absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method magnetic induction tomography mit attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils this inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution a regularized gauss newton algorithm has been implemented as a nonlinear iterative inverse solver in this algorithm one needs to solve the forward problem and recalculate the jacobian matrix for each iteration the forward problem has been solved using an edge based finite element method for magnetic vector potential a and electrical scalar potential v a so called a a v formulation a theoretical study of the general inverse eddy current problem and a derivation paying special attention to the boundary conditions of an adjoint field formula for the jacobian is given this efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region this has the advantage that it involves only the inner product of the electric fields when two different coils are excited and these are convenient computationally this paper also shows that the sensitivity maps change significantly when the conductivity distribution changes demonstrating the necessity for a nonlinear reconstruction algorithm the performance of the inverse solver has been examined and results presented from simulated data with added noise

a feti preconditioner for two dimensional edge element approximations of maxwell s equations on nonmatching grids a class of feti methods for the mortar approximation of a vector field problem in two dimensions is proposed edge element discretizations of lowest degree are considered the method proposed can be employed with geometrically conforming and nonconforming partitions our numerical results show that its condition number increases only with the number of unknowns in each subdomain and is independent of the number of subdomains and the size of the problem

modelling a linguistic variable as a hierarchical family of partitions induced by an indistinguishability operator this work shows a method to obtain a hierarchy of partitions on the universe 0 1 in such a way that each of them is compatible with a refinement of lukasiewicz indistinguishability operator the classes of the partition at a given level present a relation of antonymy between them moreover the partition at a certain level can be seen as the refinement of a previous level by means of a class of linguistic modifiers due to this fact they seem appropriate for modeling linguistic labels of a linguistic variable the associated indistinguishability operators show the increasing granularity when the number of classes rises up

solving maxwell s equations in singular domains with a nitsche type method in this paper we propose and analyze a method derived from a nitsche approach for handling boundary conditions in the maxwell equations several years ago the nitsche method was introduced to impose weakly essential boundary conditions in the scalar laplace operator then it has been worked out more generally and transferred to continuity conditions we propose here an extension to vector div curl problems this allows us to solve the maxwell equations particularly in domains with reentrant corners where the solution can be singular we formulate the method for both the electric and magnetic fields and report some numerical experiments

hybrid electric magnetic methods in eddy current problems we discuss a method of approximation of eddy current equations in bounded space that relies on the use of the electric field as primary variable in the conductive parts and of the magnetic field in the air theoretical issues about this hybrid approach are addressed is the problem well posed and one shows that edge elements offer a straightforward way to discretize such formulations the now popular a v method is then shown to come as a variant of this formulation in such a way that it allows the use of standard nodal elements however attention is called on the fact that the numerical convergence of the latter method may be in question

reasoning with graded information in medicine one frequently deals with vague information as a tool for reasoning in this area fuzzy logic suggests itself in this paper we explore the applicability of the basic ideas of fuzzy set theory in the context of medical assessment questionnaires which are commonly used for instance to support the diagnosis of psychological disorders the items of a questionnaire are answered in a graded form patients are asked to choose an element on a linear scale the derived diagnostic hypotheses are graded as well this leads to the question whether there is a logical formalism that is suitable to capture the score calculation of medical assessment questionnaires and thereby provides a mathematical justification of the way in which the calculation is typically done we elaborate two alternative approaches to this problem first we follow the lines of mathematical fuzzy logic for the proposed logic which can deal with the formation of mean values we present a hilbert style deduction system in addition we consider a variant of the prototype approach to vagueness in this case we are led to a framework for which to obtain a logical calculus turns out to be difficult yet our gain is a model that is conceptually comparably well justifiable

edge element formulations of eddy current problems abstract various formulations of eddy current problems in terms of scalar and vector potentials are reviewed in the paper the vector potentials are approximated by edge finite elements and the scalar potentials by nodal ones the formulations are ungauged leading in most cases to singular finite element equations systems special attention is paid to ensuring that the right hand sides of the equations systems are consistent the resulting numerical schemes prove to be as robust as the corresponding coulomb gauged approaches realized by nodal elements

