or and neuron in modeling fuzzy set connectives the paper introduces a neural network based model of logical connectives the basic processing unit consists of two types of generic or and and neurons structured into a three layer topology due to the functional integrity we will be referring to it as an or and neuron the specificity of the logical connectives is captured by the or and neuron within its supervised learning further analysis of the connections of the neuron obtained in this way provides a better insight into the nature of the connectives applied in fuzzy sets by emphasizing their features of locality and interactivity afterward we will study several architectures of neural networks comprising these neurons treated as their basic functional components the numerical studies embrace both the structures formed by single or and neurons and aimed at modeling logical connectives including the zimmermann zysno data set 1980 and the networks representing various decision making architectures we will also propose a realization of a pseudo median filter in which the or and neurons play an ultimate role

optimization schemes for decomposition of fuzzy relations the paper proposes an optimization environment for decomposing fuzzy relations two basic categories of approaches are developed i based on direct gradient oriented optimization methods and ii exploiting the ideas of fuzzy neurocomputation these two approaches are carefully analyzed and contrasted making use of illustrative numerical material some immediate applications to pattern classification and fuzzy interpolation are studied in detail the study includes also some generalizations of the generic decomposition problem

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

fuzzy hough transform and an mlp with fuzzy input output for character recognition abstract a neuro fuzzy system for character recognition using a fuzzy hough transform technique is presented in this paper for each character pattern membership values are determined for a number of fuzzy sets defined on the standard hough transform accumulator cells these basic fuzzy sets are combined by t norms to synthesize additional fuzzy sets whose heights form an n dimensional feature vector for the pattern a 3n dimensional fuzzy linguistic vector is generated from the n dimensional feature vector by defining three linguistic fuzzy sets namely weak moderate and strong the linguistic set membership functions are derived from the butterworth polynomials and are similar to the gain functions of low pass band pass and high pass filters respectively a multilayer perceptron mlp is trained with the fuzzy linguistic vectors by the back propagation of errors the mlp outputs represent fuzzy sets denoting similarity of an input feature vector to a number of character pattern classes recognition accuracy of the system is more than 98

higher order moreau s sweeping process mathematical formulation and numerical simulation in this paper we present an extension of moreau s sweeping process for higher order systems the dynamical framework is carefully introduced qualitative dissipativity stability existence regularity and uniqueness results are given the time discretization of these nonsmooth systems with a time stepping algorithm is also presented this differential inclusion can be seen as a mathematical formulation of complementarity dynamical systems with arbitrary dimension and arbitrary relative degree between the complementary slackness variables applications of such high order sweeping processes can be found in dynamic optimization under state constraints and electrical circuits with ideal diodes

an evolving model of online bipartite networks abstract understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e commerce services nowadays recently various attempts have been tried to propose different models resulting in either power law or exponential degree distributions however many empirical results show that the user degree distribution actually follows a shifted power law distribution the so called mandelbrot s law which cannot be fully described by previous models in this paper we propose an evolving model considering two different user behaviors random and preferential attachment extensive empirical results on two real bipartite networks delicious and citeulike show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions in addition we introduce a structural parameter p to demonstrate that the hybrid user behavior leads to the shifted power law degree distribution and the region of power law tail will increase with the increment of p the proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks

uniqueness of solutions of linear relay systems conditions are given for uniqueness of solutions of linear time invariant systems under relay feedback from a hybrid dynamical point of view this entails the deterministic specification of the discrete transition rules the results are based on the formulation of relay systems as complementarity systems and use the constructive theory of the linear complementarity problem

fuzzy set based models of neurons and knowledge based networks we will introduce and study different fuzzy set oriented computational models of neurons the generic topologies of the neurons emerging there are significantly influenced by basic logic operators and or not encountered in the theory of fuzzy sets the logical flavor of the proposed constructs is expressed in terms of operators used in their formalization and a way of their superposition in the neurons the two broad categories of neurons embrace basic aggregation neurons named and and or neurons and referential processing units such as matching dominance inclusion neurons the specific features of the neurons are flexibly modeled with the aid of triangular norms the inhibitory and excitatory characteristics are captured by embodying direct and complemented negated input signals we will propose various topologies of neural networks put together with the use of these neurons and demonstrate straightforward relationships coming off between the problem specificity and the resulting architecture of the network this limpid way of mapping the domain knowledge onto the structure of the network contributes significantly toward enhancements in learning processes in the network and substantially facilitates its interpretation

