modeling highway traffic headway distributions using superstatistics we study traffic clearance distributions i e the instantaneous gap between successive vehicles and time headway distributions by applying the beck and cohen superstatistics we model the transition from free phase to congested phase with the increase of vehicle density as a transition from the poisson statistics to that of the random matrix theory we derive an analytic expression for the spacing distributions that interpolates from the poisson distribution and wigner s surmise and apply it to the distributions of the net distance and time gaps among the succeeding cars at different densities of traffic flow the obtained distribution fits the experimental results for single vehicle data of the dutch freeway a9 and the german freeway a5

building confidence interval based fuzzy random regression models in real world regression analysis statistical data may be linguistically imprecise or vague given the co existence of stochastic and fuzzy uncertainty real data cannot be characterized by using only the formalism of random variables in order to address regression problems in the presence of such hybrid uncertain data fuzzy random variables are introduced in this study to serve as an integral component of regression models a new class of fuzzy regression models that is based on fuzzy random data is built and is called the confidence interval based fuzzy random regression model ci frrm first a general fuzzy regression model for fuzzy random data is introduced then using expectations and variances of fuzzy random variables sigma confidence intervals are constructed for fuzzy random input output data the ci frrm is established based on the sigma confidence intervals the proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming therefore we resort to some heuristics finally an illustrative example is provided

two inverse of n free methods for a m n abstract we develop a new representation for the weighted moore penrose inverse a m n of a matrix a from this novel expression we develop a gauss jordan elimination method and a qr based method for the computation of a m n one major feature of our methods is that they do not need to compute the inverse of n thus the new methods are less sensitive than the traditional q method on the conditioning of n the former is suitable for computing the generalized inverses of matrices of low order by hand and the latter is efficient and robust for matrices of high order preliminary numerical testing indicates that the qr based method is faster than the matlab s pinv function for a

metrics and t equalities abstract the relationship between metrics and t equalities is investigated the latter are a special case of t equivalences a natural generalization of the classical concept of an equivalence relation it is shown that in the construction of metrics from t equalities triangular norms with an additive generator play a key role conversely in the construction of t equalities from metrics this role is played by triangular norms with a continuous additive generator or equivalently by continuous archimedean triangular norms these results are then applied to the biresidual operator e t of a triangular norm t it is shown that e t is a t equality on 0 1 if and only if t is left continuous furthermore it is shown that to any left continuous triangular norm t there correspond two particular t equalities on f x the class of fuzzy sets in a given universe x one of these t equalities is obtained from the biresidual operator e t t by means of a natural extension procedure these t equalities then give rise to interesting metrics on f x

matrix refinement type equations abstract taking advantage of perpetuities and the asymptotic behavior of products of random matrices we obtain the direct form of the fourier transform of an l 1 solution of the following random matrix refinement type equation f x det l c f l x m p d where m r p is a random vector and l r p p c r q q are random matrices moreover the dimension of the space of all l 1 solutions of this refinement type equation is examined

evolving granular fuzzy model based control of nonlinear dynamic systems unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process the purpose is to stabilize the closed loop system under changes of the operating conditions and process parameters this paper introduces a model based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention an incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams state feedback control laws and closed loop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy lyapunov function bounded control inputs are also taken into account in the control system design we explain the role of fuzzy granular data and the use of parallel distributed compensation fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown for expositional clarity we consider online modeling and stabilization of the well known lorenz chaos as an illustrative example

statistical behavior of domain systems we study the statistical behavior of two out of equilibrium systems the first one is a quasi one dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions the second one is a one dimensional spin system with nearest neighbor interactions also under the influence of an external driving force both systems show a dynamical scaling with domain formation the statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk we find that the scaling domain size distribution of the gas and the spin systems is well fitted by the wigner surmise which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices however the study of the correlation function of the domain edges shows that the statistical behavior of the domains in both gas and spin systems is not completely well described by a circular orthogonal ensemble nor it is by other models proposed such as the coalescing random walk and the interacting random walk nevertheless we find that a simple model of independent intervals describes more closely the statistical behavior of the domains formed in these systems

gauss jordan elimination methods for the moore penrose inverse of a matrix abstract we present an alternative explicit expression for the moore penrose inverse of a matrix based on this expression we propose a gauss jordan elimination method for the computation of a its computational complexity indicates that this method is more efficient than the existing gauss jordan elimination method in the literature for a large class of problems an example is included to illustrate the new method

cycles and cocycles of fuzzy graphs abstract in this paper we show that if the fuzzy graph is a cycle then it is a fuzzy cycle if and only if is not a fuzzy tree we also examine the relationship between fuzzy bridges and cycles we introduce and examine the concepts of chords twigs 1 chains with boundary zero cycle vectors coboundary and cocycles for fuzzy graphs we show that although the set of cycle vectors fuzzy cycle vectors cocycles and fuzzy cocycles do not necessarily form vector spaces over the field z 2 of integers modulo 2 they nearly do thisallows us to introduce the concepts of fuzzy cycle rank and fuzzy cocycle rank for fuzzy graphs in a meaningful way