fuzzy sets and sheaves part ii this essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory resp of the theory of complete w valued sets hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect part ii of this series of two papers explains the sheaf theoretic basis of zadeh s operations on fuzzy sets with the exception of the complementation further the quotient problem w r t similarity relations and the quotient problem of fuzzy groups w r t fuzzy congruence relations are solved finally stratified fuzzy topologies are identified with internal topologies on constant sheaves

load balanced diffusive capture process on homophilic scale free networks abstract diffusive capture processes are known to be an effective method for information search on complex networks the biased n lions lamb model provides quick search time by attracting random walkers to high degree nodes where most capture events take place the price of the efficiency is extreme traffic concentration on top hubs we propose traffic load balancing provided by type specific biased random walks for that we introduce a multi type scale free graph generation model which embeds homophily structure into the network by utilizing type dependent random walks we show analytically and with simulations that by augmenting the biased random walk method with a simple type homophily rule we can alleviate the traffic concentration on high degree nodes by spreading the load proportionally between hubs with different types of our generated multi type scale free topologies

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

evaluative linguistic expressions vs fuzzy categories in this paper we discuss the distinction between categories characterized by verbal labels taken from a fuzzy rating scale and special class of linguistic expressions called evaluative the latter form a general class of expressions that includes gradable and evaluative adjectives and their hedges first we will provide a brief linguistic analysis of them then we outline basic principles for construction of the mathematical model of semantics of evaluative expressions in section 3 we will analyze the concepts of rating scale with verbal labels fuzzy rating scale their semantics and demonstrate that the latter cannot be identified with the semantics of evaluative expressions finally we suggest a method for construction of fuzzy rating scales on the basis of evaluative linguistic expressions the main goal of this paper is to demonstrate the power of fuzzy set theory and to show that it is capable of providing tools for advanced modeling of linguistic semantics

continuity issues of the implicational interpretation of fuzzy rules the implicational interpretation of fuzzy rules has received little attention in real world applications so far this is largely due to the fact that ensuring continuity of the resulting function is not a straightforward task this paper targets this subject departing from consistent linguistic descriptions rule bases we introduce sufficient conditions for the continuity of the implicational interpretation with mean of maximum defuzzification we demonstrate that continuity can be achieved under practically feasible conditions regardless of the dimensionality of the input

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

magnetostatic field computations in terms of two component vector potentials in this paper the magnetostatic problem is stated in terms of two component electric and magnetic vector potentials an associated numerical method based on the adoption of edge elements is proposed this procedure overcomes the cancellation problems and the complexity of the interface conditions encountered by similar approaches in the presence of magnetic inhomogeneities and discontinuities of currents and magnetic fields

linguistic characterization of time series the goal of this paper is to provide an overview of applications of special soft computing theories the fuzzy transform and fuzzy natural logic to analysis forecasting and mining information from time series the focus is especially placed on the ability of methods of fuzzy natural logic to provide information in sentences of natural language our approach is based on the decomposition of time series into three components the trend cycle seasonal component and noise the trend cycle is extracted using the f transform and its course is characterized by automatically generated linguistic description the latter is then used to forecast the trend cycle the trend cycle can be furthermore decomposed into trend general tendency and cycle the former is computed again using the f transform moreover the f1 transform makes it possible to estimate the direction of the trend which can then be characterized by expressions of natural language stagnating slightly increasing sharply decreasing etc finally we focus on selected problems of mining information from time series first we suggest an algorithm for finding intervals of monotonous behavior and then show how the theory of intermediate quantifiers a constituent of fuzzy natural logic and generalized aristotle s syllogisms can be applied to automatic summarization of information on time series

multiscale asymptotic method for maxwell s equations in composite materials in this paper we discuss the multiscale analysis of maxwell s equations in composite materials with a periodic microstructure the new contributions in this paper are the determination of higher order correctors and the explicit convergence rate for the approximate solutions see theorem 2 3 consequently we present the multiscale finite element method and derive the convergence result see theorem 4 1 the numerical results demonstrate that higher order correctors are essential for solving maxwell s equations in composite materials

