remarks on first and second order periodic boundary value problems on etudie les problemes aux valeurs limites periodiques d ordre 1 et 2 suivants u f t u u 0 u 2 et u f t u u 0 u 2 u 0 u 2 on obtient l existence de solutions extremales comme limites d iterees monotones

robust stabilization of nonlinear multiple time delay large scale systems via decentralized fuzzy control to overcome the effect of modeling errors between nonlinear multiple time delay subsystems and takagi sugeno t s fuzzy models with multiple time delays a robustness design of fuzzy control is proposed in this work in terms of lyapunov s direct method a delay dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time delay large scale systems based on this criterion and the decentralized control scheme a set of model based fuzzy controllers is then synthesized via the technique of parallel distributed compensation pdc to stabilize the nonlinear multiple time delay large scale system finally a numerical example with simulations is given to demonstrate the concepts discussed throughout this work

learning boolean concepts in the presence of many irrelevant features abstract in many domains an appropriate inductive bias is the min features bias which prefers consistent hypotheses definable over as few features as possible this paper defines and studies this bias in boolean domains first it is shown that any learning algorithm implementing the min features bias requires ln l 2 p p ln n e training examples to guarantee pac learning a concept having p relevant features out of n available features this bound is only logarithmic in the number of irrelevant features for implementing the min features bias the paper presents five algorithms that identify a subset of features sufficient to construct a hypothesis consistent with the training examples focus 1 is a straightforward algorithm that returns a minimal and sufficient subset of features in quasi polynomial time focus 2 does the same task as focus 1 but is empirically shown to be substantially faster than focus 1 finally the simple greedy mutual information greedy and weighted greedy algorithms are three greedy heuristics that trade optimality for computational efficiency experimental studies are presented that compare these exact and approximate algorithms to two well known algorithms id3 and fringe in learning situations where many irrelevant features are present these experiments show that contrary to expectations the id3 and fringe algorithms do not implement good approximations of min features the sample complexity and generalization performance of the focus algorithms is substantially better than either id3 or fringe on learning problems where the min features bias is appropriate these experiments also show that among our three heuristics the weighted greedy algorithm provides an excellent approximation to the focus algorithms

fuzzy functions with support vector machines a new fuzzy system modeling fsm approach that identifies the fuzzy functions using support vector machines svm is proposed this new approach is structurally different from the fuzzy rule base approaches and fuzzy regression methods it is a new alternate version of the earlier fsm with fuzzy functions approaches svm is applied to determine the support vectors for each fuzzy cluster obtained by fuzzy c means fcm clustering algorithm original input variables the membership values obtained from the fcm together with their transformations form a new augmented set of input variables the performance of the proposed system modeling approach is compared to previous fuzzy functions approaches standard svm lse methods using an artificial sparse dataset and a real life non sparse dataset the results indicate that the proposed fuzzy functions with support vector machines approach is a feasible and stable method for regression problems and results in higher performances than the classical statistical methods

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

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

periodic boundary value problem for integrodifferential equations of hammerstein type a general comparison result is developed for first order integrodifferential inequality of hammerstein type with periodic boundary condition it is then used to construct monotone sequences to give out the maximal and minimal solutions of a given pbvp of a first order integrodifferential equation of hammerstein type in which the increasingness of the right hand side function in the argument containing the integral operator is not assumed

supervised hierarchical clustering in fuzzy model identification this paper presents a new supervised hierarchical clustering algorithm suhiclust for fuzzy model identification the presented algorithm solves the problem of global model accuracy together with the interpretability of local models as valid linearizations of the modeled nonlinear system the algorithm combines the advantages of supervised hierarchical algorithms which are based on heuristic tree construction algorithms together with the advantages of fuzzy product space clustering the high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm which is independent of initialization and results in a parsimonious fuzzy model furthermore the usability of suhiclust is very undemanding because it delivers in contrast with many other methods reproducible results in order to get reasonable results the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion for fine tuning the interpolation smoothness controls the degree of regularization the performance is illustrated on both analytical examples and benchmark problems from the literature

on the characterizing properties of the permanental polynomials of graphs abstract let g be a graph and a g the adjacency matrix of g the permanental polynomial of g is defined as g x per x i a g if two graphs g and h have the same permanental polynomial then g is called a per cospectral mate of h a graph g is said to be characterized by its permanental polynomial if all the per cospectral mates of g are isomorphic to g it is shown that complete graphs stars regular complete bipartite graphs and odd cycles are characterized by their permanental polynomials we prove that in general the permanental polynomial cannot characterize the paths and even cycles in particular for each l 1 and m 2 we can find non isomorphic per cospectral mates of p 4 l 3 and c 4 m respectively when we restrict our consideration to connected graphs both the paths and even cycles c 4 l 2 are characterized by their permanental polynomials

