regular orbits on symplectic modules let g be a finite group and let v be a faithful kg module k a field the question is does v contain a regular g orbit the problem has been widely studied in the literature in l berger proves that the answer is positive when a is nilpotent c 1 c free for every p and char k 1 a in 6 hargraves drops the condition of being a c c free for odd primes which are not mersenne primes a simplified proof of the main results of hargraves may be found in fleischmann s paper 3 in s gow shows that the conclusion holds when a is nilpotent char k j j a 1 and both 1 a i and char k are odd in io turull studies the case in which a is supersolvable and v is a completely reducible a module theorem 2 2 of lo extends berger s result in z the author studies a particular situation in which char k 1 1 a it is proven that if h k is a p chief factor of a solvable group g p odd and a is a p subgroup of g acting faithfully on h k then h k contains a regular a orbit the nilpotent case is open in this note we suppose that v is endowed with a g invariant nonsingular symplectic form this allows us to obtain stronger results

fuzzy classifier design using genetic algorithms a new method for design of a fuzzy rule based classifier using genetic algorithms gas is discussed the optimal parameters of the fuzzy classifier including fuzzy membership functions and the size and structure of fuzzy rules are extracted from the training data using gas this is done by introducing new representation schemes for fuzzy membership functions and fuzzy rules an effectiveness measure for fuzzy rules is developed that allows for systematic addition or deletion of rules during the ga optimization process a clustering method is utilized for generating new rules to be added when additions are required the performance of the classifier is tested on two real world databases iris and wine and a simulated gaussian database the results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules the performance is also compared to other fuzzy classifiers tested on the same databases

granular prototyping in fuzzy clustering we introduce a logic driven clustering in which prototypes are formed and evaluated in a sequential manner the way of revealing a structure in data is realized by maximizing a certain performance index objective function that takes into consideration an overall level of matching to be maximized and a similarity level between the prototypes the component to be minimized the prototypes identified in the process come with the optimal weight vector that serves to indicate the significance of the individual features coordinates in the data grouping represented by the prototype since the topologies of these groupings are in general quite diverse the optimal weight vectors are reflecting the anisotropy of the feature space i e they show some local ranking of features in the data space having found the prototypes we consider an inverse similarity problem and show how the relevance of the prototypes translates into their granularity

generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

construction of fuzzy models through clustering techniques abstract in this note we will discuss fuzzy models designed with the aid of fuzzy clustering the clustering method utilizes a generalized objective function involving a collection of linear varieties in this way the model is distributed and consists of a series of local linear type models based on the revealed clusters in comparison to the algorithms existing in the literature and producing function like models the proposed one is of a relational character allowing for multidirectional accessibility a detailed identification algorithm is given and illustrated with the aid of numerical examples

temporal and dimensional effects in evolutionary graph theory the spread in time of a mutation through a population is studied analytically and computationally in fully connected networks and on spatial lattices the time t for a favorable mutation to dominate scales with the population size n as n d 1 d in d dimensional hypercubic lattices and as n mathrm ln n in fully connected graphs it is shown that the surface of the interface between mutants and nonmutants is crucial in predicting the dynamics of the system network topology has a significant effect on the equilibrium fitness of a simple population model incorporating multiple mutations and sexual reproduction

a robust self tuning scheme for pi and pd type fuzzy controllers proposes a simple but robust model independent self tuning scheme for fuzzy logic controllers flcs here the output scaling factor sf is adjusted online by fuzzy rules according to the current trend of the controlled process the rule base for tuning the output sf is defined on error e and change of error spl delta e of the controlled variable using the most natural and unbiased membership functions mfs the proposed self tuning technique is applied to both pi and pd type flcs to conduct simulation analysis for a wide range of different linear and nonlinear second order processes including a marginally stable system where even the well known ziegler nichols tuned conventional pi or pid controllers fail to provide an acceptable performance due to excessively large overshoot performances of the proposed self tuning flcs are compared with those of their corresponding conventional flcs in terms of several performance measures such as peak overshoot settling time rise time integral absolute error and integral of time multiplied absolute error in addition to the responses due to step set point change and load disturbance and in each case the proposed scheme shows a remarkably improved performance over its conventional counterpart