a comprehensive theory of trichotomous evaluative linguistic expressions in this paper a logical theory of the so called trichotomous evaluative linguistic expressions tev expressions is presented these are frequent expressions of natural language such as small very small roughly medium extremely big etc the theory is developed using the formal system of higher order fuzzy logic namely the fuzzy type theory generalization of classical type theory first we discuss informally what are properties of the meaning of tev expressions then we construct step by step axioms of a formal logical theory t e v of tev expressions and prove various properties of t e v all the proofs are syntactical and so our theory is very general we also outline construction of a canonical model of t e v the main elegancy of our theory consists in the fact that semantics of all kinds of evaluative expressions is modeled in a unified way we also prove theorems demonstrating that essential properties of the vagueness phenomenon can be captured within our theory

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

numerical analysis of electric field formulations of the eddy current model this paper deals with finite element methods for the numerical solution of the eddy current problem in a bounded conducting domain crossed by an electric current subjected to boundary conditions involving only data easily available in applications two different cases are considered depending on the boundary data input current intensities or differences of potential weak formulations in terms of the electric field are given in both cases in the first one the input current intensities are imposed by means of integrals on curves lying on the boundary of the domain and joining current entrances and exit in the second one the electric potentials are imposed by means of lagrange multipliers which are proved to represent the input current intensities optimal error estimates are proved in both cases and implementation issues are discussed finally numerical tests confirming the theoretical results are reported

maxwell eigenvalues and discrete compactness in two dimensions abstract we present an elementary proof of the discrete compactness result for a general class of hp finite elements introduced in 1 2 we discuss h convergence of 2d elements only and in this context the results are not new as the analysis of h curl conforming elements for maxwell s equations can be reduced to the long known results for raviart thomas elements 3 the work is based on the result of kikuchi 4 5 for nedelec s edge triangular elements of the lowest order and presents an alternative to techniques presented in 3 6 in particular the present version does not use an inverse inequality argument and therefore is valid for h adaptive meshes we conclude the presentation with a number of 2d computational experiments including nonconvex domains

condensation phenomena of a conserved mass aggregation model on weighted complex networks we investigate the condensation phase transitions of the conserved mass aggregation ca model on weighted scale free networks wsfns in wsfns the weight w ij is assigned to the link between the nodes i and j we consider the symmetric weight given by w ij k i k j alpha on wsfns we numerically show that a certain critical alpha c exists below which the ca model undergoes the same type of condensation transitions as those of the ca model on regular lattices however for alpha or alpha c the condensation always occurs for any density rho and omega we analytically find alpha c gamma 3 2 on the wsfn with the degree exponent gamma to obtain alpha c we analytically derive the scaling behavior of the stationary probability distribution p k infinity of finding a walker at nodes with degree k and the probability d k of finding two walkers simultaneously at the same node with degree k we find p k infinity approximately k alpha 1 gamma and d k approximately k 2 alpha 1 gamma respectively with p k infinity we also show analytically and numerically that the average mass m k on a node with degree k scales as k alpha 1 without any jumps at the maximal degree of the network for any rho as in sfns with alpha 0

the coulomb gauged vector potential formulation for the eddy current problem in general geometry well posedness and numerical approximation in this paper we prove that in a general geometric situation the coulomb gauged vector potential formulation of the eddy current problem for the time harmonic maxwell equations is well posed i e its solution exists and is unique moreover a quasi optimal error estimate for its finite element approximation with nodal elements is proved to illustrate the performances of the finite element algorithm some numerical results are also presented

a formal theory of generalized intermediate syllogisms in this paper we continue developing the formal theory of intermediate quantifiers expressions such as most few almost all a lot of many a great deal of a large part of a small part of the theory is a fuzzy logic formalization of the concept introduced by peterson in his book we will syntactically prove that 105 generalized aristotle s syllogisms introduced in this book are valid in our theory at the same time we will also prove that syllogisms listed there as invalid are invalid also in our theory therefore we believe that our theory provides a reasonable mathematical model of the generalized syllogistics