absolute stability and the lagrange dirichlet theorem with monotone multivalued mappings abstract this note presents an extension of the absolute stability problem and of the lagrange dirichlet theorem when the nonlinearities entering the model are considered within the class of monotone multivalued mappings consequently including operators with piecewise linear graphs that may represent physical effects like coulomb friction dead zones saturations elasto plasticity and unilateral constraints

brief on solution concepts and well posedness of linear relay systems in this paper we study the well posedness existence and uniqueness of solutions of linear relay systems with respect to two different solution concepts filippov solutions and forward solutions we derive necessary and sufficient conditions for well posedness in the sense of filippov of linear systems of relative degree one and two in closed loop with relay feedback to be precise uniqueness of filippov and also forward solutions follows in this case if the first non zero markov parameter is positive by means of an example it is shown that this intuitively clear condition is not true for systems with relative degree larger than two the influence of the zeno phenomenon an infinite number of relay switching times in a finite length time interval on well posedness is highlighted and although linear relay systems form a rather limited subclass of hybrid dynamical systems the consequences of the presence of the zeno behaviour is typical for many other classes of non smooth and hybrid systems

linear passive systems and maximal monotone mappings this paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set valued relations we first show that such an interconnection can be described by a differential inclusions with a maximal monotone set valued mappings when the underlying linear system is passive and the static relation is maximal monotone based on the classical results on such differential inclusions we conclude that such interconnections are well posed in the sense of existence and uniqueness of solutions finally we investigate conditions which guarantee well posedness but are weaker than passivity

on the existence uniqueness and nature of caratheodory and filippov solutions for bimodal piecewise affine dynamical systems abstract in this paper we deal with the well posedness in the sense of existence and uniqueness of solutions and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting first we show that the conditions guaranteeing uniqueness of filippov solutions in the context of general differential inclusions are quite restrictive when applied to bimodal piecewise affine systems later we present a set of necessary and sufficient conditions for uniqueness of filippov solutions for bimodal piecewise affine systems we also study the so called zeno behavior possibility of infinitely many switchings within a finite time interval for filippov solutions

direct and inverse problem in comparison of fuzzy data abstract discussed is the direct and inverse problem of comparison of two linguistic quantities specified as fuzzy sets relations in the same universe of discourse the proposed way of comparison makes use of some logical properties of connectives and implication operators stemming from the foundations of fuzzy sets a list of plausible equality indices is provided the inverse problem is formulated a set of its solutions is provided direct impacts of the discussed approach on development of fuzzy modelling are clearly indicated also it is pointed out how fuzzy sets of higher type or interval valued sets can be generated as a result of analysis of performance of any fuzzy model

modeling discrete combinatorial systems as alphabetic bipartite networks theory and applications genes and human languages are discrete combinatorial systems dcss in which the basic building blocks are finite sets of elementary units nucleotides or codons in a dna sequence and letters or words in a language different combinations of these finite units give rise to potentially infinite numbers of genes or sentences this type of dcss can be represented as an alphabetic bipartite network abn where there are two kinds of nodes one type represents the elementary units while the other type represents their combinations here we extend and generalize recent analytical findings for abns derived in peruani et al europhys lett 79 28001 2007 and empirically investigate two real world systems in terms of abns the codon gene and the phoneme language network the one mode projections onto the elementary basic units are also studied theoretically as well as in real world abns we propose the use of abns as a means for inferring the mechanisms underlying the growth of real world dcss

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

estimation of fuzzy relational matrix by using probabilistic descent method abstract fuzzy relation and fuzzy relational matrices in particular and a class of fuzzy relational systems become important in many areas of applications like diagnosis of complex systems pattern classification or control the essential task emerging there requires determination of the numerical values of the fuzzy relations in this paper we will look at this as a certain optimization problem and examine the use of a probabilistic descent method especially we will be concerned with the max min composition and its numerical representation that legitimizes the use of the abovementioned algorithm we will propose several approximations to the max and min functions that will allow us to cope with their nondifferentiable characters these modifications pertain both to the functions as well as their derivatives the results of extensive numerical studies are also reported

switching relay and complementarity systems a tutorial on their well posedness and relationships this paper reviews the relationships between switching systems defined from a partition of the state space into convex cells and relay or complementarity dynamical systems which are other classes of discontinuous systems well posedness results i e results on the existence and the uniqueness of solutions for different classes of relay and complementarity systems which are also switching systems are presented the reverse issue when can a switching system be rewritten equivalently as a relay or a complementarity system is also tackled many examples from mechanics circuits and biology illustrate the developments throughout the paper the paper focuses on systems with continuous solutions i e with no state jumps convexity is the central property