should fuzzy equality and similarity satisfy transitivity comments on the paper by m de cock and e kerre this brief paper addresses problems that were raised in the paper fuzzy sets and systems this issue in connection with modelling fuzzy equality and similarity in addition to specific comments to the cited paper we also point out the more fundamental questions underlying this discussion

statistics of atmospheric correlations for a large class of quantum systems the statistical properties of their spectrum show remarkable agreement with random matrix predictions recent advances show that the scope of random matrix theory is much wider in this work we show that the random matrix approach can be beneficially applied to a completely different classical domain namely to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterize the state of atmosphere we show that the spectrum of atmospheric correlation matrices satisfy the random matrix prescription in particular the eigenmodes of the atmospheric empirical correlation matrices that have physical significance are marked by deviations from the eigenvector distribution

a markov process associated with plot size distribution in czech land registry and its number theoretic properties the size distribution of land plots is a result of land allocation processes in the past in the absence of regulation this is a markov process leading an equilibrium described by a probabilistic equation used commonly in the insurance and financial mathematics we support this claim by analyzing the distribution of two plot types garden and build up areas in the czech land registry pointing out the coincidence with the distribution of prime number factors described by dickman function in the first case

scaling behavior near jamming in random sequential adsorption for the random sequential adsorption model we introduce the availability as a new variable corresponding to the number of available locations in which an adsorbate can be accommodated we investigate the relation of the availability to the coverage of the adsorbent surface over time power law scaling between the two is obtained both through numerical simulations and analytical techniques for both one and two dimensional rsa as well as in the case of competitive random sequential adsorption in one dimension

some properties of fuzzy reasoning in propositional fuzzy logic systems in order to analyze the logical foundation of fuzzy reasoning this paper first introduces the concept of generalized roots of theories in lukasiewicz propositional fuzzy logic luk godel propositional fuzzy logic god product propositional fuzzy logic p and nilpotent minimum logic nm the r 0 propositional fuzzy logic l next it is proved that all consequences of a theory c named d c are completely determined by its generalized root whenever c has a generalized root moreover it is proved that every finite theory c has a generalized root which can be expressed by a specific formula finally we demonstrate the existence of a non fuzzy version of fuzzy modus ponens fmp in luk god p and nm l and we provide its numerical version as a new algorithm for solving fmp

measures of specificity over continuous spaces under similarity relations we introduce the concept of specificity and indicate its importance as a measure of uncertainty for information represented using fuzzy sets or possibility distributions we provide formal measures of specificity for variables whose domain is an interval of the real line similarity relations are discussed and formalized the class of width based similarity relations is introduced we extend the measure of specificity to allow for the effect of an underlying similarity relationship the manifestation of this extension for a number of different similarity relations is investigated particularly notable results are obtained for width based similarity relationships more generally we note the connection between the size of a granule of information and its uncertainty motivated by this we investigate the effect of a similarity relationship on the perception of distance in the underlying space and use this to develop an extension of the specificity measure

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

on fuzzification of some concepts of graphs in this paper we will be interested by the extension of the concepts of internal stability external stability not external domination and some of their combination to fuzzy graphs fuzzy sets and fuzzy logical operators are used as basis tools to model these concepts

gaussian determinantal processes a new model for directionality in data determinantal point processes dpps have recently become popular tools for modeling the phenomenon of negative dependence or repulsion in data however our understanding of an analogue of a classical parametric statistical theory is rather limited for this class of models in this work we investigate a parametric family of gaussian dpps with a clearly interpretable effect of parametric modulation on the observed points we show that parameter modulation impacts the observed points by introducing directionality in their repulsion structure and the principal directions correspond to the directions of maximal i e the most long ranged dependency this model readily yields a viable alternative to principal component analysis pca as a dimension reduction tool that favors directions along which the data are most spread out this methodological contribution is complemented by a statistical analysis of a spiked model similar to that employed for covariance matrices as a framework to study pca these theoretical investigations unveil intriguing questions for further examination in random matrix theory stochastic geometry and related topics

modelling gap size distribution of parked cars using random matrix theory abstract we apply the random matrix theory to the car parking problem for this purpose we adopt a coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix the nature of interaction between the particles is consistent with the tendency of the drivers to park their cars near to each other and in the same time keep a distance sufficient for manoeuvring we show that the recently measured gap size distribution of parked cars in a number of roads in central london is well represented by the spacing distribution of a gaussian unitary ensemble