fixed point free action on groups of odd order let a be a finite abelian group that acts fixed point freely on a finite solvable group g assume that g is odd and a is of squarefree exponent coprime to 6 we show that the fitting length of g is bounded by the length of the longest chain of subgroups of a

selecting fuzzy if then rules for classification problems using genetic algorithms this paper proposes a genetic algorithm based method for selecting a small number of significant fuzzy if then rules to construct a compact fuzzy classification system with high classification power the rule selection problem is formulated as a combinatorial optimization problem with two objectives to maximize the number of correctly classified patterns and to minimize the number of fuzzy if then rules genetic algorithms are applied to this problem a set of fuzzy if then rules is coded into a string and treated as an individual in genetic algorithms the fitness of each individual is specified by the two objectives in the combinatorial optimization problem the performance of the proposed method for training data and test data is examined by computer simulations on the iris data of fisher

a review and comparison of six reasoning methods abstract five fuzzy reasoning methods are reviewed and their performance is compared with respect to a fuzzy control system model developed by an objective method based on three sets of real life data it is found from the investigation that the reasoning precision the calculation time and the number of possible input states to which a given reasoning method responds differ according to each reasoning method generally the point valued reasoning methods which are based on the assumption that connectives are crisp give better precision and shorter calculation time when the connectives are assumed to be linguistic reasoning with interval valued fuzzy sets are more appropriate to represent linguistic uncertainty for this reason type ii fuzziness generated with interval valued fuzzy sets are better handled with interval valued reasoning methods

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

an output constrained clustering approach for the identification of fuzzy systems and fuzzy granular systems this paper presents an output constrained clustering approach for fuzzy system identification and fuzzy granular system identification the approach is unlike most existing clustering algorithms for structure identification of fuzzy systems where the focus is on input or combined input output clustering the output constrained clustering algorithm divides the output space into several partitions and each output partition is considered to be a constraint then input data are projected into clusters that are based on the input distribution constrained by the output partitions by introducing the key concept of separability of a set of clusters within each output constraint the proposed approach automatically finds an appropriate small and efficient number of clusters for each output constraint to have an appropriate small and efficient number of clusters in each output constraint results in a more compact final system structure and better accuracy this better performance is illustrated by experiments using benchmark function approximation and dynamic system identification

evolutionary dynamics on degree heterogeneous graphs the evolution of two species with different fitness is investigated on degree heterogeneous graphs the population evolves either by one individual dying and being replaced by the offspring of a random neighbor voter model dynamics or by an individual giving birth to an offspring that takes over a random neighbor node invasion process dynamics the fixation probability for one species to take over a population of n individuals depends crucially on the dynamics and on the local environment starting with a single fitter mutant at a node of degree k the fixation probability is proportional to k for voter model dynamics and to 1 k for invasion process dynamics

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

evolutionary dynamics intrinsic noise and cycles of cooperation we use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner s dilemma game we show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues these quasicycles between cooperation and defection have previously been observed in computer simulations here we provide a systematic and comprehensive analytical characterization of their properties we are able to predict their power spectra as a function of the mutation rate and other model parameters and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics we also extend our analysis to the iterated prisoner s dilemma game with a win stay lose shift strategy appropriate in situations where players are subject to errors of the trembling hand type

good action on a finite group abstract let g and a be finite groups with a acting on g by automorphisms in this paper we introduce the concept of good action namely we say the action of a on g is good if h h b c h b for every subgroup b of a and every b invariant subgroup h of g this definition allows us to prove a new noncoprime hall higman type theorem if a is a nilpotent group acting on the finite solvable group g with c g a 1 a long standing conjecture states that h g l a where h g is the fitting height of g and l a is the number of primes dividing the order of a counted with multiplicities as an application of our result we prove the main theorem of this paper which states that the above conjecture is true if a and g have odd order the action of a on g is good and some other fairly general conditions are satisfied

