are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

large amplitude vibrations of imperfect antisymmetric angle ply laminated plates abstract this paper deals with the large amplitude vibrations of imperfect antisymmetric angle ply and symmetric cross ply laminated plates using the von karman type non linear plate model the basic plate equations correspond to those of the parabolic shear deformation plate theory five governing differential equations of the plate are first reduced to a single non linear time differential equation using the single mode approach to a simply supported plate this equation involves the quadratic and cubic non linearities for imperfect plates non linear to linear frequency ratios have been obtained using the perturbation method and the exact method numerical results indicate that the perturbation methods are unreliable for certain plate problems and lead to wrong conclusions it has been observed that whether the plate exhibits a hardening or softening type non linearity depends on both the initial imperfection value and the amplitude of vibration

flutter of geometrically imperfect shear deformable laminated flat panels using non linear aerodynamics abstract the dynamic instability resulting from a high supersonic flow over a simply supported laminated flat panel subjected to uniform in plane edge compression is studied the structural model incorporates geometrical non linearities transverse shear deformation and transverse normal stress effects and satisfies the traction free condition on both faces of the panel in plane edge restraints and small initial geometric imperfections are also considered aerodynamic loads based on the third order piston theory are used and the panel flutter equations are derived via galerkin s method the arclength continuation method is used to determine the static equilibrium state whose dynamic stability behavior is subsequently examined the effects of transverse shear flexibility aerodynamic non linearities initial imperfections and in plane plate theory generally overpredicts the critical flow speed and compressive load and a shear deformation theory is required when considering panels that are flexible in transverse shear when aerodynamic non linearities are included multiple flutter speeds may exist the nature of the flutter boundary for perfect panels is determined by the method of multiple scales and it is seen that the presence of aerodynamic non linearities could result in the hard flutter phenomenon results indicate that non linear aerodynamics is important for panels that are not sufficiently thin i e panels characterized by a high flutter mach number

nonlinear oscillations and chaotic dynamics of an antisymmetric cross ply laminated composite rectangular thin plate under parametric excitation in this paper nonlinear oscillations and chaotic dynamics of a simply supported antisymmetric cross ply laminated composite rectangular thin plate under parametric excitation is investigated for the first time the governing equations of motion for the antisymmetric cross ply laminated composite plate are derived by using von karman type plate equation the geometric nonlinearity and nonlinear damping are included in the governing equations of motion a two dof parametrically excited nonlinear system including the quadratic and cubic nonlinear terms is obtained by using the galerkin method based on the fourier expansion and the temporal rescaling an asymptotic perturbation method is utilized to obtain four dimensional nonlinear averaged equations on the amplitude and the phase of nonlinear oscillations of the antisymmetric cross ply laminated composite plate based on the averaged equations the steady state nonlinear responses and their stabilities are determined by using numerical approach the relations between the steady state nonlinear responses and the amplitude and frequency of parametric excitation are obtained under the certain conditions the antisymmetric cross ply laminated composite plate may have two steady state nonzero solutions in which the jumping phenomenon occurs numerical simulation is used to discover the periodic and chaotic motions in the antisymmetric cross ply laminated composite rectangular thin plate it is observed from the numerical results that the multipulse orbits exist in the antisymmetric cross ply laminated composite rectangular thin plate

structural modification based on measured frequency response functions an exact eigenproperties reallocation a structural modification method based on frequency response functions is presented in terms of an inverse eigenvalue problem the design objective is to derive multiple lumped mass damper and stiffness modifications needed to reallocate eigenvalues and specify eigenvectors of an existing structure a frequency response function based substructure coupling concept is used to get the system dynamic equations a linear algebraic equation is finally obtained to identify the necessary structural modifications the exact structural modifications are determined the existence and uniqueness of exact solutions are also investigated the feasibility of structural modification is examined under the restrictions of structural modifications in the case where infinite many exact modifications can exist the proposed method was applied to an example structure based on experiment data the minimum stiffness modifications were calculated the result of application indicates that the suggested method can derive accurate structural changes just based on minimum number of measured frequency response functions

on canonical bending relationships for plates in recent years a series of papers have appeared on algebraic relationships between the solutions e g deflections buckling loads and frequencies of a given higher order plate theory and the classical plate theory the bending relationships for example can be used to generate the transverse deflection of a plate according to the particular higher order theory from the known deflection of the same problem according to the classical plate theory in the present study relationships between the bending solutions of several higher order plate theories and the classical plate theory are obtained in a canonical form i e one set of relationships contain several theories and they can be specialized to a specific theory by assigning values to the constants appearing in the relationships numerical examples of bending solutions for rectangular plates with various boundary conditions are presented to show how the relations can be used to determine the deflections and bending moments for various theories the relationships are validated by comparing the numerical results obtained using the relationships for the mindlin plate theory against those computed using the abaqus finite element program

global and chaotic dynamics for a parametrically excited thin plate the global bifurcations and chaotic dynamics of a parametrically excited simply supported rectangular thin plate are analyzed the formulas of the thin plate are derived by von karman type equation and galerkin s approach the method of multiple scales is used to obtain the averaged equations based on the averaged equations theory of normal form is used to give the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues by maple program on the basis of the normal form global bifurcation analysis of the parametrically excited rectangular thin plate is given by a global perturbation method developed by kovacic and wiggins the chaotic motion of thin plate is found by numerical simulation

learning possibilistic graphical models from data graphical models especially probabilistic networks like bayes networks and markov networks are very popular to make reasoning in high dimensional domains feasible since constructing them manually can be tedious and time consuming a large part of recent research has been devoted to learning them from data however if the dataset to learn from contains imprecise information in the form of sets of alternatives instead of precise values this learning task can pose unpleasant problems in this paper we survey an approach to cope with these problems which is not based on probability theory as the more common approaches like e g expectation maximization but uses the possibility theory as the underlying calculus of a graphical model we provide semantic foundations of possibilistic graphical models explain the rationale of possibilistic decomposition as well as the graphical representation of decompositions of possibility distributions and finally discuss the main approaches to learn possibilistic graphical models from data

multiple resonant or non resonant parametric excitations for nonlinear oscillators the transient and steady state response of a very general non linear oscillator subject to a finite number of parametric excitations is considered by the asymptotic perturbation method three main cases are examined 1 the parametric excitations frequencies are not close to each other or close to the principal parametric resonance of the oscillator 2 the parametric excitations frequencies are close to each other but not close to the principal resonance and 3 all the parametric excitations frequencies are close to the principal resonance both the conditions for the quenching of the oscillation and the conditions for its persistence are determined the main conclusion is that the oscillation in systems with one degree of freedom cannot be fully quenched due to the action of parametric excitation because the only change is a shift in the oscillator frequencies analytical approximate results are checked by numerical integration

multi modal geometrical non linear free vibration of fully clamped composite laminated plates abstract the geometrically non linear free vibration of thin composite laminated plates is investigated using the hierarchical finite element hfem and the harmonic balance methods hbm von karman s non linear strain displacement relationships are employed and the mid plane in plane displacements are included in the model the equations of motion are developed by applying the principle of virtual work and are solved by a continuation method the convergence properties of the hfem and of the hbm are analyzed internal resonances are discovered and the consequent multi modal and multi frequency vibration of the plates is shown the variation of the plates mode shape and the effect of the fibres orientation are investigated

on the continuity of the concave integral whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set if so the hahn banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it we refer to such representation as a dual representation dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity

multivariate imprecise sklar type theorems abstract the omnipotent instrument for modeling multivariate dependence of random variables in standard probability theory has become copulas discovered by a sklar in 1959 only recently omladic and stopar prove that in the bivariate case an analogous role is played by exactly the same copulas for random variables coming from finitely additive probability spaces one of the main results of this paper is that this is true also in the general multivariate case the extension to n dimensions requires a better understanding of quasi copulas the lattice closure of copulas with respect to the pointwise order we need to develop a new equivalent definition of this notion that should be useful in other applications as well another tool we introduce and seems to be new even in the standard probability approach is multivariate quasi distributions we also expand the coherence theory for quasi copulas and quasi distributions to the multivariate situation finally our main result is a multivariate sklar type theorem in the imprecise setting