a singular field method for maxwell s equations numerical aspects for 2d magnetostatics the present paper deals with the solution of maxwell type problems by means of nodal h1 conforming finite elements in a nonconvex piecewise regular domain surrounded by a perfect conductor such a discretization cannot in general approximate the singular behavior of the electromagnetic field near reentrant corners or edges the singular field method consists of adding to the finite element discretization space some particular fields which take into account the singular behavior the latter are deduced from the singular functions associated with the scalar laplace operator the theoretical justification of this approach as well as the analysis of the convergence of the approximation are presented for a very simple model problem arising from magnetostatics in a translation invariant setting but the study can be easily extended to numerous maxwell type problems the numerical implementation of both variants is studied for a domain containing a single reentrant corner

triangular norm based predicate fuzzy logics the paper surveys the present state of knowledge on t norm based predicate fuzzy logics with their double semantics standard the set of truth values being the real interval 0 1 and general with abstract algebras of truth functions

design of natural classification kernels using prior knowledge a new class of kernels has been designed to enhance the usability of prior knowledge prior knowledge is shown to improve the generalization ability of kernel algorithms for binary classification problems the prior knowledge is expressed in natural language via fuzzy rules first the concepts of a fuzzy rule base and prior confidence region are proposed to formulate the prior knowledge then the new kernels which are referred to as natural classification kernels ncks are represented by fuzzy equivalence relations based on the formulation of prior knowledge an nck is interpreted as a measure of similarities between samples it is proven that ncks have two desired properties 1 transitivity with respect to the triangular norms and 2 the ability to provide higher similarities to spatially closer samples from the same class using transitivity a large number of ncks may be directly obtained by means of triangular norms additionally the theoretical results show that the second property makes it possible for the support vector machine svm and convex hull separation algorithm to generalize from training samples to test samples in the prior confidence region finally some synthetic datasets and a benchmark dataset are employed to validate the proposed approach

the theory of intermediate quantifiers in fuzzy natural logic revisited and the model of many abstract the fuzzy natural logic fnl is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language one of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones in our previous papers we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary contradictory subcontrary and subalterns between these quantifiers based on these relations and following peterson s book 62 we were able to suggest a formal model of the 5 square of opposition with intermediate quantifiers this paper picks up the threads of this work and has the following goals it contributes to the development of the theory of fuzzy natural logic first it gets back to some concepts of the theory of evaluative linguistic expressions introduces slight modifications and proves some not yet presented properties furthermore it improves the formal theory of intermediate quantifiers some definitions are made more precise and some new theorems are proved finally it contributes to the theory of the intermediate quantifier many and the analysis of its position in the mentioned 5 square we will show that many manifests an ambiguous relation towards the other quantifiers

a goal oriented adaptive finite element method for 3d scattered airborne electromagnetic method modeling abstractwe have developed a goal oriented adaptive unstructured finite element method based on the scattered field for 3d frequency domain airborne electromagnetic aem modeling to guarantee the em field divergence free within each element and the continuity conditions at electrical material interfaces we have used the edge based shape functions to approximate the electrical field the posterior error for finite element adaptive meshing procedure is estimated from the continuity of the normal component of the current density whereas the influence functions are estimated by solving a dual forward problem because the imaginary part of the scattered current is discontinuous and the real part is continuous we use the latter to estimate the posterior error for the multisources and multifrequencies problem in aem we calculate the weighted posterior error for each element by considering only those transmitter receiver pairs that do not adhere to our convergence criteria finally we add a minimum volume

fuzzy rule base ensemble generated from data by linguistic associations mining as there are many various methods for time series prediction developed but none of them generally outperforms all the others there always exists a danger of choosing a method that is inappropriate for a given time series to overcome such a problem distinct ensemble techniques that combine several individual forecasts are being proposed in this contribution we employ the so called fuzzy rule based ensemble this method is constructed as a linear combination of a small number of forecasting methods where the weights of the combination are determined by fuzzy rule bases based on time series features such as trend seasonality or stationarity for identification of fuzzy rule bases we use the linguistic association mining a huge experimental justification is provided

computation of maxwell singular solution by nodal continuous elements abstract in this paper we propose and analyze a nodal continuous and h 1 conforming finite element method for the numerical computation of maxwell s equations with singular solution in a fractional order sobolev space h r where r may take any value in the most interesting interval 0 1 the key feature of the method is that mass lumping linear finite element l 2 projections act on the curl and divergence partial differential operators so that the singular solution can be sought in a setting of l 2 space we shall use the nodal continuous linear finite elements enriched with one element bubble in each element to approximate the singular and non h 1 solution discontinuous and nonhomogeneous media are allowed in the method some error estimates are given and a number of numerical experiments for source problems as well as eigenvalue problems are presented to illustrate the superior performance of the proposed method

efficient solution of 3d electromagnetic eddy current problems within the finite volume framework of openfoam eddy current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively motivated by realising coupled multi physics simulations we present a new method for the solution of such problems in the finite volume framework of foam extend an extended version of the very popular openfoam software the numerical procedure involves a semi coupled multi mesh approach to solve maxwell s equations for non magnetic materials by means of the coulomb gauged magnetic vector potential a and the electric scalar potential the concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with biot savart s law to achieve a very efficient overall modelling even for complex three dimensional geometries moreover we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity to complement our numerical method an extensive validation is completing the paper which provides insight into the behaviour and the potential of our approach

a singular field method for the solution of maxwell s equations in polyhedral domains it is well known that in the case of a regular domain the solution of the time harmonic maxwell s equations allows a discretization by means of nodal finite elements this is achieved by solving a regularized problem similar to the vector helmholtz equation the present paper deals with the same problem in the case of a nonconvex polyhedron it is shown that a nodal finite element method does not approximate in general the solution to maxwell s equations but actually the solution to a neighboring variational problem involving a different function space indeed the solution to maxwell s equations presents singularities near the edges and corners of the domain that cannot be approximated by lagrange finite elements a new method is proposed involving the decomposition of the solution field into a regular part that can be treated numerically by nodal finite elements and a singular part that has to be taken into account explicitly this singular field method is presented in various situations such as electri

the mortar finite element method for 3d maxwell equations first results in the framework of domain decomposition methods we extend the main ideas of the mortar element method to the numerical solution of maxwell s equations in wave form by h curl conforming finite elements the method we propose turns out to be a new nonconforming nonoverlapping domain decomposition method where nonmatching grids are allowed at the interfaces between subdomains a model problem is considered the convergence of the discrete approximation is analyzed and an error estimate is provided the method is proven to be slightly suboptimal with a loss of a factor scriptstyle sqrt rm ln h with respect to the degree of polynomials in order to achieve this convergence result we nevertheless need extra regularity assumptions on the solution of the continuous problem

convergence and quasi optimality of adaptive finite element methods for harmonic forms numerical computation of harmonic forms typically called harmonic fields in three space dimensions arises in various areas including computer graphics and computational electromagnetics the finite element exterior calculus framework also relies extensively on accurate computation of harmonic forms in this work we study the convergence properties of adaptive finite element methods afem for computing harmonic forms we show that a properly defined afem is contractive and achieves optimal convergence rate beginning from any initial conforming mesh this result is contrasted with related afem convergence results for elliptic eigenvalue problems where the initial mesh must be sufficiently fine in order for afem to achieve any provable convergence rate

extensions of fuzzy relational compositions based on generalized quantifiers abstract the aim of this paper is to extend the fuzzy relational compositions motivated by their applications to medical diagnosis problem by bandler and kohout these compositions employ two quantifiers the universal quantifier and the existential quantifier as there exists a big gap between these two quantifiers that may be appropriately filled in by intermediate generalized quantifiers we take this as a motivation for our study in particular we introduce the concept of fuzzy relational compositions based on generalized quantifiers furthermore we show that the properties that are typically valid for standard fuzzy relational compositions are also valid for the compositions based on generalized quantifiers yet sometimes in a weaken form apart from fuzzy relational compositions the use of generalized quantifiers is also applied to images and preimages of fuzzy sets under fuzzy relations