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

features selection and possibility theory abstract a method is presented that uses both cluster analysis and possibility theory to select the most significant variables in multidimensional data the method is applied to a set of biomedical data from electron spin resonance spectroscopy measurements on patients with a brain injury

permanental polynomials of graphs abstract the first section surveys recent results on the permanental polynomial of a square matrix a i e per xi a the second section concerns the permanental polynomial of the adjacency matrix of a graph the final section is an introduction to the permanental polynomial of the laplacian matrix of a graph an appendix lists some of these latter polynomials

a validity measure for fuzzy clustering the authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c partitions without assumptions as to the number of substructures inherent in the data this function depends on the data set geometric distance measure distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used the function is mathematically justified via its relationship to a well defined hard clustering validity function the separation index for which the condition of uniqueness has already been established the performance of this validity function compares favorably to that of several others the application of this validity function to color image segmentation in a computer color vision system for recognition of ic wafer defects which are otherwise impossible to detect using gray scale image processing is discussed

periodic and almost periodic solutions of volterra integral differential equations with infinite memory abstract conditions are given which guarantee that if t 0 is sufficiently small then x t 0 de s x t s f t has a unique t periodic solution x for each continuous t periodic function f the vectors x and f are n dimensional the matrix function e s is n n with bounded total variation the proof adapts readily to provide an analogous result when x and f are almost periodic functions whose non zero fourier frequencies are bounded away from zero the results are applied to study certain perturbations of the above equation

designing fuzzy inference systems from data an interpretability oriented review fuzzy inference systems fis are widely used for process simulation or control they can be designed either from expert knowledge or from data for complex systems fis based on expert knowledge only may suffer from a loss of accuracy this is the main incentive for using fuzzy rules inferred from data designing a fis from data can be decomposed into two main phases automatic rule generation and system optimization rule generation leads to a basic system with a given space partitioning and the corresponding set of rules system optimization can be done at various levels variable selection can be an overall selection or it can be managed rule by rule rule base optimization aims to select the most useful rules and to optimize rule conclusions space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters structure optimization is of a major importance selecting variables reducing the rule base and optimizing the number of fuzzy sets over the years many methods have become available for designing fis from data their efficiency is usually characterized by a numerical performance index however for human computer cooperation another criterion is needed the rule interpretability an implicit assumption states that fuzzy rules are by nature easy to be interpreted this could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts the paper analyzes the main methods for automatic rule generation and structure optimization they are grouped into several families and compared according to the rule interpretability criterion for this purpose three conditions for a set of rules to be interpretable are defined

cooperative evolutionary learning of linguistic fuzzy rules and parametric aggregation connectors for mamdani fuzzy systems there are two tasks in the design of linguistic fuzzy models for a concrete application the derivation of the linguistic rule base and the setup of the inference system and the defuzzification method traditionally the derivation of the linguistic rule base has been considered the most important task but the use of the appropriate aggregation connectors in the inference system and the defuzzification interface can improve the fuzzy system behavior in this paper we take in consideration this idea we propose an evolutionary learning method to learn a linguistic rule base and the parametric aggregation connectors of the inference and defuzzification in a single step the aim of this methodology is to make possible a high level of positive synergy between the linguistic rule base and the aggregation connectors improving the accuracy of the linguistic mamdani fuzzy systems our proposal has shown good results solving three different applications we introduce a statistical analysis of results for validating the model behavior on the applications used in the experimental study we must remark that we present an experimental study with a double intention a to compare the behavior of the new approach in comparison with those ones that first learn the rule base and then adapt the connectors and b to analyze the rule bases obtained with fixed aggregation connectors and with the adaptive ones for showing the changes on the consequent rules changes on labels that produce a better behavior of the linguistic model than the classic ones

solution of multivariable fuzzy equations abstract a method for the solution of multivariable fuzzy equations and inequalities is proposed the proposed method is an extension of sanchez technique for a single fuzzy equation a numerical example is given