approximations of upper and lower probabilities by measurable selections a random set can be regarded as the result of the imprecise observation of a random variable following this interpretation we study to which extent the upper and lower probabilities induced by the random set keep all the information about the values of the probability distribution of the random variable we link this problem to the existence of selectors of a multi valued mapping and with the inner approximations of the upper probability and prove that under fairly general conditions although not in all cases the upper and lower probabilities are an adequate tool for modelling the available information in doing this we generalise a number of results from the literature finally we study the particular case of consonant random sets and we also derive a relationship between aumann and choquet integrals

structure optimization to enhance its natural frequencies based on measured frequency response functions abstract a measured frequency response function frf based structural modification method is presented to obtain optimal structural changes to enhance its natural frequencies structural dynamics modification sdm has been widely used for improvements of built in structures however the optimum design obtained by sdm differs from the true optimal solution when large modal changes happen in this paper a substructure coupling concept is used to get system equations in order to extend its use to large modal changes frf matrix of baseline structure and those of modification structures are coupled at the connection points under the condition of force equilibrium and geometric compatibility constraints thus exact modified modal properties can be calculated even for the case of large modal changes the optimal structural modification is calculated by combining eigenvalue sensitivities and eigenvalue reanalysis technique iteratively special attention is given to the case where baseline structure has some unidentified structural parameters to enlighten the advantage of this proposed method an application to the case of beam stiffener optimization indicates that the proposed method can provide an accurate optimal structural change just based on measured frfs without any kind of numerical models

control and separating points of modular functions let l be a complemented or sectionally complemented lattice and let x be a locally convex linear space we prove the existence of an x valued control for uniformly exhaustive sequences of x valued modular functions on l moreover if l is cr complete we prove that every countable family of cr o c nonatomic group valued modular functions on l admits separating points

sandwich theorems for set functions abstract in the present paper the following problems are treated when do there exist a a precontent and b a precharge which lies between two given set functions the obtained results yield among others several well known theorems such as bondareva s core theorem kelley s intersection number theorem and sandwich theorems of kranz gol dberg and frank as immediate consequences

compactness in spaces of inner regular measures and a general portmanteau lemma abstract this paper may be understood as a continuation of topsoe s seminal paper f topsoe compactness in spaces of measures studia math 36 1970 195 212 to characterize within an abstract setting compact subsets of finite inner regular measures w r t the weak topology the new aspect is that neither assumptions on compactness of the inner approximating lattices nor nonsequential continuity properties for the measures will be imposed as a providing step also a generalization of the classical portmanteau lemma will be established the obtained characterizations of compact subsets w r t the weak topology encompass several known ones from literature the investigations rely basically on the inner extension theory for measures which has been systemized recently by konig h konig measure and integration springer berlin 1997 h konig on the inner daniell stone and riesz representation theorems doc mat 5 2000 301 315 h konig measure and integration an attempt at unified systematization rend istit mat univ trieste 34 2002 155 214

effects of initial geometric imperfections on the interaction between forced and parametric vibrations abstract the influence of initial geometric imperfections on the response of simply supported rectangular plates subjected to periodic in plane forces is theoretically analyzed in this work the large deflection plate theory used in the analysis is derived in terms of the stress function f and lateral displacement w the temporal response is analyzed by the first order generalized asymptotic method and principal parametric and forced resonances are considered and investigated interaction between the two types of resonances is found to depend on mode shapes and imperfection amplitudes

modal interaction in circular plates abstract the dynamic analogue of the von karman equations in polar form is used to study the symmetric response of a circular plate to a harmonic external excitation the method of multiple scales is used to determine a set of ordinary differential equations governing the modulation of the phases and amplitudes of oscillation for the case of an internal or autoparametric resonance the results show that the internal resonance is responsible for coupling of the modes involved and that the excited mode is not necessarily the dominant one furthermore the results show that for a choice of parameters the multi mode response loses its stability through a hopf bifurcation resulting in periodically or chaotically modulated motions of the plate