nearest neighbour distances of diffusing particles from a single trap we present a simple method for obtaining the typical smallest distance from an absorbing trap to the nearest particle in a system of brownian particles in terms of the overall density profile we also obtain the distribution function for the minimum distance by using a quasistatic approximation for the diffusion equation we derive new results for two dimensions the characteristic distance to the nearest particle increases asymptotically as m the technique is useful in diffusion reaction systems in the smoluchowski model for bimolecular reactions an ideal spherical trap centred at the origin is surrounded by a cloud of brownian particles which are captured upon contact with the trap the reaction rate in this formulation depends on the spatial distribution of particles about the trap recently interest has focused on finer details of this distribution such as the distance of the nearest surviving particle from the trap l 31 the density distribution function of that distance is the key to several exact results concerning some diffusion reaction systems in one dimension 4 while the spatial density of the particles surrounding the trap can be easily obtained by solving a diffusion equation with the appropriate boundary conditions the distance to the nearest particle from the trap seems to require a more sophisticated analysis 13 in this paper we suggest a simple derivation for the typical distance from the trap to the nearest particle and of the distribution of those distances based upon the more readily attainable spatial density of all particles and simple facts from the statistics of extremes 5 6 to demonstrate our method we rederive the known results for one and three dimensions the simplicity of our approach together with using a quasistatic approximation 7 for solving the diffusion equation allows us to solve the two dimensional case for the first time consider first the one dimensional problem a perfect trap is located at the origin and is initially surrounded by a homogeneous density co of brownian particles which diffuse with a diffusion constant d the density c x t of the surviving particles to the right of the trap is given by the diffusion equation

a note on feller s strong law of large numbers on donne un theoreme qui donne un test integral qui determine les points limites infinis de sn n ceci etend et combine la loi forte des grands nombres de feller 1946 et les resultats de westen 1970 et erickson 1973

on the dempster shafer framework and new combination rules abstract we discuss the basic concepts of the dempster shafer approach basic probability assignments belief functions and probability functions we discuss how to represent various types of knowledge in this framework we discuss measures of entropy and specificity for belief structures we discuss the combination and extension of belief structures we introduce some concerns associated with the dempster rule of combination inherent in the normalization due to conflict we introduce two alternative techniques for combining belief structures the first uses dempster s rule while the second is based upon a modification of this rule we discuss the issue of credibility of a witness

specificity measures based on fuzzy set similarity abstract in this work we propose to define specificity measures on the basis of measures of similarity for fuzzy sets specifically we calculate specificity of a fuzzy set as the similarity between the set and its closest singleton defined on the same domain our contribution is completed by the study of the axiomatic relationship between specificity and similarity measures we also provide several illustrative examples of specificity measures obtained using our approach on the basis of different similarity measures

strong arcs in fuzzy graphs an arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted an arc is strong iff its weight is equal to the strength of connectedness of its end nodes a bridge is strong but a strong arc need not be a bridge an arc of maximum weight is strong but a strong arc need not have maximum weight in a connected graph there is a strong path a path consisting of strong arcs between any two nodes a fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes in a fuzzy tree an arc is strong iff it is a bridge and a strong path between two nodes is a path of maximum strength between them

conditional approach to possibility probability fusion here we are interested in the issue of multisource uncertain information fusion we first consider the problem of fusing multiple possibility distributions in this case we particularly investigate the issue of normalization and suggest a generalized approach to the normalization of conflicting possibility distributions we then look at the fusion of multiple probability distributions we then suggest a framework to fuse probabilistic and possibilistic uncertainty based on the idea of conditioning the probability distribution with respect to the possibility distribution we extend our approach to the case where our information about either of the distributions is imprecise the so called second order uncertainties

voronoi cell patterns theoretical model and applications we use a simple fragmentation model to describe the statistical behavior of the voronoi cell patterns generated by a homogeneous and isotropic set of points in 1d and in 2d in particular we are interested in the distribution of sizes of these voronoi cells our model is completely defined by two probability distributions in 1d and again in 2d the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell in 1d the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel in 2d both distributions depend on a single parameter the fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study we use our model to describe the voronoi cell patterns of several systems specifically we study the island nucleation with irreversible attachment the 1d car parking problem the formation of second level administrative divisions and the pattern formed by the paris metro stations

computation of weighted moore penrose inverse through gauss jordan elimination on bordered matrices abstract in this paper two new algorithms for computing the weighted moore penrose inverse a m n of a general matrix a for weights m and n which are based on elementary row and column operations on two appropriate block partitioned matrices are introduced and investigated the computational complexity of the introduced two algorithms is analyzed in detail these two algorithms proposed in this paper are always faster than those in sheng and chen 2013 and ji 2014 respectively by comparing their computational complexities in the end an example is presented to demonstrate the two new algorithms