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

disconjugacy disfocality and differentiation with respect to boundary conditions in particular under certain assumptions concerning the disconjugacy or disfocality of 1 we will consider the differentiability of solutions of 1 with respect to boundary conditions both boundary values and boundary points in so doing we will prove an analogue of a theorem of peano s which appears in hartman s text 1 theorem 3 1 p 951 with the consideration therein being with the differentiation of solutions of 1 with respect to initial conditions in this setting given a solution y x of 1 we are also interested in solutions of the linear nth order differential equation

highly unique network descriptors based on the roots of the permanental polynomial in this paper we examine the zeros of permanental polynomials as highly unique network descriptors we employ exhaustively generated networks and demonstrate that our defined graph measures based on the moduli of the zeros of permanental polynomials are quite efficient when distinguishing graphs structurally in this work we continue with a line of research that relates to the search of almost complete graph invariants these highly unique network measures may serve as a powerful tool for tackling graph isomorphism

support vector learning for fuzzy rule based classification systems to design a fuzzy rule based classification system fuzzy classifier with good generalization ability in a high dimensional feature space has been an active research topic for a long time as a powerful machine learning approach for pattern recognition problems the support vector machine svm is known to have good generalization ability more importantly an svm can work very well on a high or even infinite dimensional feature space this paper investigates the connection between fuzzy classifiers and kernel machines establishes a link between fuzzy rules and kernels and proposes a learning algorithm for fuzzy classifiers we first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function fuzzy inference on the if part of a fuzzy rule can be viewed as evaluating the kernel function the kernel function is then proven to be a mercer kernel if the reference functions meet a certain spectral requirement the corresponding fuzzy classifier is named positive definite fuzzy classifier pdfc a pdfc can be built from the given training samples based on a support vector learning approach with the if part fuzzy rules given by the support vectors since the learning process minimizes an upper bound on the expected risk expected prediction error instead of the empirical risk training error the resulting pdfc usually has good generalization moreover because of the sparsity properties of the svms the number of fuzzy rules is irrelevant to the dimension of input space in this sense we avoid the curse of dimensionality finally pdfcs with different reference functions are constructed using the support vector learning approach the performance of the pdfcs is illustrated by extensive experimental results comparisons with other methods are also provided

differentiation of solutions of boundary value problems with respect to nonlinear boundary conditions we consider solutions of boundary value problems for the ordinary differential equation y n x y y y n 1 which satisfy gi y xi yi 1 i n where x1 xn and yi r 1 i n the implicit function theorem is used to establish results in which solutions of the boundary value problems are differentiated with respect to the boundary conditions

an evolving construction scheme for fuzzy systems this paper proposes an evolving construction scheme for fuzzy systems ecsfs ecsfs begins with a simple fuzzy system and evolves its structure by adding more fuzzy terms and rules to achieve a better accuracy in a greedy way an interesting feature of ecsfs is that it is able to automatically locate mathematically meaningful points such as the extremum and inflexion points of the approximated function one by one and then adds fuzzy terms based on these points fuzzy systems with such extreme points like their fuzzy terms are more efficient than other fuzzy systems by using the same number of fuzzy rules as a result ecsfs often achieves a better accuracy for fuzzy system identification compared with the previous methods when using the same number of fuzzy rules a number of simulation results are given to illustrate the advantages of the proposed scheme

on the permanental sum of graphs abstract let g be a graph and a g the adjacency matrix of g the polynomial g x per x i a g is called the permanental polynomial of g and the permanental sum of g is the summation of the absolute values of the coefficients of g x in this paper we investigate properties of permanental sum of a graph prove recursive formulas to compute the permanental sum of a graph and show that the ordering of graphs with respect to permanental sum furthermore we determine the upper and lower bounds of permanental sum of unicyclic graphs and the corresponding extremal unicyclic graphs are also determined