analysis of generalized square of opposition with intermediate quantifiers abstract in this paper we continue the development of a formal theory of intermediate quantifiers these quantifiers are linguistic expressions such as most many few and almost all and they correspond to what are often called fuzzy quantifiers in the literature in a previous study we demonstrated that 105 generalized syllogisms with intermediate quantifiers are valid in our theory in this paper we turn our attention to another problem which is the analysis of the generalized aristotelian square of opposition which in addition to the classical quantifiers can be extended by several selected intermediate quantifiers we show that the expected relations can be well modeled in our theory our theory is developed within a special higher order fuzzy logic ukasiewicz fuzzy type theory and is very general with a high potential for applications

finite element computation of magnetic field problems with the displacement current the effectiveness of the a method in eddy current problems is widely known on the other hand the demand of high frequency computations increases in this paper a method is applied to finite element approximations for three dimensional high frequency problems with the displacement current numerical results show that a method is more appliable in wide range of frequencies

a hierarchical model of a linguistic variable in this work a theoretical hierarchical model of dichotomous linguistic variables is presented the model incorporates certain features of the approximate reasoning approach and others of the fuzzy control approach to fuzzy linguistic variables it allows sharing of the same hierarchical structure between the syntactic definition of a linguistic variable and its semantic definition given by fuzzy sets this fact makes it easier to build symbolic operations between linguistic terms with a better grounded semantic interpretation moreover the family of fuzzy sets which gives the semantics of each linguistic term constitutes a multiresolution system and thanks to that any fuzzy set can be represented in terms of the set of linguistic terms the model can also be considered a general framework for building more interpretable fuzzy linguistic variables with a high capacity of accuracy which could be used to build more interpretable fuzzy rule based systems frbs

on an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics in this work we propose a new stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations the novelty of this formulation is the fact that it always converges to the physical solution even for singular ones a detailed set of numerical experiments have been performed in order to validate our approach

a logical approach to fuzzy truth hedges the starting point of this paper are the works of hajek and vychodil on the axiomatization of truth stressing and depressing hedges as expansions of hajek s bl logic by new unary connectives they showed that their logics are chain complete but standard completeness was only proved for the expansions over godel logic we propose weaker axiomatizations over an arbitrary core fuzzy logic which have two main advantages i they preserve the standard completeness properties of the original logic and ii any subdiagonal resp superdiagonal non decreasing function on 0 1 preserving 0 and 1 is a sound interpretation of the truth stresser resp depresser connectives hence these logics accommodate most of the truth hedge functions used in the literature about of fuzzy logic in a broader sense

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

type fuzzy quantifiers determined by fuzzy measures on residuated lattices part i basic definitions and examples abstract we study fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals residuated lattices are considered as structures of truth values we present basic notions on fuzzy measures over algebras of fuzzy subsets of a given fuzzy set and the definition and necessary properties of so called fuzzy integrals residuated lattice operations are established to derive operations between fuzzy sets describing degrees in which formulas expressing relations between fuzzy sets are true finally a general definition of type 1 1 fuzzy quantifiers determined by fuzzy measures and integrals is introduced and several examples of important natural language quantifiers are modeled using this approach

a domain decomposition approach for heterogeneous time harmonic maxwell equations the time harmonic maxwell equations for a composite medium which behaves like a conductor in one part and like a perfect insulator in the other one are considered an existence and uniqueness theorem is proven for this degenerate problem in the case of dirichlet boundary conditions a finite element domain decomposition approach is then proposed for the numerical approximation of the exact solution this leads to an iteration by subdomain procedure where at each step a non degenerate boundary value problem has to be solved in each subdomain the convergence of these iterations is proven and the rate of convergence turns out to be independent of the mesh size h showing that the preconditioner implicitly defined by the iteration procedure is optimal

subtypes in fuzzy type theory abstract in this paper we introduce extension of the fuzzy type theory ftt by subtypes this demand arises in situations when for example it is useful to distinguish rational and real numbers where the set of rational numbers is a subset of the reals in the original ftt this causes a problem because we cannot assign rational numbers a special type the solution is to introduce special types for both of them and declare that the former is a subtype of the latter the resulting fuzzy type theory is denoted by sftt when constructing the frame for sftt we must realize that though all the considered functions are total if we take them as functions between subsets then they become partial

