inference of fuzzy relational tableaux from fuzzy exemplifications the paper describes a method for deriving fuzzy relational tableaux from fuzzy exemplifications in particular the work by thole zimmerman and zysno 4 is cited as they derive an operator for and using data derived from human subjects the method results in an operator or operators which is a maximal restriction of the operators implied by the data results showing the process are described and a value of and is derived using data presented in 4

stochastic identification of elastic constants for anisotropic materials this paper presents an energy based characterization technique that stochastically identifies the elastic constants of anisotropic materials by modeling the measurement noise and removing its effect unlike conventional deterministic techniques which deterministically identify the elastic constants directly from noisy measurements the technique recursively estimates the elastic constants at every acquisition of measurements using kalman filter owing to the non linear expression of the measurement model a kalman gain has been newly derived and achieves optimal estimation since the variances in addition to the means are computed the proposed technique can not only identify the elastic constants but also describe their certainty as an additional advantage the validity of the proposed technique and its superiority to the conventional technique were first demonstrated via parametric studies of low dimensional problems the proposed technique was then successfully applied to the identification of elastic constants of an anisotropic material copyright 2009 john wiley sons ltd

fuzzy groups some group theoretic analogs abstract we introduce the concepts of 1 order of a fuzzy subgroup of a finite group 2 a fuzzy abelian group and 3 a fuzzy solvable group we obtain some results involving these notions which are analogs of results from group theory also we prove analogs of two basic theorems of group theory namely cayley s theorem and lagrange s theorem

fuzzy normal subgroups and fuzzy cosets abstract we introduce here the notion of 1 i a fuzzy normal subgroup and 2 ii a fuzzy coset we prove that for a group g a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of g further we show that the level subgroups of a fuzzy normal subgroup are all normal we obtain several results which are analogs of some basic theorems of group theory in particular a fuzzy version of lagrange s theorem is established

general framework for the identification of constitutive parameters from full field measurements in linear elasticity in this paper several approaches available in the literature for identifying the constitutive parameters of linear elastic materials from full field measurements are presented and their sensitivity to a white noise added to the data is compared the first investigated approach is the virtual fields method vfm it is shown that the uncertainty of the parameters identified with the vfm when a white noise is added to the data depends on the choice of a relevant set of virtual fields optimal virtual fields exist thus minimizing the uncertainty and providing the maximum likelihood solution the other approaches investigated in this paper are based on finite element model updating femu it is proved that femu approaches actually yield equations similar to the ones derived from the vfm but with nonoptimal sets of virtual fields therefore the femu approaches do not provide the maximum likelihood solution however the uncertainty of femu approaches varies dramatically with the cost function to minimize on one hand the femu approach based on the displacement gap minimization yields equations which are very close to the ones of the vfm approach and therefore its uncertainty is almost the same as the vfm one on the other hand it is shown that other approaches based on the constitutive equation gap minimization or the equilibrium gap minimization provide biased solutions for all the approaches very fast algorithms converging in only two iterations have been devised they are finally applied to real experimental data obtained on an orthotropic composite material results confirm the success of two methods the vfm approach which provides the maximum likelihood solution and the femu approach based on the displacement gap minimization

identification of orthotropic elastic constants using the eigenfunction virtual fields method abstract the virtual fields method vfm pierron and grediac 2012 an inverse method based on the principle of virtual work pvw is being increasingly used to estimate mechanical properties of materials from full field deformations obtained from techniques such as digital image correlation moire and speckle interferometry and grid methods by making specific choices for virtual fields vfs in pvw one obtains a system of algebraic equations which is then solved for the unknown material constants recently a new variant of vfm known as the eigenfunction virtual fields method evfm has been proposed subramanian 2013 in evfm principal components of the measured i e true strain fields are used to systematically generate vfs we extend evfm to orthotropic elastic materials in this work and estimate the relevant material parameters from full field strain data generated from a finite element model of an unnotched iosipescu test varying levels of gaussian white noise are added to the synthetic strain data to evaluate the sensitivity of evfm to input noise it is observed that for low to moderate noise the material properties estimated by the proposed method are relatively insensitive to noise however when noise levels are high the proposed method yields large variance in some of the computed properties when compared to the state of the art optimized piecewise continuous vfm toussaint et al 2006 pierron and grediac 2012 some of the large variance in properties estimated from noisy data using evfm is traced to the sensitivity of the third dominant eigenfunction and modifications to the proposed method to address this issue are suggested