subtractive clustering based modeling of job sequencing with parametric search in this paper an extended subtractive clustering based fuzzy system identification method and the sugeno type reasoning mechanism are used for modeling job sequencing problems this approach can be used to build a fuzzy model of the sequencing system from an existing sequence output data and possible job attributes input data the single machine weighted flowtime problem is used as an example to demonstrate the proposed methodology the effects of data scarcity on the modeling performance is studied by using three data sets with varying degrees of available data furthermore a parametric search on various clustering parameters is performed to identify the best model as a result of parametric search ranges of clustering parameters that provide best models are also identified

on the bivariate permanent polynomials of graphs abstract in 1980 balasubramanian and parthasarathy introduced the bivariate permanent polynomials of graphs and conjectured that this polynomial is a graph characterizing polynomial that is any two graphs with the same bivariate permanent polynomial are isomorphic in this paper we give counterexamples to this conjecture by a computer search furthermore we show that several well known families of graphs are determined by the bivariate permanent polynomial complete graphs complete bipartite graphs regular complete multipartite graphs cycles and their complements

fuzzy c means optimality of solutions and effective termination of the algorithm abstract in this paper the solutions produced by the fuzzy c means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established an equivalent mathematical program is defined for the c means problem utilizing a generalized norm then the properties of the resulting optimization problem are investigated it is shown that the gradient of the resulting objective function at the solution produced by the c means algorithm in this case takes a special structure which can be used in terminating the algorithm moreover the local optimality of the solution obtained is checked utilizing the hessian of the criterion function the solution is a local minimum point if the hessian matrix at this point is positive semidefinite simple rules are proposed to help in checking the definiteness of the matrix

per spectral characterizations of graphs with extremal per nullity abstract a graph g is said to be determined by its permanental spectrum if any graph having the same permanental spectrum as g is isomorphic to g in this paper we introduce the permanental nullity of a graph the multiplicity of the number zero in the permanental spectrum of a graph to study graphs determined by their permanental spectra first we determine all graphs of order n whose permanental nullities are n 2 n 3 n 4 and n 5 respectively then we show that all graphs with the permanental nullity n 2 n 3 or n 5 and all non bipartite graphs with the permanental nullity n 4 are determined by their permanental spectra in particular we prove that the complete bipartite graphs are determined by their permanental spectra

a unified parameterized formulation of reasoning in fuzzy modeling and control a unified parameterized formulation for the reasoning process in fuzzy modeling and control is developed in this paper first by selecting a suitable parameterized family of triangular functions and extending to the n ary operation the parameterized form of mamdani s approximation and formal logical reasoning approaches is introduced next by unifying the inference mechanism for both approaches a unified parameterized reasoning function is developed it is also proved that for crisp input variables the two methods of inference from a set of rules i e first aggregate then infer fati and first infer then aggregate fita generate identical fuzzy outputs the proposed reasoning formulation introduces four reasoning parameters depending on these parameters the reasoning operation varies continuously among the extreme cases in each step of the inference in order to reduce the computational effort a fast algorithm for computing the parameterized family of triangular functions is suggested further a simplified parameterized reasoning formulation is also suggested in which the defuzzified output can be calculated directly from the individual consequent fuzzy sets this simplified formulation is comparable with sugeno s and yager s heuristic simplified reasoning functions some examples demonstrate the validity of the results

enhanced fuzzy system models with improved fuzzy clustering algorithm although traditional fuzzy models have proven to have high capacity of approximating the real world systems they have some challenges such as computational complexity optimization problems subjectivity etc in order to solve some of these problems this paper proposes a new fuzzy system modeling approach based on improved fuzzy functions to model systems with continuous output variable the new modeling approach introduces three features i an improved fuzzy clustering ifc algorithm ii a new structure identification algorithm and iii a nonparametric inference engine the ifc algorithm yields simultaneous estimates of parameters of c regression models together with fuzzy c partitioning of the data to calculate improved membership values with a new membership function the structure identification of the new approach utilizes ifc instead of standard fuzzy c means clustering algorithm to fuzzy partition the data and it uses improved membership values as additional input variables along with the original scalar input variables for two different choices of regression methods least squares estimation or support vector regression to determine ldquofuzzy functionsrdquo for each cluster with novel ifc one could learn the system behavior more accurately compared to other fsm models the nonparametric inference engine is a new approach which uses the alike nearest neighbor method for reasoning empirical comparisons indicate that the proposed approach yields comparable or better accuracy than fuzzy or neuro fuzzy models based on fuzzy rules bases as well as other soft computing methods