the structure of generalized intermediate syllogisms abstract in this paper we continue development of the formal theory of intermediate quantifiers which are expressions of the natural language most many few etc in the previous paper we demonstrated that 105 generalized syllogisms are valid in our theory we introduce the generalization of all the figures and we show that for the proof of validity of all the generalized syllogisms we need to prove the validity of only few of them so that the validity of the other ones immediately follows

reasoning about mathematical fuzzy logic and its future this paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author our goal is to think of the state of the art in mathematical fuzzy logic mfl and to outline some of the tasks on which in the author s opinion mfl should focus in the future in our discussion we will mention not only the basic theory but also its extension called fuzzy logic in broader sense flb the paradigm of the latter is to be the logic of natural human reasoning whose most essential characteristic is the use of natural language besides brief description of flb we will also mention some of its applications on the basis of that we will ponder on other possible directions for research namely the possibility of using fln as a metatheory of fuzzy mathematics as a proper tool for modeling of the main manifestations of the phenomenon of vagueness and as a reasonable tool for developing models of linguistic semantics

deterministic weighted scale free small world networks abstract we propose a deterministic weighted scale free small world model for considering pseudofractal web with the co evolution of topology and weight considering the fluctuations in traffic flow constitute a main reason for congestion of packet delivery and poor performance of communication networks we suggest a recursive algorithm to generate the network which restricts the traffic fluctuations on it effectively during the evolutionary process we provide a relatively complete view of topological structure and weight dynamics characteristics of the networks such as weight and strength distribution degree correlations average clustering coefficient and degree cluster correlations as well as the diameter

a feti domain decomposition method for edge element approximations in two dimensions with discontinuous coefficients a class of finite element tearing and interconnecting feti methods for the edge element approximation of vector field problems in two dimensions is introduced and analyzed first an abstract framework is presented for the analysis of a class of feti methods where a natural coarse problem associated with the substructures is lacking then a family of feti methods for edge element approximations is proposed it is shown that the condition number of the corresponding method is independent of the number of substructures and grows only polylogarithmically with the number of unknowns associated with individual substructures the estimate is also independent of the jumps of both of the coefficients of the original problem numerical results validating our theoretical bounds are given the method and its analysis can be easily generalized to raviart thomas element approximations in two and three dimensions

a correction function method for the wave equation with interface jump conditions abstract in this paper a novel method to solve the constant coefficient wave equation subject to interface jump conditions is presented in general such problems pose issues for standard finite difference solvers as the inherent discontinuity in the solution results in erroneous derivative information wherever the stencils straddle the given interface here however the recently proposed correction function method cfm is used in which correction terms are computed from the interface conditions and added to affected nodes to compensate for the discontinuity in contrast to existing methods these corrections are not simply defined at affected nodes but rather generalized to a continuous function within a small region surrounding the interface as a result the correction function may be defined in terms of its own governing partial differential equation pde which may be solved in principle to arbitrary order of accuracy the resulting scheme is not only arbitrarily high order but also robust having already seen application to poisson problems and the heat equation by extending the cfm to this new class of pdes the treatment of wave interface discontinuities in homogeneous media becomes possible this allows for example for the straightforward treatment of infinitesimal source terms and sharp boundaries free of staircasing errors additionally new modifications to the cfm are derived allowing compatibility with explicit multi step methods such as runge kutta rk4 without a reduction in accuracy these results are then verified through numerous numerical experiments in one and two spatial dimensions

antonyms and linguistic quantifiers in fuzzy logic abstract the paper is a contribution to the theory of fuzzy logic in broader sense flb namely the discussion of linguistic expressions fundamental for it the evaluating linguistic predications the pairs nominal syntagm antonym and the theory of linguistic quantifiers the aim is to develop a theory of natural human reasoning whose characteristic feature is the use of natural language formalism of flb is based on the theory of fuzzy logic in narrow sense with evaluated syntax which provides us means for modelling of the concepts of intension possible world and extension characterization of some of the main properties of the above expressions is provided we also propose a modified definition of the linguistic variable