rough prime ideals and rough fuzzy prime ideals in semigroups in this paper we shall introduce the notions of rough prime ideals and rough fuzzy prime ideals in a semigroup and give some properties of such ideals also we will discuss the relations between the upper lower rough prime ideals and the upper lower approximations of their homomorphism images

symbolic dynamics and characterization of complexity abstract symbolic dynamics deals with robust properties of dynamics without digging into numbers for one dimensional maps there have been some new results periodic window theorem generalized composition rule construction of median words without using harmonics and antiharmonics incorporation of discrete symmetry to analyze symmetry breaking and symmetry restoration etc this new understanding has been applied to ordinary differential equations in particular the systematics of stable periodic solutions in the lorenz model has been shown to be given basically by symbolic dynamics of the cubic map symbolic dynamics may be used to extract invariant characteristics from time series its relation with grammatical complexity will also be commented on

roughness in cayley graphs in this paper rough approximations of cayley graphs are studied and rough edge cayley graphs are introduced furthermore a new algebraic definition for pseudo cayley graphs containing cayley graphs is proposed and a rough approximation is expanded to pseudo cayley graphs in addition rough vertex pseudo cayley graphs and rough pseudo cayley graphs are introduced some theorems are provided from which properties such as connectivity and optimal connectivity are derived this approach opens new research fields such as data networks

symbolic dynamics analysis of nonstationary data from a model of a magnetic system with solitons the probability distribution of a complexity measure is used to characterize chaotic states an estimator of the algorithmic complexity of a time series of symbolic words is calculated within a fixed length time window which sweeps through the time series analyzed the words are derived through a symbolic dynamics scheme applied in an m dimensional delay coordinate space time intervals instead of the variables of the system are used the chaotic states of a model of a magnetic domain wall are characterized better by the methods presented than with the use of fractal dimensions and new intermittent states of the system were easily identified using an artificial nonstationary signal composed of different chaotic states of the bloch wall as a test for chaos chaos intermittency we demonstrate that the method developed is suitable for the detection and characterization of intermittency it is also shown that nonstationarity in the form of a slow monotonic drift in the control parameter may extend the stability range of periodic states of the spatially extended system studied a trackinglike phenomenon

rough ideals in semigroups abstract we shall introduce the notion of a rough left right two sided bi ideal in a semigroup which is an extended notion of a left right two sided bi ideal in a semigroup and give some properties of such ideals

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

rough 3 valued algebras rough set theory is an important tool for dealing with granularity and vagueness in information systems this paper studies a kind of rough set algebra the collection of all the rough sets of an approximation space can be made into a 3 valued lukasiewicz algebra we call the algebra a rough 3 valued lukasiewicz algebra in this paper we focus on the rough 3 valued lukasiewicz algebras which are a special kind of 3 valued lukasiewicz algebras firstly we examine whether the rough 3 valued lukasiewicz algebra is an axled 3 valued lukasiewicz algebra secondly we present the condition under which the rough 3 valued lukasiewicz algebra is also a 3 valued post algebra then we investigate the 3 valued post subalgebra problem of the rough 3 valued lukasiewicz algebra finally this paper studies the relationship between the rough 3 valued lukasiewicz algebra and the boolean algebra constructed by all the exact sets of the corresponding approximation space

the ϑ lower and t upper fuzzy rough approximation operators on a semigroup in this paper we consider a semigroup as a universal set and investigate the properties of q lower and t upper fuzzy rough approximation operators a new fuzzy algebraic structure called a tl fuzzy rough semigroup is introduced and some related properties are studied finally the homomorphism properties of q lower and t upper fuzzy rough approximation operators are investigated

a short note on algebraic t rough sets our aim in this paper is to introduce the concept of a set valued homomorphism for groups which is a generalization of ordinary homomorphism then using the definitions of lower inverse and upper inverse we introduce the definition of uniform set valued homomorphism and prove that every set valued homomorphism is uniform finally the concept of probabilistic t rough set is defined

roughness in rings in this paper basic notions of the rough set theory will be given in fact the paper concerns a relationship between rough sets and ring theory we shall introduce the notion of rough subring resp ideal with respect to an ideal of a ring which is an extended notion of a subring resp ideal in a ring and we shall give some properties of the lower and the upper approximations in a ring

the lower and upper approximations in a hypergroup this paper presents a relationship between rough sets and hypergroup theory we analyze the lower and upper approximations of a subset with respect to an invertible subhypergroup and we consider some particular situations moreover the notion of a rough subhypergroup is introduced finally fuzzy rough subhypergroups are introduced and characterized