design of a new adaptive neuro fuzzy inference system based on a solution for clustering in a data potential field in this study we propose a new method for building adaptive neuro fuzzy inference systems anfis via datasets in order to improve the performance of conventional anfis to handle noisy data we focus on ameliorating the cluster data space established from a given dataset to achieve this we propose a weighted clustering process in the joint input output data space thus during the clustering process the cluster with the smallest potential distance which is a combination of the euclidean distance and the size of the clusters has priority when obtaining the surveyed sample based on this principle we formulate a new algorithm for synthesizing an anfis via the proposed data potential field called anfis pf which has the following features it establishes a data potential field that covers the entire initial data space a cluster data space is built based on the generated data potential field and the anfis is synthesized using this cluster data space finally we performed experiments using datasets with and without noise to demonstrate the effectiveness of the proposed method in several applications including dynamic response noisy datasets obtained from a magnetorheological damper

fuzzy system modeling in pharmacology an improved algorithm in this paper we propose an improved fuzzy system modeling algorithm to address some of the limitations of the existing approaches identified during our modeling with pharmacological data this algorithm differs from the existing ones in its approach to the cluster validity problem i e number of clusters the projection schema i e input membership assignment and rule determination and significant input determination the new algorithm is compared with the bazoon turksen model which is based on the well known sugeno yasukawa approach the comparison was made in terms of predictive performance using two different data sets the first comparison was with a two variable nonlinear function prediction problem and the second comparison was with a clinical pharmacokinetic modeling problem it is shown that the proposed algorithm provides more precise predictions determining the degree of significance for each input variable allows the user to distinguish their relative importance

improved structure optimization for fuzzy neural networks fuzzy neural network based inference systems are well known universal approximators which can produce linguistically interpretable results unfortunately their dimensionality can be extremely high due to an excessive number of inputs and rules which raises the need for overall structure optimization in the literature various input selection methods are available but they are applied separately from rule selection often without considering the fuzzy structure this paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously first a method is developed to select the most significant rules along with a refinement stage to remove unnecessary correlations an improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model leading to a balanced tradeoff between interpretability and accuracy simulation results confirm the efficacy of the proposed method

periodic boundary value problems for nonlinear higher order ordinary differential equations we study a class of boundary value problems for linear and nonlinear ordinary differential equations of higher order we study the solution set and present a maximum principle as a consequence we show the validity of the monotone method and obtain the extremal solutions between the upper and lower solutions

periodic solutions for functional differential equations with infinite lead and delay abstract this paper discusses the existence of periodic solutions for functional differential equations with infinite lead and delay on the basis of fixed point theorems topological degree theories comparison principles and differential inequality methods some general results are proved

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

discrete interval type 2 fuzzy system models using uncertainty in learning parameters fuzzy system modeling fsm is one of the most prominent tools that can be used to identify the behavior of highly nonlinear systems with uncertainty conventional fsm techniques utilize type 1 fuzzy sets in order to capture the uncertainty in the system however since type 1 fuzzy sets express the belongingness of a crisp value x of a base variable x in a fuzzy set a by a crisp membership value mua x they cannot fully capture the uncertainties due to imprecision in identifying membership functions higher types of fuzzy sets can be a remedy to address this issue since the computational complexity of operations on fuzzy sets are increasing with the increasing type of the fuzzy set the use of type 2 fuzzy sets and linguistic logical connectives drew a considerable amount of attention in the realm of fuzzy system modeling in the last two decades in this paper we propose a black box methodology that can identify robust type 2 takagi sugeno mizumoto and linguistic fuzzy system models with high predictive power one of the essential problems of type 2 fuzzy system models is computational complexity in order to remedy this problem discrete interval valued type 2 fuzzy system models are proposed with type reduction in the proposed fuzzy system modeling methods fuzzy c means fcm clustering algorithm is used in order to identify the system structure the proposed discrete interval valued type 2 fuzzy system models are generated by a learning parameter of fcm known as the level of membership and its variation over a specific set of values which generate the uncertainty associated with the system structure