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

a centered formulation of takagi sugeno rules for improved learning efficiency abstract we derive the gradient descent optimization equations for takagi sugeno fuzzy rule bases learning with symmetric triangular membership functions minimum operator as and operator and affine output functions standard sugeno rules a new type of affine output takagi sugeno rules called centred takagi sugeno rules is proposed as proved on a simple example it enables to avoid convergence problems which appear in precisely defined cases especially when there are many rules or when the variation domain of the inputs is not centred around zero gradient descent is tested for the approximation of a specially built one input one output analytical function including a discontinuity and a high curvature point and for the approximation of two input functions test and theoretical results are consistent and show that the proposed method is more efficient when the stated conditions are verified

trade off between accuracy and interpretability experience oriented fuzzy modeling via reduced set vectors this paper focuses on accuracy and interpretability issue of fuzzy model approaches in order to balance the trade off between both of the aspects a new fuzzy model based on experience oriented learning algorithm is proposed firstly support vector regression svr with presented mercer kernels is employed to generate the initial fuzzy model and the available experience on the training data secondly a bottom up simplification algorithm is introduced to generate reduced set vectors for simplifying the structure of the initial fuzzy model at the same time the parameters of the simplified model derived are adjusted by a hybrid learning algorithm including linear ridge regression algorithm and gradient descent method based on a new performance measure finally taking the results from two dimensional sinc function approximation and fuzzy control of the bar and beam system the proposed fuzzy model preserves nice accuracy and interpretability

learning in the framework of fuzzy lattices a basis for rigorous versatile learning is introduced theoretically that is the framework of fuzzy lattices or fl framework for short which proposes a synergetic combination of fuzzy set theory and lattice theory a fuzzy lattice emanates from a conventional mathematical lattice by fuzzifying the inclusion order relation learning in the fl framework can be effected by handling families of intervals where an interval is treated as a single entity block the way explained here illustrations are provided in a lattice defined on the unit hypercube where a lattice interval corresponds to a conventional hyperbox a specific scheme for learning by clustering is presented namely spl sigma fuzzy lattice learning scheme or spl sigma fll scheme for short inspired from adaptive resonance theory art learning by the spl sigma fll is driven by an inclusion measure spl sigma of the corresponding cartesian product to be introduced here we delineate a comparison of the spl sigma fll scheme with various neural fuzzy and other models applications are shown to one medical data set and two benchmark data sets where spl sigma fll s capacity for treating efficiently real numbers as well as lattice ordered symbols separately or jointly is demonstrated due to its efficiency and wide scope of applicability the spl sigma fll scheme emerges as a promising learning scheme

fuzzy rule based models with interactive rules and their granular generalization abstract processing realized in fuzzy rule based models is associated with matching individual rules with the existing input data and aggregation of the levels of matching and conclusions of the rules rules are processed as individual entities in this study we introduce an augmentation of fuzzy models by facilitating interaction among the rules leading to more flexible type membership functions of fuzzy sets forming conditions of the rules thus resulting in substantially advanced topology of the partition of the input space different ways of realizing interaction among the rules are studied in the sequel we develop a granular fuzzy model implied by the rule based model showing how granular parameters of the original rule based model enhance its quality expressed in terms of coverage of experimental data the two evaluation criteria of the constructed granular model namely coverage and specificity are studied experimental results are reported for a series of publicly available data

regular orbits of linear groups with an application to the k gv problem 1 abstract let p be a prime g a finite group of order coprime to p and v a faithful f pg module suppose g has a normal quasi simple irreducible subgroup h we show that either g has a regular orbit on vectors or h is an alternating group and v a minimal module or h n and p are contained in a short explicit list together with the work of robinson and thompson this leads to a solution of the k gv problem for primes p 211

learning control using fuzzified self organizing radial basis function network this note describes an approach to integrating fuzzy reasoning systems with radial basis function rbf networks and shows how the integrated network can be employed as a multivariable self organizing and self learning fuzzy controller in particular by drawing some equivalence between a simplified fuzzy control algorithm sfca and a rbf network we conclude that the rbf network can be interpreted in the context of fuzzy systems and can be naturally fuzzified into a class of more general networks referred to as fbfn with a variety of basis functions not necessarily globally radial synthesized from each dimension by fuzzy logical operators on the other hand as a result of natural generalization from rbf to sfca we claim that the fuzzy system like rbf is capable of universal approximation next the fbfn is used as a multivariable rule based controller but with an assumption that no rule base exists leading to a challenging problem of how to construct such a rule base directly from the control environment we propose a simple and systematic approach to performing this task by using a fuzzified competitive self organizing scheme and incorporating an iterative learning control algorithm into the system we have applied the approach to a problem of multivariable blood pressure control with a fbfn based controller having six inputs and two outputs representing a complicated control structure

