdown probability filter parameter optimization procedures are also presented finally the effectiveness of pwm filters is demonstrated through simulations that include temporal spectrum and bispectrum analysis

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

some representable de morgan algebras the stone theorems give us a representation of boolean algebras the structure associated to classical logic through set algebras the present paper deals with the representation of de morgan algebras one of the most important structures associated to multiple valued logic through fuzzy set algebras let us recall that a de morgan algebra 9 a v n is a structure such that pi a v is a distributive lattice with supremum u and infimum 0 and n is a decreasing involution in 9 such that n 0 u and n u 0 and consequently satisfies the de morgan laws we call these mappings n 9 9 strong negations or involutions of 40 see for instance 8 on the other hand let us recall that zadeh 3 defined the fuzzy subset of a universe x being characterized by a mapping a x 0 11 the generalized characteristic function which sends each x e x into the membership grade of x belonging to a as usual we denote by p x the set of fuzzy subsets of x f x o 11 and by q x n u the lattice obtained by defining f7 and u between fuzzy sets through a 7 b x min a x b x and a u b x max a x b x this lattice is distributive with supremum x defined by x x 1 for all x e x infimum 0 defined by 0 x 0 for all x e x and such that the boolean algebra of the boolean elements of f x is the boolean algebra of the classical subsets of x p x n u c the concept of fuzzy subset of a universe x is generalized goguen 4 by defining fuzzy subsets taking values in a lattice l a v it can still be more widely generalized by defining fuzzy subsets that for all x e x take values in different lattices thus if 9 r 1 x e x is a family of lattices r a v with supremum 1 and inlimum o we can define a fuzzy subset of x taking values in 5 as any mapping a x 1 u r such hat a x e r for all x e x if we denote by p x the set of fuzzy subsets of x taking values in r and define n and u through a n b x a x a b x and a u b x a x v b x then p x n u happens to be a lattice 463 0022 247 84 3 00

fuzzy n ary polygroups related to fuzzy points recently fuzzy n ary sub polygroups were introduced and studied by davvaz corsini and leoreanu fotea b davvaz p corsini v leoreanu fotea fuzzy n ary sub polygroups comput math appl 57 2008 141 152 now in this paper the concept of email protected q fuzzy n ary sub polygroups email protected email protected email protected email protected fuzzy n ary sub polygroups and fuzzy n ary sub polygroup with thresholds of an n ary polygroup are introduced and some characterizations are described also we give the definition of implication based fuzzy n ary sub polygroups in an n ary polygroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

a note on modified estimative prediction limits and distributions in this paper a modification of the estimative prediction limit is derived for which the coverage probability equals the target value to third order accuracy under ordinary repeated sampling it provides an explicit approximate solution to the equation given by barndorff nielsen cox 1996 which determines an upper prediction limit for an unobserved random variable the corresponding predictive density is specified in a simple closed form and its main properties are emphasised

the measure of the degree of truth and the grade of membership abstract a method is presented to define the meaning of a fuzzy proposition and of a fuzzy set through the construction of fuzzy propositions with non ambiguous intermediate truth values

more on fuzzy lattices in this paper the concept of an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter in a lattice is introduced which is a generalization of the concept as given by davvaz and kazanci 2011 18 characterizations for an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are provided different classes of lattices are characterized by the properties of these fuzzy sublattices ideals filters using the notions of a fuzzy sublattice ideal filter with thresholds characterization of a fuzzy sublattice ideal filter an q k fuzzy sublattice ideal filter and q k fuzzy sublattice ideal filter are discussed

application of two dimensional generalized mean filtering for removal of impulse noises from images a new method for removing impulse noises from images is proposed the filtering scheme is based on replacing the central pixel value by the generalized mean value of all pixels inside a sliding window the concepts of thresholding and complementation which are shown to improve the performance of the generalized mean filter are introduced the threshold is derived using a statistical theory the actual performance of the proposed filter is compared with that of file commonly used median filter by filtering noise corrupted real images the hardware complexity of the two types of filters are also compared indicating the advantages of the generalized mean filter

generalized fuzzy interior ideals in semigroups using the idea of quasi coincidence of a fuzzy point with a fuzzy set the concept of an a b fuzzy interior ideal which is a generalization of a fuzzy interior ideal in a semigroup is introduced and related properties are investigated

characterizations of regular ordered semigroups in terms of α β fuzzy generalized bi ideals in this paper the concept of an a b fuzzy generalized bi ideal in an ordered semigroup is introduced which is a generalization of the concept of a fuzzy generalized bi ideal in an ordered semigroup using this concept some characterization theorems are provided the upper lower parts of an q fuzzy generalized bi ideal are introduced and some characterizations of regular ordered semigroups are given also we consider the concept of implication based fuzzy generalized bi ideals in an ordered semigroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

a simple predictive density based on the p formula the predictive density proposed by harris 1989 is based on integrating the density for a new observation with respect to the estimated sampling distribution of the maximum likelihood estimator of the unknown parameter this has good properties but is rather complicated to compute even for simple models an approximation to the harris proposal is considered which consists of approximating the sampling distribution of the maximum likelihood estimator of the unknown parameter by barndorff nielsen s 1983 p formula and then using a laplace approximation with o n 1 correction terms for integrating out the parameter the result can generally be expressed in terms of standard likelihood derivatives and takes a quite simple form for exponential families and for location models

determination of α resolution in lattice valued first order logic lf x key issues for resolution based automated reasoning in lattice valued first order logic lf x are investigated with truth values in a lattice valued logical algebraic structure lattice implication algebra lia the determination of resolution at a certain truth value level called a resolution in lf x is proved to be equivalently transformed into the determination of a resolution in lattice valued propositional logic lp x based on lia the determination of a resolution of any quasi regular generalized literals and constants under various cases in lp x is further analyzed specified and subsequently verified hence the determination of a resolution in lf x can be accordingly solved to a very broad extent which not only lays a foundation for the practical implementation of automated reasoning algorithms in lf x but also provides a key support for a resolution based automated reasoning approaches and algorithms in lia based linguistic truth valued logics

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

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle