mapping techniques for isogeometric analysis of elliptic boundary value problems containing singularities abstract the method of auxiliary mapping mam introduced by babuska and oh 2 is an effective method for dealing with singularities in elasticity 16 mam was extended to boundary element method bem in the framework of mesh free particle methods 17 reproducing polynomial particle methods 20 and also to infinite domain problems 18 similarly we consider nurbs geometrical mappings that are able to generate crack singularities for isogeometric analysis of elliptic boundary value problems however the mapping techniques proposed in this paper are different from mam in order to generate singular shape functions mam uses conformal mappings that locally change the physical domain whereas the nurbs mappings used for design of engineering system are not allowed to alter the physical domain for isogeometric analysis moreover unlike mam the proposed method makes it possible to independently control the radial and angular direction of the function to be approximated as far as the point singularities are concerned we prove error estimates in sobolev norms and demonstrate that the proposed mapping technique is highly effective for isogeometric analysis of elliptic boundary value problems with singularities mesh refinements to deal with singularities are compared with the mapping technique in the isogeometic analysis framework

axiomatics for fuzzy rough sets abstract a fuzzy t rough set consists of a set x and a t similarity relation r on x where t is a lower semi continuous triangular norm we generalize the farinas prade definition for the upper approximation operator a i x i x of a fuzzy t rough set x r given originally for the special case t min to the case of arbitrary t we propose a new definition for the lower approximation operator a i x i x of x r our definition satisfies the two important identities a a a and a a a as well as a number of other interesting properties we provide axiomatics to fully characterize those upper and lower approximations

multi dimensional fuzzy reasoning this paper suggests a method of multi dimensional fuzzy reasoning concerned with both modus ponens and modus tollens it also discusses an example to show how the method works

on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

fuzzy sets and residuated logic abstract the properties of a set theory rzf defined in a logic weaker than intuitionistic logic are investigated using natural models rzf is intended to act as a framework for fuzzy set theory more general and applicable than heyting valued structures such as topoi the theory rzf contains an interpretation of classical set theory and is consistent relative to this theory it is also a suitable theory for the expression of attributes of uncertainty and vagueness since a certain subclass of the sets definable in this theory are crisp or two valued and behave classically whereas sets in general obey only residuated logic of which the ukasiewicz semantics on 0 1 the real interval is a particular realisation

a computational approach to approximate and plausible reasoning with applications to expert systems the intended purpose of this paper is twofold proposing a common basis for the modeling of uncertainty and imprecision and discussing various kinds of approximate and plausible reasoning schemes in this framework together with probability different kinds of uncertainty measures credibility and plausibility functions in the sense of shafer possibility measures in the sense of zadeh and the dual measures of necessity sugeno s g fuzzy measures are introduced in a unified way the modeling of imprecision in terms of possibility distribution is then presented and related questions such as the measure of the uncertainty of fuzzy events the probability and possibility qualification of statements the concept of a degree of truth and the truth qualification of propositions are discussed at length deductive inference from premises weighted by different kinds of measures by uncertainty or by truth values in the framework of various multivalued logics is fully investigated then deductive inferences from imprecise or fuzzy premises are dealt with patterns of reasoning where both uncertainty and imprecision are present are also addressed the last section is devoted to the combination of uncertain or imprecise pieces of information given by different sources on the whole this paper is a tentative survey of quantitative approaches in the modeling of uncertainty and imprecision including recent theoretical proposals as well as more empirical techniques such as the ones developed in expert systems such as mycin or prospector the management of uncertainty and imprecision in reasoning patterns being a key issue in artificial intelligence

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

cut finite element methods for elliptic problems on multipatch parametric surfaces we develop a finite element method for the laplace beltrami operator on a surface described by a set of patchwise parametrizations the patches provide a partition of the surface and each patch is

fuzzy relational equations with generalized connectives and their applications the idea of fuzzy relational equation with generalized connectives is introduced and algorithms of resolution of this class equations are presented in details it is clearly shown that some types of well known fuzzy relational equations sup min inf max can be treated as special cases of a wise class of equations under discussion applicational aspects are carefully investigated presenting the advantages of the proposed approach

error estimation of perturbations under cri the analysis of stability and robustness of fuzzy reasoning is an important issue in areas like intelligent systems and fuzzy control an interesting aspect is to what extent the perturbation of input in a fuzzy reasoning scheme causes the oscillation of the output in particular when the error limits restrictions of the input values are given what the error limits of the output values are in this correspondence we estimate the upper and lower bounds of the output error affected by the perturbation parameters of the input and obtain the limits of the output values when the input values range over some interval in many fuzzy reasoning schemes under compositional rule of fuzzy inference cri

associatively tied implications we say that an implication operator a on a complete lattice l is associatively tied if there is a binary operation t on l that ties a that is the identity a a gamma a t holds for all in l this property extends to multiple valued logic the following equivalence in classical logic x y z x y z we show that in this case there exists an associative binary operation ta that ties a hence the nomenclature we study properties of that ta when a is associatively tied we then seek a characterization for the validity of associative tiedness for an implication a phrased in terms of a and two adjoints of it

practical inference with systems of gradual implicative rules a general approach to practical inference with gradual implicative rules and fuzzy inputs is presented gradual rules represent constraints restricting outputs of a fuzzy system for each input they are tailored for interpolative reasoning our approach to inference relies on the use of inferential independence it is based on fuzzy output computation under an interval valued input a double decomposition of fuzzy inputs is done in terms of alpha cuts and in terms of a partitioning of these cuts according to areas where only a few rules apply the case of 1 d and 2 d inputs is considered as well as higher dimensional cases an application to a cheese making process illustrates the approach

neuro fuzzy reasoning for occluded object recognition abstract to tackle the problem of occluded object recognition first we give a new interpretation to the multidimensional fuzzy reasoning and then realize that new interpretation through backpropagation type neural network at the learning stage of the neural network fuzzy linguistic statements are used once learned the nonfuzzy features of an occluded object can be classified at the time of classification of the nonfuzzy features of an occluded object we use the concept of fuzzy singleton an effective approach to recognize an unknown scene which consists of a set of occluded objects is to detect a number of significant local features on the boundary of the unknown scene thus the major problems fall into the selection of the appropriate set of features local for representing the object in the training stage as well as in the detection of these features in the recognition process the features should be invariant to scale orientation and minor distortions in boundary shape the performance of the proposed scheme is tested through several examples

the influence of some fuzzy implication operators on the accuracy of a fuzzy model part ii abstract the influence of fuzzy implication operators and the connective also on the accuracy of a fuzzy model of a d c series motor is considered some typical fuzzy implication operators are applied to the construction of a fuzzy model of a d c series motor a root mean square error is used as the criterion of the fuzzy model s adequacy to the real system a number of mathematical operations necessary for the implementation of the fuzzy model are used as the criterion by which the fuzzy model s applicability if estimated from the point of view of computing techniques the best types of fuzzy relations representing fuzzy models of a real system are chosen in order to secure the least root mean square error with minimal number of mathematical operations necessary for computer implementation

convergence analysis of the batch gradient based neuro fuzzy learning algorithm with smoothing l 1 2 regularization for the first order takagi sugeno system abstract it has been proven that takagi sugeno systems are universal approximators and they are applied widely to classification and regression problems the main challenges of these models are convergence analysis and their computational complexity due to the large number of connections and the pruning of unnecessary parameters the neuro fuzzy learning algorithm involves two tasks generating comparable sparse networks and training the parameters in addition regularization methods have attracted increasing attention for network pruning particularly the l q 0 q 1 regularizer after l 1 regularization which can obtain better solutions to sparsity problems the l 1 2 regularizer has a specific sparsity capacity and it is representative of l q 0 q 1 regularizations however the nonsmoothness of the l 1 2 regularizer may lead to oscillations in the learning process in this study we propose a gradient based neuro fuzzy learning algorithm with a smoothing l 1 2 regularization for the first order takagi sugeno fuzzy inference system the proposed approach has the following three advantages i it enhances the original l 1 2 regularizer by eliminating the oscillation of the gradient in the cost function during the training ii it performs better by pruning inactive connections where the number of the redundant connections for removal is higher than that generated by the original l 1 2 regularizer while it is also implemented by simultaneous structure and parameter learning processes and iii it is possible to demonstrate the theoretical convergence analysis of this learning method which we focus on explicitly we also provide a series of simulations to demonstrate that the smoothing l 1 2 regularization can often obtain more compressive representations than the current l 1 2 regularization

a new least squares stabilized nitsche method for cut isogeometric analysis we derive a new stabilized symmetric nitsche method for enforcement of dirichlet boundary conditions for elliptic problems of second order in cut isogeometric analysis cutiga we consider c1 spli

multistage fuzzy inference formulated as linguistic truth value propagation and its learning algorithm based on back propagating error information multistage fuzzy inference where in the consequence in an inference stage is passed to the next stage as a fact is studied and formulated as a type of linguistic truth value propagation based on a concept of linguistic similarities between conditional propositions in successive stages the formulation is useful in studying the characteristics of multistage fuzzy inference and reveals its structural relationship to multilayer perceptrons the learning algorithm for multistage fuzzy inference is then derived using backpropagating error information the algorithm provides a means of automatically training the multistage fuzzy inference network using input output exemplar patterns intermediate membership functions based on simulation results which are generated automatically in the intermediate stage are proposed the intermediate stage fuzzy classifies the input space using intermediate membership functions in this way intermediate membership functions provide information regarding regional characteristics in exemplar patterns

existence and uniqueness of srb measure on c 1 generic hyperbolic attractors let m be a smooth riemannian manifold we show that for c1 generic f in rm diff 1 m if f has a hyperbolic attractor f then there exists a unique srb measure supported on f moreover the srb measure happens to be the unique equilibrium state of potential function psi f in c 0 lambda f defined by psi f x log det df e u x x in lambda f where e u x is the unstable space of txm

the extended generalized finite element method an overview of the method and its applications an overview of the extended generalized finite element method gefm xfem with emphasis on methodological issues is presented this method enables the accurate approximation of solutions that involve jumps kinks singularities and other locally non smooth features within elements this is achieved by enriching the polynomial approximation space of the classical finite element method the gefm xfem has shown its potential in a variety of applications that involve non smooth solutions near interfaces among them are the simulation of cracks shear bands dislocations solidification and multi field problems copyright 2010 john wiley sons ltd

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

on the robustness of type 1 and interval type 2 fuzzy logic systems in modeling research on the robustness of fuzzy logic systems flss an imperative factor in the design process is very limited in the literature specifically when a system is subjected to small deviations of the sampling points operating points it is of great interest to find the maximum tolerance of the system which we refer to as the system s robustness in this paper we present a methodology for the robustness analysis of interval type 2 flss it2 flss that also holds for t1 flss hence making it more general a procedure for the design of robust it2 flss with a guaranteed performance better than or equal to their t1 counterparts is then proposed several examples are performed to demonstrate the effectiveness of the proposed methodologies it was concluded that both t1 and it2 flss can be designed to achieve robust behavior in various applications and preference one or the other in general is application dependant it2 flss having a more flexible structure than t1 flss exhibited relatively small approximation errors in the several examples investigated the methodologies presented in this paper lay the foundation for the design of flss with robust properties that will be very useful in many practical modeling and control applications

empirical measures of partially hyperbolic attractors in this paper we study the limit measures of the empirical measures of lebesgue almost every point in the basin of a partially hyperbolic attractor they are strongly related to a notion named gibbs u state which can be defined in a large class of diffeomorphisms with less regularity and which is the same as pesin sinai s notion for partially hyperbolic attractors of c 1 alpha diffeomorphisms in particular we prove that for partially hyperbolic c 1 alpha diffeomorphisms with one dimensional center and for lebesgue almost every point 1 the center lyapunov exponent is well defined but 2 the sequence of empirical measures may not converge in order to prove 2 we build a diffeomorphism with historical behavior which is transitive contrary to the well known example of bowen we also give some consequences on srb measures and large deviations

perturbation of fuzzy reasoning we propose the concepts of maximum and average perturbations of fuzzy sets and estimate maximum and average perturbation parameters for various methods of fuzzy reasoning

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

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

a generic c1 expanding map has a singular s r b measure we show that for a generic c1 expanding map t of the unit circle there is a unique equilibrium state for log t that is an s r b measure for t and whose statistical basin of attraction has lebesgue measure 1 we also present some results related to the question of whether a generic c1 expanding map preserves a finite measure absolutely continuous with respect to lebesgue measure

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

quadratic maps without asymptotic measure an interval map is said to have an asymptotic measure if the time averages of the iterates of lebesgue measure converge weakly we construct quadratic maps which have no asymptotic measure we also find examples of quadratic maps which have an asymptotic measure with very unexpected properties e g a map with the point mass on an unstable fix point as asymptotic measure the key to our construction is a new characterization of kneading sequences

on pesin s entropy formula for dominated splittings without mixed behavior abstract for c 1 diffeomorphisms we prove that the pesin s entropy formula holds for some invariant measure supported on any topological attractor that admits a dominated splitting without mixed behavior we also prove shub s entropy conjecture for diffeomorphisms having such kind of splittings

a general method for constructing left continuous t norms a new method for constructing left continuous t norms is introduced and analyzed in this paper we shall construct via embedding a left continuous t norm from any countable residuated totally and densely ordered commutative integral monoid moreover we can construct a left continuous t norm from any countable totally ordered commutative integral monoid which is not necessarily densely ordered and residuated a special case the embedding of such monoids on lexicographic product spaces is investigated in detail and several examples are demonstrated the results shed some light to chang s mv algebra to a recently proposed extraordinary t norm and to the standard semantics of the recently introduced logic ii mtl of hajek

graded parametric cutfem and cutiga for elliptic boundary value problems in domains with corners we develop a parametric cut finite element method for elliptic boundary value problems with corner singularities where we have weighted control of higher order derivatives of the solution to a neig

quotients with respect to similarity relations abstract the problem of the quotient w r t a similarity relation is closely related to poincare s paradox and central problems in cluster analysis amazingly this problem remains open for more than 30 years as a generalization of strong m categories we introduce the concept of m valued sets which leads to the definition of the category m set in m set we give a complete solution of the quotient problem

observations on the monoidal t norm logic the paper is a contribution to the theory of the monoidal t norm based logic mtl and stronger logics analogous to the well known extensions of the basic fuzzy logic lukasiewicz godel and product logic main attention is payed to the logic iimtl mtl plus the characteristic axioms ii1 ii2 of product logic

parallel fuzzy inference based on a level sets and generalized means abstract in this paper a parallel fuzzy inference method is proposed in which inference consequences are unified on the basis of level sets and generalized means it has the following advantages over conventional methods 1 it can control the degree to which the fuzziness and specificity of given facts are reflected to those of unified inference consequences 2 it can deduce unified inference consequences in the form of normal and convex fuzzy sets which can thus be treated as fuzzy numbers and 3 it effectively matches systems that include fuzzy set operations based on the extension principle this paper first reviews the generalized mean and describes the computational steps of the proposed inference method then the properties of this method are investigated and the control mechanism of the fuzziness and specificity in unified inference consequences reflecting those in given facts are presented the efficient inference computations are also provided taking advantage of the level set based scheme of the proposed inference method next a learning algorithm is derived for the proposed inference method based on the error back propagation by feeding fuzzy exemplar patterns it can automatically adjust the above mentioned degree of fuzziness and specificity as well as the fuzzy sets in conditional propositions the simulation studies show the feasibility of the proposed inference method

mathematical fuzzy logic as a tool for the treatment of vague information the paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language by a semantics and by a calculus for the derivation of formulas besides this logical approach also a more algebraic approach is discussed and the paper ends with some hints toward applications which are based upon these theoretical considerations

similarity of fuzzy choice functions in this paper two new concepts are introduced the similarity and the d equality of fuzzy choice functions we investigate the way the similarity and d equality behave with respect to some fundamental concepts of fuzzy revealed preference theory

a small set of axioms for residuated logic we show that a set of three axioms together with modus ponens suffices to build up a formal system for the class r of all quadruples l t j in which l is a partially ordered set with a top element and t is a triangular norm on l that has a residuated implication j we show that this r is not a variety

implication operators in fuzzy logic the choice of fuzzy implication as well as other connectives is an important problem in the theoretical development of fuzzy logic and at the same time it is significant for the performance of the systems in which fuzzy logic technique is employed there are mainly two ways in fuzzy logic to define implication operators 1 an implication operator is considered as the residuation of conjunction operator and 2 it is directly defined in terms of negation conjunction and disjunction operators the purpose of this paper is to determine the number of implication operators defined in the second way for some usual negation conjunction and disjunction operators in fuzzy logic

cutfem discretizing geometry and partial differential equations we discuss recent advances on robust unfitted finite element methods on cut meshes these methods are designed to facilitate computations on complex geometries obtained for example from computer

fuzzy logic and meteorological variables a case study of solar irradiance solar irradiance is an extreme case of an uncertain variable when measured on an hourly or shorter time interval in this paper solar irradiance has been considered as a case study for physical fuzzy modelling of a climate variable the uncertainty of the solar irradiance is treated as a fuzzy uncertainty whilst other variables are considered crisp the approach is robust as it does not rely on statistical assumptions and it is a possible alternative to modelling complex systems to our knowledge this is the first time that a physical model of a meteorological variable based on fuzzy numbers has been proposed previous rule based fuzzy meteorological models are only descriptive and cannot be extrapolated to non measured cases when compared with previous non fuzzy models of solar irradiance the fuzzy model shows an improved performance and when compared with experimental data the performance can be evaluated by fuzzy indices that take into account the uncertainty of the data and the model output

enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and or corners summary the mapping method was introduced in jeong et al 2013 for highly accurate isogeometric analysis iga of elliptic boundary value problems containing singularities the mapping method is concerned with constructions of novel geometrical mappings by which push forwards of b splines from the parameter space into the physical space generate singular functions that resemble the singularities in other words the pullback of the singularity into the parameter space by the novel geometrical mapping a non uniform rational basis spline nurbs surface mapping becomes highly smooth one of the merits of iga is that it uses nurbs functions employed in designs for the finite element analysis however push forwards of rational nurbs may not be able to generate singular functions moreover the mapping method is effective for neither the k refinement nor the h refinement in this paper highly accurate stress analysis of elastic domains with cracks and or corners are achieved by enriched iga in which push forwards of nurbs via the design mapping are combined with push forwards of b splines via the novel geometrical mapping the mapping technique in a similar spirit of x fem or gfem we propose three enrichment approaches enriched iga for corners enriched iga for cracks and partition of unity iga for cracks copyright 2013 john wiley sons ltd

a unified real time approximate reasoning approach for use in intelligent control part 1 theoretical development taking account of the fuzzy nature of human decision making processes and real time properties this paper establishes a unified approximate reasoning model based on possibility theory rather than on relational matrix computation both fuzzy and random uncertainties can be coped with in the model in the case of sensor based situations a simpler reasoning scheme is derived by introducing the concepts of matching measures the proposed models may provide another possibility for on line reasoning in real time expert system applications in part 1 the theoretical foundations are provided while in part 2 their application to multivariate blood pressure control is described