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

fuzzy logic approaches to structure preserving dimensionality reduction sammon s 1969 nonlinear projection method is computationally prohibitive for large data sets and it cannot project new data points we propose a low cost fuzzy rule based implementation of sammon s method for structure preserving dimensionality reduction this method uses a sample and applies sammon s method to project it the input data points are then augmented by the corresponding projected output data points the augmented data set thus obtained is clustered with the fuzzy c means fcm clustering algorithm each cluster is then translated into a fuzzy rule to approximate the sammon s nonlinear projection scheme we consider both mamdani assilian and takagi sugeno models for this different schemes of parameter estimation are considered the proposed schemes are applied on several data sets and are found to be quite effective to project new points i e such systems have good predictability

stablization of an inverted pendulum by a high speed fuzzy logic controller hardware system abstract a high speed fuzzy controller hardware system employing min max operations is presented it has fifteen control rule boards and one defuzzifier grades of membership are represented with 0 v 5 v corresponding to 0 0 1 0 this fuzzy controller facilitates approximate reasoning at 1 000 000 fips fuzzy inferences per second and is able to be used for various purposes by programming on each control rule board it handles fuzzy linguistic information of the form nl negative large nm negative medium ns negative small zr approximately zero ps positive small pm positive medium pl positive large and ng negation this fuzzy controller hardware system makes an inverted pendulum stand on a vehicle by using seven control rules two pendulums 5 mm diameter 15 cm length 3 5 g weight respectively 10 mm 50 cm and 50 g can be stabilized by the same rule set it is much easier to produce control rules than to solve the nonlinear differential equations representing the dynamics of an inverted pendulum this fuzzy controller hardware system can be applied to attitude control of a space booster rocket and satellite an automatic aircraft landing system pattern recognition stabilization of nuclear fuel rods in a reactor an intelligent sensor and many other applications which need swift approximate reasoning

a neuro fuzzy system modeling with self constructing rule generationand hybrid svd based learning we propose an approach for neuro fuzzy system modeling a neuro fuzzy system for a given set of input output data is obtained in two steps first the data set is partitioned automatically into a set of clusters based on input similarity and output similarity tests membership functions associated with each cluster are defined according to statistical means and variances of the data points included in the cluster then a fuzzy if then rule is extracted from each cluster to form a fuzzy rule base second a fuzzy neural network is constructed accordingly and parameters are refined to increase the precision of the fuzzy rule base to decrease the size of the search space and to speed up the convergence we develop a hybrid learning algorithm which combines a recursive singular value decomposition based least squares estimator and the gradient descent method the proposed approach has advantages of determining the number of rules automatically and matching membership functions closely with the real distribution of the training data points besides it learns faster consumes less memory and produces lower approximation errors than other methods

evolutionary fuzzy modeling this study is concerned with a general methodology of identification of fuzzy models unlike numeric models fuzzy models operate at a level of information granules fuzzy sets and this aspect brings up an important design requirement of transparency of the model we propose a three phase development framework by distinguishing between structural and parametric optimization processes the underlying topology of the model dwells on fuzzy neural networks architectures governed by fuzzy logic and equipped with parametric flexibility two general optimization mechanisms are explored the structural optimization is realized via genetic programming whereas for the ensuing detailed parametric optimization we proceed with gradient based learning the main advantages of this approach are discussed in detail the study is illustrated with the aid of a numeric example that provides a detailed insight into the performance of the fuzzy models and quantifies crucial design issues

explicit inverses of some tridiagonal matrices abstract we give explicit inverses of tridiagonal 2 toeplitz and 3 toeplitz matrices which generalize some well known results concerning the inverse of a tridiagonal toeplitz matrix

evolutionary games on cycles with strong selection evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success quantified by the probability that a single mutant takes over a population graph structures compared to the well mixed case can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant properties of the associated mean fixation times can be more intricate especially when selection is strong the intuition is that fixation of a beneficial mutant happens fast in a dominance game that fixation takes very long in a coexistence game and that strong selection eliminates demographic noise here we show that these intuitions can be misleading in structured populations we analyze mean fixation times on the cycle graph under strong frequency dependent selection for two different microscopic evolutionary update rules death birth and birth death we establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size depending on the underlying game we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring death birth update in contrast if selection for an offspring occurs before random removal birth death update then strong selection can remove demographic noise almost entirely