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

two renewal theorems for general random walks tending to infinity necessary and sufficient conditions for the existence of moments of the first passage time of a random walk s n into x for fixed x 0 and the last exit time of the walk from x are given under the condition that s n a s the methods which are quite different from those applied in the previously studied case of a positive mean for the increments of s n are further developed to obtain the order of magnitude as x of the moments of the first passage and last exit times when these are finite a number of other conditions of interest in renewal theory are also discussed and some results for the first time for which the random walk remains above the level x on k consecutive occasions which has applications in option pricing are given

generalized random sequential adsorption in one dimension the process of random sequential adsorption in one dimension is generalized so that the rate at which a particle is placed in an empty space is dependent on the size of the space being destroyed and on the sizes of the two spaces created on either side of the particle we write down the equation for this process involving p z the probability of choosing to deposit a particle of size z and f x y mod z the rate at which spaces of length x and y are created from a space of length x y z given that a particle of size z is deposited a scaling theory is given for this process and solutions are presented for two special cases the results of a numerical simulation of a third case are presented

the statistical properties of the city transport in cuernavaca mexico and random matrix ensembles we analyse the statistical properties of the city bus transport in cuernavaca mexico and show that the subsequent bus arrivals display probability distributions conforming to those given by the unitary ensemble of random matrices

exact dynamics of stochastic linear delayed systems application to spatiotemporal coordination of comoving agents delayed dynamics result from finite transmission speeds of a signal in the form of energy mass or information in stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic oscillatory and unstable evolution despite the vast literature quantifying this rich behavior is limited by a lack of explicit analytic studies of high dimensional stochastic delay systems here we fill this gap for systems governed by a linear langevin equation of any number of delays and spatial dimensions with additive gaussian noise by exploiting laplace transforms we are able to derive an exact time dependent analytic solution of the langevin equation by using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables as an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment we propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay we highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and or in their spatial separation we also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay

rehabilitation of the gauss jordan algorithm in this paper a gauss jordan algorithm with column interchanges is presented and analysed we show that in contrast with gaussian elimination the gauss jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability for solutions obtained by gauss jordan with column interchanges a more satisfactory bound for the residual norm can be given the analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by gaussian elimination and that in most practical situations the residuals are equally small this is confirmed by numerical experiments moreover timing experiments on a cyber 205 vector computer show that the algorithm presented has good vectorisation properties

discussion from imprecise to granular probabilities gert de cooman s work is an important contribution to a better understanding of how to deal with imprecise probabilities but there is an important issue which is not addressed how can imprecise probabilites be dealt with not in isolation but in the broader context of imprecise probability distributions imprecise events and imprecise relations what is needed for this purpose is the concept of granular probability a probability which is defined in terms of a generalized constraint of the form x isr r where x is the constrained variable r is a constraining realtion of r is an indexing variable which defines the modality of the constraint that is its semantics a few examples are used as illustrations

explicit expressions of the generalized inverses and condensed cramer rules in this paper we obtain an explicit representation of the 2 inverse a 2 t s of a matrix a c m n with the prescribed range t and null space s as special cases new expressions for the moore penrose inverse a and drazin inverse a d are derived through explicit expressions we re derive the condensed cramer rules of werner for minimal norm least squares solution of linear equations ax b and propose two new condensed cramer rules for the unique solution of a class of singular system ax b x r a k b r a k k ind a finally condensed determinantal expressions for a a d a a a a a ndaa d are also presented

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

fuzzy adaptive decentralized output feedback control for large scale nonlinear systems with dynamical uncertainties in this paper an adaptive fuzzy decentralized robust output feedback control approach is proposed for a class of large scale strict feedback nonlinear systems with the unmeasured states the large scale nonlinear systems in this paper are assumed to possess the unstructured uncertainties unmodeled dynamics and unknown high frequency gain sign fuzzy logic systems are used to approximate the unstructured uncertainties k filters are designed to estimate the unmeasured states and a dynamical signal and a special nussbaum gain function are introduced into the control design to solve the problem of unknown high frequency gain sign and dominate unmodeled uncertainties respectively based on the backstepping design and adaptive fuzzy control methods an adaptive fuzzy decentralized robust output feedback control scheme is developed it is proved that the proposed adaptive fuzzy control approach can guarantee that all the signals in the closed loop system are uniformly and ultimately bounded and the tracking errors converge to a small neighborhood of the origin the effectiveness of the proposed approach is illustrated by using simulation results

modelling the gap size distribution of parked cars abstract we have measured the distribution of distances between parked cars in a number of roads in central london we compare the results with models of random sequential adsorption or random car parking models as they are often called our empirical results do not agree with these models and hence we introduce alternative models for the parking process the first model we propose is one where cars can only park if the space is greater than or equal to a chosen minimum size where the extra space can be used for manoeuvering the results of this model suggest that in addition to a deposition process a re positioning process is required to explain our empirical results hence we introduce a further model where at each time step with probability p a car is randomly placed on a line if the space is empty and with probabilty 1 p is placed in a space but then rolls to the nearest parked car so that it is y distance from the nearest car with probability f y we concentrate on two specific probabilities f y and find that for one case the gap size distribution agrees with the empirical results