roughness in mv algebras in this paper by considering the notion of an mv algebra we consider a relationship between rough sets and mv algebra theory we introduce the notion of rough ideal with respect to an ideal of an mv algebra which is an extended notion of ideal in an mv algebra and we give some properties of the lower and the upper approximations in an mv algebra

roughness based on fuzzy ideals the theory of rough set proposed by pawlak and the theory of fuzzy set proposed by zadeh are complementary generalizations of classical set theory many sets are naturally endowed with two binary operations addition and multiplication one concept which does this is a ring this paper concerns a relationship between rough sets fuzzy sets and ring theory it is a continuation of ideas presented by kuroki and wang n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 we consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal in fact we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring some characterizations of the above approximations are made and some examples are presented

rough sets induced by ideals in lattices this paper is to study the rough sets within the context of lattices we study the special properties of the rough sets which can be constructed by means of the congruences determined by ideals of lattice also the properties of the generalized rough sets with respect to ideals of lattice are investigated finally we give an example of their application in formal concept analysis

roughness and fuzziness in quantales abstract rough set theory and fuzzy set theory are two useful mathematical tools for dealing with uncertainty and granularity in information systems motivated by the studies of roughness and fuzziness in algebraic systems and partially ordered sets such as semigroups rings and lattices in this paper we introduce first the notions of fuzzy prime semi prime primary ideals of quantales and investigate their properties several characterizations of such ideals are presented then we introduce the concepts of weak fuzzy prime ideals and strong fuzzy prime ideals of quantales and establish relationships between these ideals and fuzzy prime ideals of quantales by applying rough set theory to fuzzy ideals of quantales we furthermore define rough fuzzy prime semi prime primary ideals of quantales generalizing yang and xu s work on quantales to the fuzzy environment finally relationships between the upper resp lower rough fuzzy ideals of quantales and the upper resp lower approximations of their homomorphic images are also discussed

roughness in quantales rough set theory is a useful mathematical tool for dealing with the uncertainty and granularity in information systems in this paper rough approximations are introduced into quantales a kind of partially ordered algebraic structure with an associative binary multiplication the notions of upper lower rough prime semi prime primary ideals of quantales are proposed and verified to be the extended notions of usual prime semi prime primary ideals of quantales respectively global order properties of all lower upper rough ideals of a quantale are also investigated the rough radical of an upper rough ideal in a quantale is defined and the prime radical theorem of rings is generalized to upper rough ideals of quantales some results about homomorphic images of rough ideals and rough prime ideals of semigroups and rings are also generalized and improved in the field of quantales

pawlak s approximations in γ semihypergroups the c semihypergroup is a generalization of a semigroup a generalization of a semihypergroup and a generalization of a c semigroup in this paper we discuss the roughness of c subsemihypergroups and c hyperideals bi c hyperideals in c semihypergroups in addition we consider rough sets with respect to the idempotent regular relations in a quotient c semihypergroup the upper approximations with respect to green s equivalence relations are derived in the context of c subsemihypergroups and c hyperideals

reference points and roughness in this paper we introduce the notion of a reference point and provide local approximations for a subset of the universe the notion of a reference point naturally gives rise to a rough approximations framework wherein several approximations are possible on the same set also we present an extension to the decision theoretic rough set model by using reference points

bayesian structural inference for hidden processes we introduce a bayesian approach to discovering patterns in structurally complex processes the proposed method of bayesian structural inference bsi relies on a set of candidate unifilar hidden markov model uhmm topologies for inference of process structure from a data series we employ a recently developed exact enumeration of topological e machines a sequel then removes the topological restriction this subset of the uhmm topologies has the added benefit that inferred models are guaranteed to be e machines irrespective of estimated transition probabilities properties of e machines and uhmms allow for the derivation of analytic expressions for estimating transition probabilities inferring start states and comparing the posterior probability of candidate model topologies despite process internal structure being only indirectly present in data we demonstrate bsi s effectiveness in estimating a process s randomness as reflected by the shannon entropy rate and its structure as quantified by the statistical complexity we also compare using the posterior distribution over candidate models and the single maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values we apply bsi to in class examples of finite and infinite order markov processes as well to an out of class infinite state hidden process

roughness in modules the theory of rough sets was proposed by pawlak in 1982 the relations between rough sets and algebraic systems have been already considered by many mathematicians important algebraic structures are groups rings and modules rough groups and rough rings have been investigated by biswas and nanda kuroki and wang and davvaz in this paper we consider an r module as a universal set and we introduce the notion of rough submodule with respect to a submodule of an r module which is an extended notion of a submodule in an r module we also give some properties of the lower and the upper approximations in an r module