an analysis of the fixation probability of a mutant on special classes of non directed graphs there is a growing interest in the study of evolutionary dynamics on populations with some non homogeneous structure in this paper we follow the model of lieberman et al lieberman et al 2005 na

fixed point free action with some regular orbits abstract let the finite group a be acting on a finite solvable group g and suppose that no non trivial element of g is fixed under the action of all the elements of a assume furthermore that a g 1 a long standing conjecture is that then the fitting height of g is bounded by the length of the longest chain of subgroups of a in 3 this was proved in the case where for every proper subgroup b of a and every b invariant elementary abelian section s of g there exists some v s such that c b v c b s we say that b has a regular orbit on s in the present paper we establish the conjecture assuming only that some of these sections have regular orbits

fixation time in evolutionary graphs a mean field approach using an analytical method we calculate average conditional fixation time of mutants in a general graph structured population of two types of species the method is based on markov chains and uses a mean field approximation to calculate the corresponding transition matrix analytical results are compared with the results of simulation of the moran process on a number of network structures

hybridizing genetic algorithms with sharing scheme and evolution strategies for designing approximate fuzzy rule based systems genetic algorithms and evolution strategies are combined in order to build a multi stage hybrid evolutionary algorithm for learning constrained approximate mamdani type knowledge bases from examples the genetic algorithm niche concept is used in two of the three stages composing the learning process with the purpose of improving the accuracy of the designed fuzzy rule based systems the proposed genetic fuzzy rule based system is used to solve an electrical engineering problem and the results obtained are compared with other methods presenting different characteristics

gradual inference rules in approximate reasoning abstract gradual inference rules of the form the more x is f the more y is g or of similar forms with the less instead of the more which express a progressive change of the degree to which the entity y satisfies the gradual property g when the degree to which the entity x satisfies the gradual property f is modified are often encountered in commonsense reasoning a representation of such rules by means of fuzzy sets is proposed and discussed this representation turns out to be based on a special implication function already considered in multiple valued logic patterns of reasoning involving gradual inference rules are formalized their links with interpolation mechanisms are pointed out

analytical calculation of average fixation time in evolutionary graphs the ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics fixation probability and average fixation time aft are two important parameters to quantify this ability in this paper we introduce an analytical approach for exact calculation of aft using this method we obtain aft for two types of evolutionary graphs cycle graph as a highly homogeneous graph and star graph as a highly heterogeneous graph we use symmetries of these graphs to calculate aft analytical results are confirmed with simulation we also examine the effect of adding some random edges to each of these structures

fitness dependence of the fixation time distribution for evolutionary dynamics on graphs evolutionary graph theory models the effects of natural selection and random drift on structured populations of competing mutant and nonmutant individuals recent studies have found that fixation times in such systems often have right skewed distributions little is known however about how these distributions and their skew depend on mutant fitness here we calculate the fitness dependence of the fixation time distribution for the moran birth death process in populations modeled by two extreme networks the complete graph and the one dimensional ring lattice obtaining exact solutions in the limit of large network size we find that with non neutral fitness the moran process on the ring has normally distributed fixation times independent of the relative fitness of mutants and nonmutants in contrast on the complete graph the fixation time distribution is a fitness weighted convolution of two gumbel distributions when fitness is neutral the fixation time distribution jumps discontinuously and becomes highly skewed on both the complete graph and the ring even on these simple networks the fixation time distribution exhibits a rich fitness dependence with discontinuities and regions of universality extensions of our results to two fitness moran models times to partial fixation and evolution on random networks are discussed

a fuzzy clustering based rapid prototyping for fuzzy rule based modeling this paper presents different approaches to the problem of fuzzy rules extraction by using fuzzy clustering as the main tool within these approaches we describe six methods that represent different alternatives in the fuzzy modeling process and how they can be integrated with a genetic algorithms these approaches attempt to obtain a first approximation to the fuzzy rules without any assumption about the structure of the data because the main objective is to obtain an approximation the methods we propose must be as simple as possible but also they must have a great approximative capacity and in that way we work directly with fuzzy sets induced in the variables input space the methods are applied to four examples and the errors obtained are specified in the different cases