markov chain of distances between parked cars we describe the distribution of distances between parked cars as a solution of certain markov processes and show that its solution is obtained with the help of a distributional fixed point equation under certain conditions the process is solved explicitly the resulting probability density is compared with the actual parking data measured in the city

gap size distribution functions of a random sequential adsorption model of segments on a line we performed extensive simulations accompanied by a detailed study of a two segment size random sequential model on the line we followed the kinetics towards the jamming state but we paid particular attention to the characterization of the jamming state structure in particular we studied the effect of the size ratio on the mean gap size the gap size dispersion gap size skewness and gap size kurtosis at the jamming state we also analyzed the above quantities for the four possible segment to segment gap types we ranged the values of the size ratio from one to twenty in the limit of a size ratio of one one recovers the classical car parking problem we observed that at low size ratios the jamming state is constituted by short streaks of small and large segments while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment this view of the jamming state structure as a function of the size ratio is supported by the various measured quantities the present work can help provide insight for example on how to minimize the interparticle distance or minimize fluctuations around the mean particle to particle distance

on the specificity of a possibility distribution abstract the specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation as such it is a measure of amount of uncertainty or information we investigate a number of issues related to specificity measures we discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution we describe unifying view for constructing specificity measures we look at the relationship of the specificity of a distribution and its negation we consider the case where the base set is continuous

owa operators in regression problems we consider an application of fuzzy logic connectives to statistical regression we replace the standard least squares least absolute deviation and maximum likelihood criteria with an ordered weighted averaging owa function of the residuals depending on the choice of the weights we obtain the standard regression problems high breakdown robust methods least median least trimmed squares and trimmed likelihood methods as well as new formulations we present various approaches to numerical solution of such regression problems owa based regression is particularly useful in the presence of outliers and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers

fuzzy end nodes in fuzzy graphs we define a fuzzy end node in a fuzzy graph and show that no node can be both a cut node and a fuzzy end node in a fuzzy tree every node is either a cut node or a fuzzy end node but the converse is not true we also show that any nontrivial fuzzy tree has at least two fuzzy end nodes and we characterize fuzzy cycles that have no cut nodes or no fuzzy end nodes

conditional edge fault tolerant hamiltonicity of dual cubes the dual cube is an interconnection network for linking a large number of nodes with a low node degree it uses low dimensional hypercubes as building blocks and keeps the main desired properties of the hypercube a dual cube dc n has n 1 links per node where n is the degree of a cluster n cube and one more link is used for connecting to a node in another cluster in this paper assuming each node is incident with at least two fault free links we show a dual cube dc n contains a fault free hamiltonian cycle even if it has up to 2n 3 link faults the result is optimal with respect to the number of tolerant edge faults

spacing distribution functions for the one dimensional point island model with irreversible attachment we study the configurational structure of the point island model for epitaxial growth in one dimension in particular we calculate the island gap and capture zone distributions our model is based on an approximate description of nucleation inside the gaps nucleation is described by the joint probability density p xy n x y which represents the probability density to have nucleation at position x within a gap of size y our proposed functional form for p xy x y describes excellently the statistical behavior of the system we compare our analytical model with extensive numerical simulations our model retains the most relevant physical properties of the system

some applications of the study of the image of a fuzzy number in this paper we present a characterization of the image of a fuzzy number in terms of the extremes of its level sets then we deduce some consequences we show some relationships between the image of two fuzzy numbers and the images of their usual operations and it is proved that the continuity of some fuzzy numbers is preserved under the usual operations as applications we introduce a fuzzy regression model involving a parametric family of fuzzy semidistances between fuzzy numbers with finite image and an ordering process of fuzzy numbers with compact support that satisfies specificity type properties

full rank representation of generalized inverse at s 2 and its application in this paper we introduce a full rank representation of the generalized inverse a t s 2 of a given complex matrix a which is based on an arbitrary full rank decomposition of g where g is a matrix such that r g t and n g s using this representation we introduce the minor of the generalized inverse a t s 2 as a special case of the minor a determinantal representation of the generalized inverse a t s 2 is obtained as an application we use an example to demonstrate that this representation is correct