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

the lower and upper approximations in a quotient hypermodule with respect to fuzzy sets this paper provides a continuation of ideas presented by davvaz and mahdavipour b davvaz m mahdavipour roughness in modules inform sci 176 2006 3658 3674 the notion of hypermodule is a generalization of the notion of module in this paper we consider the quotient hypermodule m a and interpret the lower and upper approximations as subsets of the quotient hypermodule m a then we introduce the concept of quotient rough sub hypermodule also using the concept of fuzzy sets we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub hypermodules and level rough sets this relation is characterized as a necessary and sufficient condition

effects of coarse graining on the scaling behavior of long range correlated and anti correlated signals abstract we investigate how various coarse graining signal quantization methods affect the scaling properties of long range power law correlated and anti correlated signals quantified by the detrended fluctuation analysis specifically for coarse graining in the magnitude of a signal we consider i the floor ii the symmetry and iii the centro symmetry coarse graining methods we find that for anti correlated signals coarse graining in the magnitude leads to a crossover to random behavior at large scales and that with increasing the width of the coarse graining partition interval this crossover moves to intermediate and small scales in contrast the scaling of positively correlated signals is less affected by the coarse graining with no observable changes when 1 while for 1 a crossover appears at small scales and moves to intermediate and large scales with increasing for very rough coarse graining 3 based on the floor and symmetry methods the position of the crossover stabilizes in contrast to the centro symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales thus indicating a much stronger effect of the centro symmetry compared to the floor and the symmetry method for coarse graining in time where data points are averaged in non overlapping time windows we find that the scaling for both anti correlated and positively correlated signals is practically preserved the results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences

an attractor in a solar time series a time series analysis of observed solar radio pulsations suggests that there must be a low dimensional attractor the power spectrum cannot be interpreted as a superposition of periodic components estimates of the maximum lyapunov exponent and of the kolmogorov entropy give some indications for a deterministic chaos in order to study the limitations inherent in small data samples we include data from the lorenz model and an artificial noise record consequences for the physical modelling of the pulsation event are discussed

θ t fuzzy rough approximation operators and the tl fuzzy rough ideals on a ring in this paper we consider a ring as a universal set and study t fuzzy rough approximation operators with respect to a tl fuzzy ideal of a ring first some new properties of generalized t fuzzy rough approximation operators are obtained then a new fuzzy algebraic structure tl fuzzy rough ideal is defined and its properties investigated and finally the homomorphism of t fuzzy rough approximation operators is studied

finite correlation dimension for stochastic systems with power law spectra abstract we discuss a counter example to the traditional view that stochastic processes lead to a non convergence of the correlation dimension in computed or measured time series specifically we show that a simple class of colored random noises characterized by a power law power spectrum have a finite and predictable value for the correlation dimension these results have implications on the experimental study of deterministic chaos as they indicate that the soie observation of a finite fractal dimension from the analysis of a time series is not sufficient to infer the presence of a strange attractor in the system dynamics we demonstrate that the types of random noises considered herein may be given an interpretation in terms of their fractal properties the consequent exploitation of the non gaussian behavior of these random noises leads us to the introduction of a new time series analysis method which we call multivariate scaling analysis we apply this approach to characterize several global properties of random noise

roughness in n ary hypergroups this paper is aimed at studying the rough sets within the context of the commutative n ary hypergroups for this approach the presentation of a detailed study of the various types of n ary subhypergroups is of the greatest importance this study was initiated in v leoreanu fotea several types of n ary subhypergroups italian journal of pure and applied mathematics in press subsequently we shall use the findings in this study to define the upper and lower approximation of a subset with respect to an invertible n ary subhypergroup of a commutative n ary hypergroup in the final part the concept of n ary rough subhypergroup is introduced