special virtual fields for the direct determination of material parameters with the virtual fields method 2 application to in plane properties this paper deals with the direct identification of mechanical parameters that govern the in plane constitutive law of orthotropic materials those parameters are extracted from heterogeneous strain fields that occur in a short beam specimen tested in a iosipescu fixture the procedure used is the virtual fields method with special virtual fields the case of linear elasticity is first addressed it is shown that the parameters are directly extracted with this method no iterative calculations are required the stability is also discussed in different cases a non linear shear response is then considered the parameter that governs this non linearity is also directly identified with the special virtual fields

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

on the definition of a fuzzy subgroup abstract using the idea of quasi coincidence of a fuzzy point with a fuzzy set some new concepts of a fuzzy subgroup are introduced and their acceptibility is investigated some fundamental properties of one such viable fuzzy subgroup are obtained

on the direct product of fuzzy subgroups abstract anthony and sherwood 1979 1980 redefined the fuzzy subgroup the idea introduced by rosenfeld 1971 foster 1979 introduced the concept of product fuzzy subgroups using rosenfeld s definition in this paper the product fuzzy subgroups will be redefined according to anthony and sherwood s definition

anisotropic linear elastic parameter estimation using error in the constitutive equation functional a modified error in the constitutive equation based approach for identification of heterogeneous and linear anisotropic elastic parameters involving static measurements is proposed and explored following an alternating minimization procedure associated with the underlying optimization problem the new strategy results in an explicit material parameter update formula for general anisotropic material this immediately allows us to derive the necessary constraints on measured data and thus restrictions on physical experimentation to achieve the desired reconstruction we consider a few common materials to derive such conditions then we exploit the invariant relationships of the anisotropic constitutive tensor to propose an identification procedure for space dependent material orientations finally we assess the numerical efficacy of the developed tools against a few parameter identification problems of engineering interest

constitutive error based parameter estimation technique for plate structures using free vibration signatures abstract in this paper a variant of constitutive equation error based material parameter estimation procedure for linear elastic plates is developed from partially measured free vibration sig natures it has been reported in many research articles that the mode shape curvatures are much more sensitive compared to mode shape themselves to localize inhomogeneity complying with this idea an identification procedure is framed as an optimization problem where the proposed cost function measures the error in constitutive relation due to incompatible curvature strain and moment stress fields unlike standard constitutive equation error based procedure wherein a solution of a couple system is unavoidable in each iteration we generate these incompatible fields via two linear solves a simple yet effective penalty based approach is followed to incorporate measured data the penalization parameter not only helps in incorporating corrupted measurement data weakly but also acts as a regularizer against the ill posedness of the inverse problem explicit linear update formulas are then developed for anisotropic linear elastic material numerical examples are provided to show the applicability of the proposed technique finally an experimental validation is also provided

on the direct determination of invariant parameters governing anisotropic plate bending problems abstract many papers deal with the determination of flexural rigidities of anisotropic plates from only one specimen subjected to one or several loading conditions in such a problem one of the main questions is the best identification of the unknown parameters according to the type of material the shape of the specimen and the loading conditions it seems that no general rule giving the best configuration leading to an accurate determination has been established one of the main reasons is the anisotropic nature of the tested plates which leads the mechanical configuration to be dependent on the material itself this problem would be avoided by the direct measurement of invariant parameters from which the rigidities are easily deduced these invariant parameters reveal the intrinsic elastic behavior of the tested plate contrary to the rigidities usually considered which are directional quantities this paper describes a procedure for the identification of invariant parameters governing the bending of anisotropic plates it is shown that the whole displacement field processing of the surface strain fields obtained in two particular loading cases directly provides those parameters a numerical simulation shows the stability of the present method

on some product of fuzzy subgroups abstract a kind of product of fuzzy subsets subgroups of a group is defined analogously to the pointwise product of functions via a triangular norm t we call this product the t product some properties of the t product of fuzzy subgroups of a group are investigated in particular we are interested in the fuzzy subgroups of the internal direct product of subgroups of a group