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

full rank representations of outer inverses based on the qr decomposition abstract an efficient algorithm for computing a t s 2 inverses of a given constant matrix a based on the qr decomposition of an appropriate matrix w is presented correlations between the derived representation of outer inverses and corresponding general representation based on arbitrary full rank factorization are derived in particular cases we derive representations of 2 4 and 2 3 inverses numerical examples on different test matrices dense or sparse are presented as well as the comparison with several well known methods for computing the moore penrose inverse and the drazin inverse

gauss jordan elimination method for computing outer inverses this paper deals with the algorithm for computing outer inverse with prescribed range and null space based on the choice of an appropriate matrix g and gauss jordan elimination of the augmented matrix g i the advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure for different input matrices in particular we derive representations of the moore penrose inverse the weighted moore penrose inverse the drazin inverse as well as 2 4 and 2 3 inverses numerical examples on different test matrices are presented as well as the comparison with well known methods for generalized inverses computation

discussion further thoughts on possibilistic previsions a rejoinder this is a rejoinder to the comments moral scozzafava utkin zadeh fuzzy sets and systems 2005 by a number of authors on my paper about possibilistic previsions

capture zone areas in submonolayer nucleation effects of dimensionality and short range interactions simulation results for the asymptotic scaled capture zone distribution czd for the case of irreversible nucleation and growth of point islands are presented for substrate dimension d 1 2 3 and 4 and compared with a recent conjecture based on the wigner distribution poor agreement is found between the predicted wigner distributions and the asymptotic czd in the limit of infinite df corresponding to the ratio of monomer hopping rate d to deposition rate f our results also indicate that for d 2 and 3 the asymptotic czd for point islands is independent of model details and dimension however for d 1 and d 4 the resulting distribution is significantly more sharply peaked we also find that in contrast to the island size distribution for which mean field like behavior is observed in d 3 and above the asymptotic czd is significantly broadened by fluctuations even in d 4

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

fuzzy morphisms between graphs a generic definition of fuzzy morphism between graphs gfm is introduced that includes classical graph related problem definitions as sub cases such as graph and subgraph isomorphism the gfm uses a pair of fuzzy relations one on the vertices and one on the edges each relation is a mapping between the elements of two graphs these two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph the theory extends the properties of fuzzy relation to the problem of generic graph correspondence we introduce two complementary interpretations of gfm from which we derive several interesting properties the first interpretation is the generalization of the notion of association compatibility the second is the new notion of edge morphism one immediate application is the introduction of several composition laws each property has a theoretical and a practical interpretation in the problem of graph correspondence that is explained throughout the paper special attention is paid to the formulation of a non algorithmical theory in order to propose a first step towards a unified theoretic framework for graph morphisms

bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

types of arcs in a fuzzy graph the concept of connectivity plays an important role in both theory and applications of fuzzy graphs depending on the strength of an arc this paper classifies arcs of a fuzzy graph into three types namely a strong b strong and d arcs the advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely we analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges fuzzy trees and fuzzy cycles using the concept of a strong b strong and d arcs an arc of a fuzzy tree is a strong if and only if it is an arc of its unique maximum spanning tree also we identify different types of arcs in complete fuzzy graphs

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

quantification of the level of crowdedness for pedestrian movements abstract within the realm of pedestrian research numerous measures have been proposed to estimate the level of crowdedness experienced by pedestrians however within the field of pedestrian traffic flow modelling there does not seem to be consensus on the question which of these measures performs best this paper shows that the shape and scatter within the resulting fundamental diagrams differs a lot depending on the measure of crowdedness used the main aim of the paper is to establish the advantages and disadvantages of the currently existing measures to quantify crowdedness in order to evaluate which measures provide both accurate and consistent results the assessment is not only based on the theoretical differences but also on the qualitative and quantitative differences between the resulting fundamental diagrams computed using the crowdedness measures on one and the same data set the qualitative and quantitative functioning of the classical grid based measure is compared to with the x t measure an exponentially weighted distance measure and a voronoi diagram measure the consistency of relating these measures for crowdedness to the two macroscopic flow variables velocity and flow the computational efficiency and the amount of scatter present within the fundamental diagrams produced by the implementation of the different measures are reviewed it is found that the voronoi diagram and x t measure are the most efficient and consistent measures for crowdedness

a logic with imprecise probabilities and an application to automated reasoning using rewriting techniques a new probabilistic logic for handling imprecise probabilities is introduced implemented in a rewriting system and used to carry out an experiment each well formed formula of the probabilistic logic is labeled with two values that represent possible minimum and maximum probabilities associated with the event related to the unlabeled formula the aim of this logic is to facilitate application of rules to obtain an approximation of the probability interval associated with an event without the necessity of knowing the precise probability of other events the logic is described as a formal theory by means of its language semantics and a proof theory the soundness of the proof theory has been proven rewriting techniques are a powerful method for testing the behavior of a formal proof calculus through translation of calculus inference rules into rewrite rules implementation of the logic rules in a rewriting language such as maude allows an automated reasoning system to be easily obtained which can be consulted by applications we developed a small game application and an experiment to test the application

random sequential adsorption with restructuring in two dimensions a modified version of the random sequential adsorption model for the deposition of spherical particles onto a plane is presented successive particles are added via randomly positioned vertical trajectories and if they do not stick to the plane at first contact follow the path of steepest descent on the previously deposited particles before being adsorbed all particles reaching a stable position in contact with three previously adsorbed particles are removed the limiting coverage is found to be 0 610 56 or 0 000 05 larger than that of the standard rsa model and is shown to be reached exponentially with the number of trials the size distribution of connected clusters of spheres is analysed and is found to exhibit an exponential decay for large cluster sizes