fuzzy neural networks with reference neurons as pattern classifiers a heterogeneous neural network consisting of logic neurons and realizing mappings in 0 1 hypercubes is presented the two kinds of neurons studied are utilized to perform matching functions equality or reference neurons and aggregation operations aggregation neurons all computations are driven by logic operations widely used in fuzzy set theory the network is heterogeneous in its nature and includes two types of neurons organized into a structure detecting individual regions of patterns using reference neurons and combining them to yield a final classification decision

technical communique on uniqueness of solutions to relay feedback systems this note deals with the uniqueness of solutions to relay feedback systems and presents an improved criterion over that in lootsma et al automatica 35 3 1999 467

well posedness analysis of switch driven piecewise affine systems the well posedness problem existence and uniqueness of solutions of a class of multi modal piecewise affine systems is addressed where binary switches individually act under autonomous switching first a new transition rule on the discrete state called the switch based transition rule is introduced and some relations with the mode based transition rule are discussed next a sufficient condition for such a multi modal system to be well posed for all external inputs is derived in terms of well posedness of its subsystems of lower complexity bimodal systems finally an easily checkable condition for the bimodal system to be well posed for all external inputs is given which consequently allows us to algebraically determine well posedness of the multi modal systems in question

specificity shift in solving fuzzy relational equations abstract studied is a system of n fuzzy relational equations with a max t composition x k r y k where the input output fuzzy sets x k and y k are available while the fuzzy relation r needs to be determined the solution to these equations is derived through a new paradigm of specificity shift the main objective is to modify a level of specificity of the fuzzy sets relational constraint so that the modified constraints allow for the use of some standard theoretical results of the theory of fuzzy relational equations that otherwise would have been found totally unjustifiable in more detail the specificity of the available input fuzzy sets becomes gradually increased while an opposite tendency is observed for the output fuzzy sets the optimization of the specificity levels is discussed in detail numerical studies are also included finally the use of the specificity shift is discussed in a conjunction with the exploitation of standard gradient based techniques

processing in relational structures fuzzy relational equations abstract the paper provides an overview of methodology for processing fuzzy information in relational structures completed in terms of fuzzy relational equations the origin and the central role of relational calculus in general and fuzzy sets in particular is explained with special emphasis paid to its role and representation capabilities it is pointed out that fuzzy relational equations play a significant role as a platform for a uniform development of techniques in fuzzy sets many of the problems and frameworks developed in fuzzy sets so far can be easily translated into the language of fuzzy relational equations which immediately takes a significant advantage of their solid well developed formalisms techniques and clarity of exposition we will study the role of approximate solutions to fuzzy relational equations as a convenient tool to handle probabilistic type of uncertainty moreover those solutions can easily explain the origin and generate a way in which fuzzy sets of higher generality such as for instance type 2 sets interval valued sets can be algorithmically determined finally we study the role of equations in diverse fields of applications making use of an ample framework of general systems theory

heterogeneous fuzzy logic networks fundamentals and development studies the recent trend in the development of neurofuzzy systems has profoundly emphasized the importance of synergy between the fundamentals of fuzzy sets and neural networks the resulting frameworks of the neurofuzzy systems took advantage of an array of learning mechanisms primarily originating within the theory of neurocomputing and the use of fuzzy models predominantly rule based systems being well established in the realm of fuzzy sets ideally one can anticipate that neurofuzzy systems should fully exploit the linkages between these two technologies while strongly preserving their evident identities plasticity or learning abilities to be shared by the transparency and full interpretability of the resulting neurofuzzy constructs interestingly this synergy still becomes a target yet to be satisfied this study is an attempt to address the fundamental interpretability challenge of neurofuzzy systems our underlying conjecture is that the transparency of any neurofuzzy system links directly with the logic fabric of the system so the logic fundamentals of the underlying architecture become of primordial relevance having this in mind the development of neurofuzzy models hinges on a collection of logic driven processing units named here fuzzy logic neurons these are conceptually simple logic oriented elements that come with a well defined semantics and plasticity owing to their diversity such neurons form essential building blocks of the networks the study revisits the existing categories of logic neurons provides with their taxonomy helps understand their functional features and sheds light on their behavior when being treated as computational components of any neurofuzzy architecture the two main categories of aggregative and reference neurons are deeply rooted in the fundamental operations encountered in the technology of fuzzy sets including logic operations linguistic modifiers and logic reference operations the developed heterogeneous networks come with a well defined semantics and high interpretability which directly translates into the rule based representation of the networks as the network takes advantage of various logic neurons this imposes an immediate requirement of structural optimization which in this study is addressed by utilizing various mechanisms of genetic optimization genetic algorithms we discuss the development of the networks elaborate on the interpretation aspects and include a number of illustrative numeric examples