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

nonlinear oscillations bifurcations and chaos of functionally graded materials plate abstract an analysis on the nonlinear dynamics of a simply supported functionally graded materials fgms rectangular plate subjected to the transversal and in plane excitations is presented in a thermal environment for the first time material properties are assumed to be temperature dependent based on reddy s third order plate theory the nonlinear governing equations of motion for the fgm plates are derived using hamilton s principle galerkin s method is utilized to discretize the governing partial equations to a two degree of freedom nonlinear system including the quadratic and cubic nonlinear terms under combined parametric and external excitations the resonant case considered here is 1 1 internal resonance and principal parametric resonance the asymptotic perturbation method is utilized to obtain four dimensional nonlinear averaged equation the numerical method is used to find the nonlinear dynamic responses of the fgm rectangular plate it was found that periodic quasi periodic solutions and chaotic motions exist for the fgm rectangular plates under certain conditions it is believed that the forcing excitations f1 and f2 can change the form of motions for the fgm rectangular plate

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

canonical sequences of monotone measures abstract it is an important feature of a monotone measure that it is not additive in general in the paper we propose the mathematical tool based on canonical sequences of monotone measures for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures it turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures we also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure

the fuzzy kalman filter state estimation using possibilistic techniques a new method to implement fuzzy kalman filters is introduced the combination of possibilistic techniques and the extended kalman filter has special application in fields where inaccurate information is involved the novelty of this article comes from the fact that by using possibility distributions instead of gaussian distributions a fuzzy description of the expected state and observation is sufficient to obtain a good estimation some characteristics of this approach are that uncertainty does not need to be symmetric and that a wide region of possible values for the expectations is allowed to implement the algorithm this approach also contributes a method to propagate uncertainty through the process model and the observation model based on trapezoidal possibility distributions finally several examples of a real mobile robot moving through a localization process while using qualitative landmarks are shown

bayesian conditioning in possibility theory abstract in this paper possibility measures are viewed as upper bounds of ill known probabilities since a possibility distribution is a faithful encoding of a set of lower bounds of probabilities bearing on a nested collection of subsets two kinds of conditioning can be envisaged in this framework namely revision and focusing on the one hand revision by a sure event corresponds to adding an extra constraint enforcing that this event is impossible on the other hand focusing amounts to a sensitivity analysis on the conditioned probability measures induced by the lower bound constraints when focusing on a particular situation the generic knowledge encoded by the probability bounds is applied to this situation without aiming at modifying the generic knowledge it contrasts with revision where the generic knowledge is modified by the new constraint this paper proves that focusing applied to a possibility measure yields a possibility measure again which means that the conditioning of a family of probabilities induced by lower bounds bearing on probabilities of nested events can be faithfully handled on the possibility representation itself relationships with similar results in the belief function setting are pointed out lastly the application of possibilistic focusing to exception tolerant inference is suggested

random sets as imprecise random variables given a random set coming from the imprecise observation of a random variable we study how to model the information about the probability distribution of this random variable specifically we investigate whether the information given by the upper and lower probabilities induced by the random set is equivalent to the one given by the class of the probabilities induced by the measurable selections together with sufficient conditions for this we also give examples showing that they are not equivalent in all cases

totally balanced games and games of flow a class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games the proof relies on the max flow min cut theorem of ford and fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation

non linear vibration analysis of arbitrarily laminated thin rectangular plates on elastic foundations abstract solutions to free undamped large amplitude vibrations of arbitrarily laminated thin rectangular plates on elastic foundations based on an assumed mode shape are determined simply supported and clamped boundary conditions with both movable and immovable edges are considered the governing equations of motion of plates on linear winkler pasternak foundations and a non linear winkler foundation are provided using von karman s theory the galerkin s method reduces the von karman equation to a time dependent ordinary differential equation solutions are then obtained and compared using the runge kutta method the direct numerical integration method and the perturbation method the effects on the non linear frequency of several parameters such as amplitude material lamination aspect ratio boundary conditions as relate to movable and immovable edges and the influence of elastic foundation constants are provided