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

on the structure of f indistinguishability operators abstract some properties concerning the structure of f indistinguishability operators are analyzed it is shown that any of such operators is generated by a family of fuzzy subsets this result since it gives the way to construct f indistinguishabilities facilitates new applications of fuzzy relations the links between f indistinguishability operators and a kind of generalized metrics in the unit interval which are also explored are used to define the canonical generators of an f indistinguishability operator that is the fuzzy partition associated with the operator

on the size distribution of poisson voronoi cells abstract poisson voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices although this particular space tessellation is intensively studied by mathematicians in two and three dimensional 3d spaces there is no exact result known for the size distribution of voronoi cells motivated by the simple form of the distribution function in the 1d case a simple and compact analytical formula is proposed for approximating the voronoi cell s size distribution function in the practically important 2d and 3d cases as well denoting the dimensionality of the space by d d 1 2 3 the f y const y 3 d 1 2 exp 3 d 1 y 2 compact form is suggested for the normalized cell size distribution function by using large scale computer simulations the viability of the proposed distribution function is studied and critically discussed

nearest neighbour spacing distributions of the β hermite ensemble of random matrices the evolution with of the distributions of the spacing s between nearest neighbour levels of unfolded spectra of random matrices from the hermite ensemble he is investigated by monte carlo simulations the random matrices from the he are real symmetric and tridiagonal where which can take any positive value is the reciprocal of the temperature in the classical electrostatic interpretation of eigenvalues the distribution of eigenvalues coincide with those of the three classical gaussian ensembles for 1 2 4 the use of the he ensemble results in an incomparable speed up and efficiency of numerical simulations of all spectral characteristics of large random matrices generalized gamma distributions are shown to be excellent approximations of the nearest neighbor spacing nns distributions for any while being still simple they account both for the level repulsion in s when s 0 and for the whole shape of the nns distributions in the range of s which is accessible to experiment or to most numerical simulations the exact nns distribution of the goe 1 is in particular significantly better described by a generalized gamma distribution than it is by the wigner surmise while the best generalized gamma approximation coincides essentially with the wigner surmise for 2 they describe too the evolution of the level repulsion between that of a poisson distribution and that of a goe distribution when increases from 0 to 1 the distribution of ln s related to the electrostatic interaction energy between neighbouring charges is accordingly well approximated by a generalized gumbel distribution for any 0 the distributions of the minimum nn spacing between eigenvalues of matrices from the he obtained both from as calculated eigenvalues and from unfolded eigenvalues are brody distributions which are classically used to characterize the spectral fluctuations of various physical systems

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

using trapezoids for representing granular objects applications to learning and owa aggregation we discuss the role and benefits of using trapezoidal representations of granular information we focus on the use of level sets as a tool for implementing many operations on trapezoidal sets we point out the simplification that the linearity of the trapezoid brings by requiring us to perform operations on only two level sets we investigate the classic learning algorithm in the case when our observations are granule objects represented as trapezoidal fuzzy sets an important issue that arises is the adverse effect that very uncertain observations have on the quality of our estimates we suggest an approach to addressing this problem using the specificity of the observations to control its effect we next consider the owa aggregation of information represented as trapezoids an important problem that arises here is the ordering of the trapezoidal fuzzy sets needed for the owa aggregation we consider three approaches to accomplish this ordering based on the location specificity and fuzziness of the trapezoids from these three different approaches three fundamental methods of ordering are developed one based on the mean of the 0 5 level sets another based on the length of the 0 5 level sets and a third based on the difference in lengths of the core and support level sets throughout this work particular emphasis is placed on the simplicity of working with trapezoids while still retaining a rich representational capability

fuzzy graphs in the evaluation and optimization of networks abstract referring to some predecessing models the paper introduces the concept of fuzzy vertex graphs a way is shown for modeling various quantitatively featurable functional capabilities of computer communication and similar networks it is shown that functional capability of distributed hierarchical multicomponent systems networks can be described by the directed rooted tree model according to the above fuzzy graph idea the problem of optimizing the overall functional capability with given component vertex set is introduced the fuzzy formulae based on the algebraic connectives which are to be optimized are constructed in the main part of the paper a series of results are presented concerning some special however important cases also the hypotheses founded on some computer experiments are formulated finally the application of these results and hypotheses are shown by the example of a distributed communication switching system family being in development in hungary

characterizations of the possibility probability transformations and some applications abstract possibility distributions were proposed by zadeh in 1978 as a useful counterpart to probability distributions transformations between the two distributions have also been studied since then in this study we characterize axiomatically a class of such transformations covering also the arising accumulation transformation aat due to dubois et al moreover some new properties and views at aat are introduced and discussed we also present three interesting applications of possibility probability theory in decision making that involves uncertain decision makings modification and adjustments of the uncertainty degrees and finally evaluation of the utilities of the uncertain information represented by the possibility distributions