the rational complementarity problem abstract an extension of the linear complementarity problem lcp of mathematical programming is the so called rational complementarity problem rcp this problem occurs if complementarity conditions are imposed on input and output variables of linear dynamical input state output systems the resulting dynamical systems are called linear complementarity systems since the rcp is crucial both in issues concerning existence and uniqueness of solutions to complementarity systems and in time simulation of complementarity systems it is worthwhile to consider existence and uniqueness questions of solutions to the rcp in this paper necessary and sufficient conditions are presented guaranteeing existence and uniqueness of solutions to the rcp in terms of corresponding lcps using these results and proving that the corresponding lcps have certain properties we can show uniqueness and existence of solutions to linear mechanical systems with unilateral constraints electrical networks with diodes and linear dynamical systems subject to relays and or coulomb friction

complementarity modeling of hybrid systems a complementarity framework is described for the modeling of certain classes of mixed continuous discrete dynamical systems the use of such a framework is well known for mechanical systems with inequality constraints but we give a more general formulation which also applies for instance to switching control systems the main theoretical results in the paper are concerned with uniqueness of smooth continuations the solution of this problem requires the construction of a map from the continuous state to the discrete state a crucial technical tool is the so called linear complementarity problem from mathematical programming and we introduce various generalizations of this problem

reorientation of linear switched systems using state feedback a characterisation is obtained for the controlled and conditioned invariants of a linear switched system under feedback the existence of a maximal consistent subspace with feedback is shown and is computed a few sufficient conditions under which the feedback has no effect on the controlled and conditioned invariants are obtained sufficient conditions for achieving the minimal jump subspace with feedback when it exists were also derived the impossibility of forcing the jump subspace to a trivial subspace with state feedback is shown some sufficient conditions on the feedback for the consistent and jump subspaces to intersect trivially have also been stated

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

exploring the random genesis of co occurrence networks using the network random generation models from gustedt 2009 we simulate and analyze several characteristics such as the number of components the degree sequence and the clustering coefficient of the generated networks this is done for a variety of distributions fixed value bernoulli poisson binomial that are used to control the parameters of generation process these parameters are in particular the size of newly appearing sets of objects the number of contexts in which new elements appear initially the number of objects that are shared with parent contexts and the time period inside which a context may serve as a parent context aging the results show that these models allow to fine tune the generation process such that the graphs adopt properties as they can be found in real world graphs

existence and uniqueness of solutions for a class of piecewise linear dynamical systems we consider the class of dynamical systems that arises when inputs and outputs of a linear system are connected pairwise by means of piecewise linear algebraic relations it is not assumed that these relations define inputs in terms of outputs or vice versa in particular the relations need not be lipschitzian we obtain conditions for existence and uniqueness of solutions of such dynamical systems in the class of piecewise bohl functions

brief paper time scaling symmetry and zeno solutions symmetries are often helpful in reducing the complexity of the analysis of dynamical systems here we discuss a symmetry that combines a transformation in space with a scaling of time examples are given of a number of nonsmooth dynamical systems in which a symmetry of this type occurs the time scaling symmetry can be combined with return mapping analysis to achieve a dimension reduction in addition to the one already obtained from considering the return map the method is applied in a study of zeno behavior in linear systems with relay feedback

fuzzy neural networks a survey abstract in this paper a fuzzy neural network will be a layered feedforward neural net that has fuzzy signals and or fuzzy weights we survey recent results on learning algorithms and applications for fuzzy neural networks

n body decomposition of bipartite author networks in this paper we present a method to project co authorship networks that accounts in detail for the geometrical structure of scientists collaborations by restricting the scope to three body interactions we focus on the number of triangles in the system and show the importance of multi scientist more than two collaborations in the social network this motivates the introduction of generalized networks where basic connections are not binary but involve arbitrary number of components we focus on the three body case and study numerically the percolation transition