a sandwich theorem for precharges abstract in the present paper the following question is treated given two arbitrary set functions on an arbitrary set system when can one find a precharge that lies in between a number of necessary and sufficient conditions for the existence of such a precharge is derived and it is shown how these conditions can be simplified in special cases

decompositions of supermodular functions and s decomposable measures abstract we consider supermodular functions and decomposable measures defined on complete lattice and with values in complete lattice ordered semigroup for such supermodular functions and decomposable measures on lattice with relative complement hewitt yosida decomposition type theorem and lebesgue decomposition theorem are proved

possibilistic and probabilistic likelihood functions and their extensions common features and specific characteristics we deal with conditional probability in the sense of de finetti and with t conditional possibility with t a triangular norm we prove that dubois and prade conditional possibility is a particular min conditional possibility and then we compare the two notions of conditioning by an inferential point of view moreover we study t conditional possibilities as functions of the conditioning event putting in evidence analogies and differences with conditional probabilities this allows to characterize likelihood functions and their aggregations consistent either with a t conditional possibility or a conditional probability this analysis highlights many syntactical coincidences nevertheless the main difference is a weak form of monotonicity which arises only in the possibilistic case

a robust lot sizing problem with ill known demands the paper deals with a lot sizing problem with ill known demands modeled by fuzzy intervals whose membership functions are possibility distributions for the values of the uncertain demands optimization criteria in the setting of possibility theory that lead to choose robust production plans under fuzzy demands are given some algorithms for determining optimal robust production plans with respect to the proposed criteria and for evaluating production plans are provided some computational experiments are presented

when fuzzy measures are upper envelopes of probability measures abstract fuzzy measures which are upper envelopes of probability measures may play an important role to develop a general theory of bayesian statistics especially from a technical point of view a widely accepted generalized bayes rule would be applicable for those kind of fuzzy measures we give sufficient general conditions to ensure that fuzzy measures are upper envelopes of probability measures they are applied to some special classes of important types of fuzzy measures namely sugeno fuzzy plausibility and possibility measures the proof of the main result is based on recently systemized inner extension procedures within abstract measure theory

direct component modal synthesis technique for system dynamic analysis a method for substructure modal synthesis to determine the modal parameters of a structure is investigated the order of the solution matrix does not depend on the number of substructure modes used instead it depends only on the number of connections between substructures the eigensolution determined by this method is exact since the system dynamic matrix equation is not needed in this method numerical computations required for the solution are drastically reduced the eigensolutions of the system in any frequency range can be obtained independently computation is reduced because lower or higher eigensolutions outside the interested frequency range are not required to be calculated the results obtained by this technique and the analytical method are compared and they are identical

a set of practical experiments to validate the fuzzy kalman filter abstract the fuzzy kalman filter fkf was recently reformulated with a number of basic examples included in order to demonstrate its applicability we now look ahead to its practical implementation introducing deep analysis which includes very detailed simulations and complete real applications this will allow us to not only validate the fkf but also to draw important conclusions which will help users in the adjustment of the fuzzy filter parameters and the choosing of possibilistic distributions

nonlinear dynamic behaviors of clamped laminated shallow shells with one to one internal resonance abstract this paper investigates one to one internal resonance of laminated shallow shells with rigidly clamped edges it is assumed that the natural frequencies 2 and 3 of two asymmetric second and third vibration modes have the relationship 2 3 the displacements are expressed by using eigenvectors for linear vibration modes calculated by the ritz method applying galerkin s procedure to the equation of motion nonlinear differential equations are derived by considering the first vibration mode in addition to the two asymmetric vibration modes quadratic nonlinear terms expressing the interaction between the asymmetric and the first modes appear in the differential equations shooting method is used to obtain the steady state response when the driving frequency is near 2 the dynamic characteristics of the shells with the internal resonance are discussed

when upper probabilities are possibility measures abstract a characteristic property is given for a pair of upper and lower probabilities induced by lower probability bounds on a finite set of events to coincide with possibility and necessity measures approximations of upper probabilities by possibility measures are discussed the problem of combining possibility distributions viewed as upper probabilities is investigated and the basic fuzzy set intersections are justified in this framework