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

filtered noise can mimic low dimensional chaotic attractors this contribution presents four results first calculations indicate that when examined by the grassberger procaccia algorithm alone filtered noise can mimic low dimensional chaotic attractors given the ubiquity of signal filtering in experimental investigations this is potentially important second a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor third it is shown that a criterion derived by eckmann and ruelle physica d 56 185 1992 to estimate the minimum number of data points required in a grassberger procaccia calculation can be used to provide a further check on these dimension estimates fourth it is shown that surrogate data techniques recently published by theiler and his colleagues in nonlinear modeling and forecasting edited by m casdagli and s eubanks addison wesley reading ma 1992 can successfully distinguish between linearly correlated noise and nonlinear structure these results and most particularly the first indicate that grassberger procaccia results must be interpreted with far greater circumspection than has previously been the case and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data when filtered signals are examined by this algorithm alone a finite noninteger value of mathit d 2 is consistent with low dimensional chaotic behavior but it is certainly not a definitive diagnostic of chaos

rough variables with values in measurable spaces an x valued rough variable is introduced as a measurable function from a rough space to a measurable space x based on the concept of x valued rough variables some properties of x valued rough variables are studied furthermore the concept of convergence is presented and convergence of x valued rough variables is discussed

the lower and upper approximations in a fuzzy group in this paper we shall introduce the notion of a rough subgroup with respect to a normal subgroup of a group and give some properties of the lower and the upper approximations in a group also we will discuss a rough subgroup with respect to a t level subset of a fuzzy normal subgroup

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

generalized lower and upper approximations in a ring in this paper the concepts of set valued homomorphism and strong set valued homomorphism of a ring are introduced and related properties are investigated the notions of generalized lower and upper approximation operators constructed by means of a set valued mapping which is a generalization of the notion of lower and upper approximation of a ring are provided we also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by davvaz b davvaz roughness in rings information science 164 2004 147 163 in a ring and discuss some significant properties of them

estimating and improving the signal to noise ratio of time series by symbolic dynamics we investigate the effect of symbolic encoding applied to times series consisting of some deterministic signal and additive noise as well as time series given by a deterministic signal with randomly distributed initial conditions as a model of event related brain potentials we introduce an estimator of the signal to noise ratio snr of the system by means of time averages of running complexity measures such as shannon and r enyi entropies and prove its asymptotical equivalence with the linear snr in the case of shannon entropies of symbol distributions a snr improvement factor is defined exhibiting a maximum for intermediate values of noise amplitude in analogy to stochastic resonance phenomena we demonstrate that the maximum of the snr improvement factor can be shifted toward smaller noise amplitudes by using higher order r enyi entropies instead of the shannon entropy for a further improvement of the snr a half wave encoding of noisy time series is introduced finally we discuss the effect of noisy phases on the linear snr as well as on the snr defined by symbolic dynamics it is shown that longer symbol sequences yield an improvement of the latter

optimum tests for fixed effects and variance components in balanced models abstract for any analysis of variance model with balanced data involving both fixed and random effects uniformly most powerful unbiased umpu and uniformly most powerful invariant unbiased umpiu tests are derived for the significance of a fixed effect or a variance component under the assumption of normality of random effects the tests coincide with the usual f tests robustness of the umpiu test against suitable deviations from normality is established

symbolic dynamics of event related brain potentials we apply symbolic dynamics techniques such as word statistics and measures of complexity to nonstationary and noisy multivariate time series of electroencephalograms eeg in order to estimate event related brain potentials erp their significance against surrogate data as well as between different experimental conditions is tested these methods are validated by simulations using stochastic dynamical systems with time dependent control parameters and compared with traditional erp analysis techniques continuous eeg data are cut into epochs according to stimuli events presented to the subjects these ensembles of time series can be considered as ensembles of trajectories given by some dynamical systems we employ a statistical mechanics approach motivated by the frobenius perron equation and apply it to coarse grained symbolic descriptions of the dynamics we develop time dependent measures of complexity founded on running cylinder sets and show that these quantities are able to distinguish simulated data obtained by different control parameters as well as experimental data between different experimental conditions as a first finding our approach restores the well known erp components and it reveals additionally qualitative changes in the eeg that cannot be detected by means of the traditional techniques we criticize the prerequisites of the traditional approach to erp analysis and propose to consider erp instead in terms of dynamical system theory and information theory

rough ideals under relations associated to fuzzy ideals in this paper we deal with the theory of rough ideals started in davvaz 2004 we show that the approximation spaces built from an equivalence relation compatible with the ring structure i e associated to a two sided ideal are too naive in order to develop practical applications we propose the use of certain crisp equivalence relations obtained from fuzzy ideals these relations make available more flexible approximation spaces since they are enriched with a wider class of rough ideals furthermore these are fully compatible with the notion of primeness semiprimeness the theory is illustrated by several examples of interest in engineering and mathematics