rule base self generation and simplification for data driven fuzzy models data driven fuzzy modeling has been used in a wide variety of applications however in fuzzy rule based models acquired from numerical data redundancy often exists in the form of redundant rules or similar fuzzy sets this results in unnecessary structural complexity and decreases the interpretability of the system in this paper a rule base self extraction and simplification method is proposed to establish interpretable fuzzy models from numerical data a fuzzy clustering technique associated with the proposed fuzzy partition validity index is used to extract the initial fuzzy rule base and find out the optimal number of fuzzy rules to reduce the complexity of fuzzy models while keeping good model accuracy some approximate similarity measures are presented and a parameter fine tuning mechanism is introduced to improve the accuracy of the simplified model using the proposed similarity measures the redundant fuzzy rules are removed and similar fuzzy sets are merged to create a common fuzzy set in the rule base the simplified rule base is computationally efficient and linguistically interpretable the approach has been successfully applied to fuzzy models of non linear function approximation dynamical system modeling and mechanical property prediction for hot rolled steels

cluster centric fuzzy modeling in this study we propose a cluster oriented development of fuzzy models an overall design process is focused on an efficient usage of fuzzy clustering fuzzy c means fcm in particular to form information granules clusters that are used in the construction of the fuzzy model fuzzy models are regarded as mappings from information granules expressed in the input and output spaces this position motivates us to look at the development of the models through the perspective of the construction and efficient usage of information granules this study directly associates fuzzy clustering with fuzzy modeling both in terms of conceptual and algorithmic linkages the augmented fcm method is formed predominantly for modeling purposes so that a balance between the structural content present in the input and output spaces is achieved and this way the performance of the resulting fuzzy model is optimized it is shown that the cluster oriented modeling gives rise to the mamdani like fuzzy rules and a zero order takagi sugeno model under a certain decoding scheme we identify an interesting and direct linkage between the developed fuzzy models and a fundamental idea of encoding decoding or granulation degranulation encountered in processing fuzzy sets and granular computing in general furthermore refinements of zero order fuzzy models are investigated leading to first order fuzzy models with linear functions standing in the conclusions of the rules a series of experiments is reported where we used synthetic and real world data using which an issue of generalization capabilities is elaborated in detail

an identification algorithm in fuzzy relational systems abstract the paper presents an effective identification method in fuzzy relational systems we propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques the usefulness of the method provided is demonstrated by means of two numerical examples also a possible way of generating a linguistic decision making algorithm is discussed

direct products of groups and regular orbits abstract we prove the following result let p be a prime and let g be a finite p solvable group that is a direct product of two non cyclic subgroups of coprime order and let v be some faithful irreducible module for g over some field in characteristic p then g has a regular orbit that is there exists some v v such that c g v 1

fuzzy self organizing map abstract kohonen s self organizing map is one of the best known neural network models in this paper we introduce a fuzzy version of the model called fuzzy self organizing map we replace the neurons of the original model by fuzzy rules which are composed of fuzzy sets the fuzzy sets define an area in the input space where each fuzzy rule fires the output of each rule is a singleton the outputs are combined together by a weighted average where the firing strengths of the fuzzy rules act as the weights the weighted average gives a continuous valued output for the system thus the fuzzy self organizing map performs a mapping from a n dimensional input space to one dimensional output space the learning capability of the fuzzy self organizing map enables it to model a continuous valued function to an arbitrary accuracy the learning is done by first self organizing the centers of the fuzzy sets according to kohonen s self organizing map learning laws after that the fuzzy sets and the outputs of the fuzzy rules are initialized finally in the last phase of the new learning method the fuzzy sets are tuned by an algorithm similar to kohonen s learning vector quantization 2 1 simulation results of a two dimensional sinc function show good accuracy and fast convergence