limit theorems for partially hyperbolic systems we consider a large class of partially hyperbolic systems containing among others affine maps frame flows on negatively curved manifolds and mostly contracting diffeomorphisms if the rate of mixing is sufficiently high the system satisfies many classical limit theorems of probability theory

algebraic structures in fuzzy logic abstract common features in various fuzzy logical systems are investigated it turns out that adjoint couples and residuated lattices are very often present though not always explicitly expressed some minor new results are also proved

representation and use of imprecise temporal knowledge in dynamic systems abstract in this paper the importance of representation and use of imprecise temporal knowledge for problem solving in industrial dynamic systems is emphasized first a representation of imprecise temporal knowledge is then given for describing the dynamic behavior of systems a novel problem on on line temporal matching and numeric matching is presented and a method for solving this problem is proposed a method for fuzzy proposition reasoning and temporal reasoning is put forward finally as two application examples the fault diagnosis of a fluidized catalytic cracking unit is taken up to illustrate the usefulness of the proposed knowledge representation and methods

robustness of fuzzy reasoning via logically equivalence measure abstract in this paper we discuss robustness of fuzzy reasoning after proposing the definition of perturbation of fuzzy sets based on some logic oriented equivalence measure we present robustness results for various fuzzy logic connectives fuzzy implication operators inference rules and fuzzy reasoning machines and discuss the relations between the robustness of fuzzy reasoning and that of fuzzy conjunction and implication operators the robustness results are presented in terms of equalities of fuzzy sets based on some logic oriented equivalence measure and the maximum of which ensures the corresponding equality holds is derived

robustness of interval valued fuzzy inference since interval valued fuzzy set intuitively addresses not only vagueness lack of sharp class boundaries but also a feature of uncertainty lack of information interval valued fuzzy reasoning plays a vital role in intelligent systems including fuzzy control classification expert systems and so on to utilize interval valued fuzzy inference better it is very important to study the fundamental properties of interval valued fuzzy inference such as robustness in this paper we first discuss the robustness of interval valued fuzzy connectives and then investigate the robustness of interval valued fuzzy reasoning in terms of the sensitivity of interval valued fuzzy connectives and maximum perturbation of interval valued fuzzy sets these results reveal that the robustness of interval valued fuzzy reasoning is directly linked to the selection of interval valued fuzzy connectives

perturbation of fuzzy sets and fuzzy reasoning based on normalized minkowski distances in this paper we extend the concept of the perturbation of fuzzy sets based on normalized minkowski distances and present some new conclusions on perturbation raised by various operations of fuzzy sets these operations are induced by triangular norms and conorms furthermore we discuss the perturbation of fuzzy reasoning

the chaining syllogism in fuzzy logic we analyze the validity of the chaining syllogism in fuzzy systems i e whether two fuzzy rules if f then g and if g then h imply the rule if f then h conditions are given under which this basic deduction scheme holds if a is predicated of all b and b of all c a must necessarily be predicated of all c the chaining syllogism according to aristotle s prior analytics

decay of correlations dedicated to micheline ishay i would like to thank p boyland l chierchia v donnay g de martino c gole j l lebowitz m lyubich m rychlik i g schwarz s vaienti and especially g gallavotti for helpful and enlightening discussions particularly warm thanks go to n chernov for carefully reading and finding a mistake in an early version the present paper benefits from several improvements due to his sharp criticism in addition i am indebted to p collet and most of all m wojtkowski for introducing me to the magical world of cones finally i thank j milnor director of the institute for mathematical sciences at stony brook university where i was visiting during part of this work and the italian c n r gnfm for providing travel funds