computing the permanental polynomials of graphs let m be an nn matrix with entries mij i j 1 2 n the permanent of m is defined to be per m i 1nmi i where the sum is taken over all permutations of 1 2 n the permanental polynomial of m is defined by per xinm where in is the identity matrix of size n in this paper we give recursive formulas for computing permanental polynomials of the laplacian matrix and the signless laplacian matrix of a graph respectively

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

development of a systematic methodology of fuzzy logic modeling this paper proposes a systematic methodology of fuzzy logic modeling for complex system modeling it has a unified parameterized reasoning formulation an improved fuzzy clustering algorithm and an efficient strategy of selecting significant system inputs and their membership functions the reasoning mechanism introduces 4 parameters whose variation provides a continuous range of inference operation as a result we are no longer restricted to standard extremes in any step of reasoning the fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input output data the fuzzy rules are generated through fuzzy c means fcm clustering major bottlenecks are addressed and analytical solutions are suggested we also address the classification process to extend the derived fuzzy partition to the entire output space in order to select suitable input variables among a finite number of candidates unlike traditional approaches we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required furthermore a clustering technique called fuzzy fine clustering is introduced to assign the input membership functions in order to evaluate the proposed methodology two examples a nonlinear function and a gas furnace dynamic procedure are investigated in detail the significant improvement of the model is concluded compared to other fuzzy modeling approaches

type i and type ii fuzzy system modeling abstract two system modeling approaches are proposed with a unification of fuzzy methodologies type i and type ii knowledge representation are reviewed together with their proposed approximate reasoning schemes type i representation and inference are based on boolean normal forms type i models are myopic because in these models either the disjunctive or the conjunctive boolean normal forms are selected rather arbitrarily for knowledge representation and inference and then they are fuzzified whereas in type ii models representation and inference are based on fuzzy disjunctive and conjunctive normal forms which are derived from the fuzzy truth tables

multipoint boundary value problems for ordinary differential systems solutions u x of the first order system u x u satisfying the multipoint boundary conditions kj 1mju xj r are differentiated with respect to the com components of r and with respect to the boundary points xj where m1 mk are n n constant real matrices r rn and x1 xk

an input output clustering approach to the synthesis of anfis networks a useful neural network paradigm for the solution of function approximation problems is represented by adaptive neuro fuzzy inference systems anfis data driven procedures for the synthesis of anfis networks are typically based on clustering a training set of numerical samples of the unknown function to be approximated some serious drawbacks often affect the clustering algorithms adopted in this context according to the particular data space where they are applied to overcome such problems we propose a new anfis synthesis procedure where clustering is applied in the joint input output data space using this approach it is possible to determine the consequent part of sugeno first order rules and therefore the hyperplanes characterizing the local structure of the function to be approximated successively the fuzzy antecedent part of each rule is determined using a particular fuzzy min max classifier which is based on the adaptive resolution mechanism the generalization capability of the resulting anfis architecture is optimized using a constructive procedure for the automatic determination of the optimal number of rules simulation tests and comparisons with respect to other neuro fuzzy techniques are discussed in the paper in order to assess the efficiency of the proposed approach

right focal point boundary value problems for ordinary differential equations and variational equations where x g x such problems are called right focal point boundary value problems in the last few years a number of papers have appeared dealing with such boundary value problems most notable in the case when 1 is linear are papers by elias 11 muldowney 7 8 and peterson 19 io and for nonlinear considerations the papers by henderson 3 4 jackson 5 and peterson 11 121 in those papers several analogues of known results for conjugate type boundary value problems are considered for eq l we will have need of the hypotheses

a variety of differentiability results for a multi point boundary value problem the goal of this work is to address differentiability of solutions of a nonlinear dynamic system with multi point boundary conditions described by x f t x m 1k mmx tm r where r rn and for each 1 m k mm is an n n constant matrix and tm t the solution of this system is defined on a measure chain t and x denotes a generalized derivative known as the delta derivative