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

a genetic learning process for the scaling factors granularity and contexts of the fuzzy rule based system data base abstract in this contribution we propose a new method to automatically learn the knowledge base of a fuzzy rule based system by finding an appropriate data base using a genetic algorithm and considering a simple generation method to derive the rule base our genetic process learns all the components of the data base number of labels working ranges and membership function shapes for each linguistic variable using a non linear scaling function to adapt the fuzzy partition contexts

ordering distance and closeness of fuzzy sets abstract in dense rule bases where the observation usually overlaps with several antecedents in the rule base various algorithms are used for approximate reasoning and control if the antecedents are located sparsely and the observation does not overlap as a rule with any of the antecedents function approximation techniques combined with the resolution principle lead to applicable conclusions this kind of approximation is possible only if a new concept of ordering and distance i e a metric in the state space and a partial ordering among convex and normal fuzzy sets cnf sets is introduced so the fuzzy distance of two cnf sets can be defined and by this distance closeness and similarity of cnf sets as well

voter models on heterogeneous networks we study simple interacting particle systems on heterogeneous networks including the voter model and the invasion process these are both two state models in which in an update event an individual changes state to agree with a neighbor for the voter model an individual imports its state from a randomly chosen neighbor here the average time t n to reach consensus for a network of n nodes with an uncorrelated degree distribution scales as n ensuremath mu 1 2 ensuremath mu 2 where ensuremath mu k is the k text th moment of the degree distribution quick consensus thus arises on networks with broad degree distributions we also identify the conservation law that characterizes the route by which consensus is reached parallel results are derived for the invasion process in which the state of an agent is exported to a random neighbor we further generalize to biased dynamics in which one state is favored the probability for a single fitter mutant located at a node of degree k to overspread the population char22 the fixation probability char22 is proportional to k for the voter model and to 1 k for the invasion process

logic minimization as an efficient means of fuzzy structure discovery established methods of boolean minimization have previously unseen potential as an efficient and unrestricted means of fuzzy structure discovery becoming particularly useful within a design methodology for the automatic development of fuzzy models traditionally used in digital systems design logic minimization tools allow us to exploit the fundamental links between binary two valued and fuzzy multivalued logic in this paper we show how logic optimization plays an integral role in a two phase fuzzy model design process adaptive logic processing is realized as the discovered boolean structures are augmented with fuzzy granules and then refined by adjusting connections of fuzzy neurons helping to further capture the numeric details of the target systems behavior accurate and highly interpretable fuzzy models are the result of the entire development process

martingales and fixation probabilities of evolutionary graphs evolutionary graph theory is the study of birth death processes that are constrained by population structure a principal problem in evolutionary graph theory is to obtain the probability that some initial population of mutants will fixate on a graph and to determine how that fixation probability depends on the structure of that graph a fluctuating mutant population on a graph can be considered as a random walk martingales exploit symmetry in the steps of a random walk to yield exact analytical expressions for fixation probabilities they do not require simplifying assumptions such as large population sizes or weak selection in this paper we show how martingales can be used to obtain fixation probabilities for symmetric evolutionary graphs we obtain simpler expressions for the fixation probabilities of star graphs and complete bipartite graphs than have been previously reported and show that these graphs do not amplify selection for advantageous mutations under all conditions

fuzzy connective based hierarchical aggregation networks for decision making abstract decision making is usually based on the aggregation of several criteria although the aggregation can be performed at one level in simple cases in more complex situations it becomes necessary that it be performed in a hierarchical manner in a multilevel framework this is particularly true in many engineering applications in this paper we investigate the use of fuzzy connectives in multilayer networks to arrive at appropriate overall aggregation functions the characteristics of suitable fuzzy connectives are studied and an iterative algorithm to determine the type of aggregation function and its parameters at each node in the network is proposed we believe that our aggregation scheme is powerful and flexible since we use several types of aggregation connectives and since the parameters of the network can be determined using a simple algorithm the behavior of the network can also be modified depending on the desired attitude conditions for unique convergence of the algorithm in simple cases are discussed and examples of applications of the method are also presented

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

the fitting length of finite soluble groups ii fixed point free automorphisms abstract let g be a finite soluble group and let h g be the fitting length of g if is a fixed point free automorphism of g that is c g 1 we denote by w the composition length of a long standing conjecture is that h g w and it is known that this bound is always true if the order of g is coprime to the order of in this paper we find some bounds to h g in function of w without assuming that g 1 in particular we prove the validity of the universal bound h g 7 w 2 this improves the exponential bound known earlier from a special case of a theorem of dade