unstable entropies and variational principle for partially hyperbolic diffeomorphisms abstract we study entropies caused by the unstable part of partially hyperbolic systems we define unstable metric entropy and unstable topological entropy and establish a variational principle for partially hyperbolic diffeomorphisms which states that the unstable topological entropy is the supremum of the unstable metric entropy taken over all invariant measures the unstable metric entropy for an invariant measure is defined as a conditional entropy along unstable manifolds and it turns out to be the same as that given by ledrappier young though we do not use increasing partitions the unstable topological entropy is defined equivalently via separated sets spanning sets and open covers along a piece of unstable leaf and it coincides with the unstable volume growth along unstable foliation we also obtain some properties for the unstable metric entropy such as affineness upper semi continuity and a version of shannon mcmillan breiman theorem

robustness of fuzzy reasoning and spl delta equalities of fuzzy sets fuzzy reasoning methods or approximate reasoning methods are extensively used in intelligent systems and fuzzy control in this paper the author discusses how errors in premises affect conclusions in fuzzy reasoning that is he discusses the robustness of fuzzy reasoning after reviewing his previous work 1996 he presents robustness results for various implication operators and inference rules all the robustness results are formulated in terms of spl delta equalities of fuzzy sets two fuzzy sets are said to be spl delta equal if they are equal to an extent of spl delta

neuro genetic approach to multidimensional fuzzy reasoning for pattern classification to tackle the pattern classification problems first we give a new interpretation to the multidimensional fuzzy implication mfi this new interpretation of mfi is used for multidimensional fuzzy reasoning mfr for pattern classification we realize the new interpretation through multilayer perceptron the learning scheme of the network is based on genetic algorithm ga a weight smoothing scheme is also proposed to improve neural network s generalization capability the smoothing constraint is incorporated into the objective function of the network to reflect the neighborhood correlation and to seek those solutions which have smooth connection weights at the learning stage of the neural network fuzzy linguistic statements have been used once learned the nonfuzzy features of a pattern can be classified using a fuzzy masking the performance of the proposed scheme is tested through synthetic data finally we apply the proposed scheme to the vowel recognition problem of one indian language

a new theory consistency index based on deduction theorems in several logic systems based on deduction theorems completeness theorems and by means of the theory of truth degrees of formulas and the concept of divergence degrees of theories the present paper proposes another new index reflecting the extent to which a general theory is consistent in five different logic systems i e classical two valued logic system c 2 lukasiewicz fuzzy logic system luk godel fuzzy logic system god product fuzzy logic system p and the r 0 fuzzy logic system l the concepts of normal consistency and almost inconsistency of theories in the above mentioned logic systems are introduced and sufficient and necessary conditions for theories being normal consistent or almost inconsistent are given finally comparison with the existing concept of consistency degrees of theories is analyzed

fuzzy relation equations and inequalities abstract this paper generalizes a method of solution of fuzzy relation equations introduced by sanchez 1976 and developed by pedrycz 1982 we find the greatest or the least solution of a composite l fuzzy relation equation with arbitrary monotone composition

aspects of an adaptive hp finite element method adaptive strategy conforming approximation and efficient solvers the main components needed for an adaptive hp version finite element algorithm are discussed an adaptive hp refinement strategy effective methods for constructing conforming hp approximations and efficient solvers for the large ill conditioned systems of linear equations together these provide the methodology for an effective adaptive hp version algorithm the presentation emphasizes the links between the differing components showing how the algorithms may be implemented efficiently in practice the main principles are illustrated by use of concrete examples so that a non expert may develop their own adaptive hp code the performance of the whole algorithm is illustrated for some representative problems taken from linear elasticity

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

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

multi criteria decision making with interval criteria satisfactions using the golden rule representative value a multi criteria decision function allows one to aggregate an alternative s satisfaction to the individual criteria to obtain the alternative s overall satisfaction to a decision problem we provide a rule based approach to the construction of these decision functions here we make use of a measure based representation of the importance associated with subsets of criteria we then focus on the use of this multi criteria decision function in the situation where the individual criteria satisfactions are interval valued to have the capability of implementing the required ordering and comparing operations in the case of interval valued information we use the golden rule to provide a scalar representative value for these intervals