constant net time headway as a key mechanism behind pedestrian flow dynamics we show that keeping a constant lower limit on the net time headway is the key mechanism behind the dynamics of pedestrian streams there is a large variety in flow and speed as functions of density for empirical data of pedestrian streams obtained from studies in different countries the net time headway however stays approximately constant over all these different data sets by using this fact we demonstrate how the underlying dynamics of pedestrian crowds naturally follows from local interactions this means that there is no need to come up with an arbitrary fit function with arbitrary fit parameters as has traditionally been done further by using not only the average density values but the variance as well we show how the recently reported stop and go waves helbing et al phys rev e 75 046109 2007 emerge when local density variations take values exceeding a certain maximum global average density which makes pedestrians stop

the bipancycle connectivity of the hypercube paths and cycles are popular interconnection networks due to their simplicity and low degrees and therefore an efficient way of embedding them into an interconnection network is of particular importance many path embedding aspects and cycle embedding aspects such as hamiltonicity hamiltonian connectivity panconnectivity bipanconnectivity pancyclicity vertex pancyclicity and edge pancyclicity have been proposed and extensively studied in fact these discussions are meaningful for interconnection networks of resource allocated systems or heterogeneous computing systems in this paper we propose a new cycle embedding aspect called bipancycle connectivity that combines the concepts of vertex pancyclicity and bipanconnectivity a bipartite graph is bipancycle connected if an arbitrary pair of vertices x y is contained by common cycles called bipanconnected cycles that include a cycle of every even length ranging from minc x y to n where minc x y denotes the length of the minimum cycle that contains x and y and n is the number of vertices in this paper we introduce a new graph called the cycle of ladders we show that the hypercube is bipancycle connected by presenting algorithms to embed the cycle of ladders into the hypercube

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

an improved method for the computation of the moore penrose inverse matrix abstract in this article we provide a fast computational method in order to calculate the moore penrose inverse of singular square matrices and of rectangular matrices the proposed method proves to be much faster and has significantly better accuracy than the already proposed methods while works for full and sparse matrices

node connectivity and arc connectivity of a fuzzy graph the fuzzy graph approach is more powerful in cluster analysis than the usual graph theoretic approach due to its ability to handle the strengths of arcs effectively the concept of node strength sequence is introduced and is studied in a complete fuzzy graph two new connectivity parameters in fuzzy graphs namely fuzzy node connectivity k and fuzzy arc connectivity k are introduced and obtained the fuzzy analogue of whitney s theorem fuzzy node cut fuzzy arc cut and fuzzy bond are defined fuzzy bond is a special type of a fuzzy bridge it is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode it is shown that k k for a fuzzy tree and it is the minimum of the strengths of its strong arcs the relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph also a new clustering technique based on fuzzy arc connectivity is introduced

the representation and computation of generalized inverse at s 2 this paper presents a novel representation for the generalized inverse a t s 2 based on this we give an algorithm to compute this generalized inverse as an application we use gauss jordan elimination to compute the weighted moore penrose inverse a m n and the drazin inverse a d

strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity models this paper studies the asymptotic properties of the quasi maximum likelihood estimator of generalized autoregressive conditional heteroscedasticity garch 1 1 models without strict stationarity constraints and considers applications to testing problems the estimator is unrestricted in the sense that the value of the intercept which cannot be consistently estimated in the explosive case is not fixed a specific behavior of the estimator of the garch coefficients is obtained at the boundary of the stationarity region but except for the intercept this estimator remains consistent and asymptotically normal in every situation the asymptotic variance is different in the stationary and nonstationary situations but is consistently estimated with the same estimator in both cases tests of strict stationarity and nonstationarity are proposed the tests developed for the classical garch 1 1 model are able to detect nonstationarity in more general garch models a numerical illustration based on stock indices and individual stock returns is proposed

combining uncertain information of differing modalities in this paper we consider approaches for combining separately possibilistic uncertainty probabilistic uncertainty and situations where both forms of uncertainty appear an approach to probability aggregation using rational consensus with equi weighting is developed this aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty the analysis is based on combinations of bounding cases of probability distributions measures of conflict and the effect on information are developed next possibility transformations are used and illustrated by three representative possibility cases the resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before finally a general approach to combining possibility distributions directly using quality criteria is described an example is provided to illustrate the basic possibility distribution aggregation fusion developed

stability of perpetuities for a series of randomly discounted terms we give an integral criterion to distinguish between almost sure absolute convergence and divergence in probability to oo these being the only possible forms of asymptotic behavior this solves the existence problem for a one dimensional perpetuity that remains from a 1979 study by vervaat and yields a complete characterization of the existence of distributional fixed points of a random affine map in dimension one