on the elastic characterization of composite plates with vibration data this paper takes a global look at a method of obtaining the elastic constants of the material of a rectangular plate sample by explicitly inputting the geometrical shapes and frequencies of a sufficient number of experimental vibration modes into a computational procedure that essentially compares experimental frequencies with analytical predictions there are many aspects of this method that have important bearing on accuracy ease of use and computational economy the issues that arise include vibration representation functions selection of experimental mode shapes and frequencies for analysis goodness of experimental data frequency sensitivity of the elastic constants influence of diagonal modes where relevant plate thickness plate aspect ratio material orthotropy ratio and orientation of reinforcing fibers in laminate composites whereas some of these factors have been discussed separately in other works this paper attempts bring the method completely into focus in one place with an examination of all the factors believed to influence the efficiency of the method

fuzzy subgroups some characterizations the notion of a fuzzy set was first introduced in 1965 by zadeh 12 since then the theory of fuzzy sets has gone through remarkably rapid strides with well over 4000 papers by now see for example the bibliography 3 several textbooks for example 2 and 6 and an international journal solely devoted to it s the theory has found wideranging applications in such diverse fields as automata control theory decision theory and social behavior pattern studies to name just a few for an interesting expository account see rosenfeld lo and also the book review 7 in 9 rosenfeld introduced the notion of a fuzzy group and showed that many concepts of group theory can be extended in an elementary manner to develop the theory of fuzzy groups in particular he characterized all the fuzzy subgroups of cyclic groups of prime order 9 proposition 5 101 fuzzy groups were further investigated by das in 1 where he characterized all the fuzzy subgroups of finite cyclic groups l theorem 4 21 in this connection he introduced the notion of level subgroups of a fuzzy subgroup which is based on the notion of a level subset introduced earlier by zadeh for a finite group das showed that these level subgroups of a fuzzy subgroup form a chain 1 corollary 3 11 and also constructed a fuzzy subgroup whose chain of level subgroups is maximal in the following special cases when the group is i a direct product of cyclic groups of prime orders ii abelian l theorem 3 41 we analyze the level subgroups of a fuzzy subgroup in more detail and investigate whether the family of level subgroups of a fuzzy subgroup deter

regularized virtual fields method for mechanical properties identification of composite materials abstract this paper presents a new material parameters identification method based on the virtual fields method vfm where a regularization term coming from a micromechanical model has been added in this regularized virtual fields method rvfm the system of equations associated to the vfm is solved within a constrained optimization framework the method was applied to virtual scanning electron microscope in situ tests aiming at determining the local properties of uni directional composites loaded in the transverse direction and for which the strain fields were obtained through digital image correlation dic the method was tested for composites with various volume fractions and properties contrasts and under different boundary conditions the potentials and limitations of the algorithm in the presence of noisy images were investigated and compared to that of the vfm and the other finite element based methods the corresponding results indicate that the proposed rvfm is more efficient than the other identification techniques in terms of both accuracy and computational time an optimum size of region of interest was also determined by taking into account dic magnification requirements and based on the accuracy of the identified parameters this kind of study can be very useful for determining a priori the level of resolution in the imaging system required for a favorable accuracy of the identified parameters

products of fuzzy subgroups fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not of course this requires an appropriate modification of the closure property which takes the form of an inequality in this paper a study of products of fuzzy subgroups is begun some results are expected the product of fuzzy subgroups is a fuzzy subgroup products with the same but permuted factors are isomorphic and there is a natural isomorphism from any factor into the product functions called t norms are used to construct products of fuzzy subgroups different t norms yielding different products since a fuzzy subgroup must satisfy an inequality generalizing closure and the strength of that inequality is important some results relate the t norm used in forming the product to the strength of the ensuing inequality when can complicated fuzzy subgroups be expressed as products of simple ones this question is addressed for fuzzy subgroups of finite abelian groups

fuzzy subgroup some characterizations ii abstract we consider an analysis of fuzzy subgroups in terms of the corresponding family of level subgroups given a finite chain of subgroups of a group g we prove that there exists a fuzzy subgroup of g whose level subgroups are exactly the subgroups of this chain as a corollary we obtain an interpretation of the number of chains of subgroups of a group g in which a subgroup h is a member when the group g is a supersolvable group some further interpretation of this number is obtained

spectral functionals nonholonomic dirac operators and noncommutative ricci flows we formulate a noncommutative generalization of the ricci flow theory in the framework of spectral action approach to noncommutative geometry grisha perelman s functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic dirac operators and corresponding spectral triples we derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe non holonomic riemannian configurations