generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

simulations of singularity dynamics in liquid crystal flows a c0 finite element approach in this paper we present a c 0 finite element method for a 2d hydrodynamic liquid crystal model which is simpler than existing c 1 element methods and mixed element formulation the energy law is formally justified and the energy decay is used as a validation tool for our numerical computation a splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time independent the latter avoids solving a linear system at every time step and largely reduces the computational time especially when direct linear system solvers are used our approach is verified by comparing its computational results with those obtained by c 1 elements and by mixed formulation through numerical experiments of a few other splittings and explicit implicit strategies we recommend a fast and reliable algorithm for this model a number of examples are computed to demonstrate the algorithm

on certain linear mappings between inner product and squared distance matrices abstract we obtain the spectral decomposition of four linear mappings the first is a mapping of the linear hull of all centered inner product matrices onto the linear hull of all the induced squared distance matrices it is based on the natural generalization of the cosine law of elementary euclidean geometry the other three mappings studied are 1 the adjoint and 1 extensions and applications particularly to multidimensional scaling are discussed in some detail

an algorithm for generalized fuzzy binary linear programming problems abstract fuzzy binary linear programming fblp problems are very essential in many fields such as assignment and assembly line balancing problems in operational research multiple projects locations and candidates selection cases in management science as well as representing and reasoning with prepositional knowledge in artificial intelligence although fblp problems play a significant role in human decision environment not very much research has focused on fblp problems this work first proposes a simple means of expressing a triangular fuzzy number as a linear function with an absolute term a method of linearizing absolute terms is also presented the developed goal programming gp model weighted by decision makers dms preference aims to optimize the expected objective function and minimize the sum of possible membership functions deviations after presented a novel way of linearizing product terms the solution algorithm is proposed to generate a crisp trade off promising solution that is also an optimal solution in a certain sense three examples equipment purchasing choice investment project selection and assigning clients to project leaders illustrate that the proposed algorithm can effectively solve generalized fblp problems

nonparabolic dissipative systems modeling the flow of liquid crystals we study a simplified system which retains most of the interesting mathematical properties of the original ericksen leslie equations for the flow of liquid crystals this is a coupled nonparabolic dissipative dynamic system we derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions we also discuss uniqueness and some stability properties of the system 1995 john wiley sons inc

nonlinear theory of defects in nematic liquid crystals phase transition and flow phenomena this is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals it also includes some new results concerning disclinations line defects which have not been published elsewhere

interactive multiple objective programming subject to flexible constraints abstract an interactive decision support system is introduced which aids in solving multiple objective programming problems subject to strict and flexible constraints integral part is an extension of a well known fuzzy sets approach evaluating possible solutions by their degrees of membership to objectives and constraints this approach is linked to classical multiple objective programming models if the decision maker cannot determine membership functions a priori the system suggests functions dependent on the given information and interactive modifications are allowed

towards the ideal solution in a learning problem with different t norm operators abstract the ideal solution of a learning problem is discussed our learning problem is that of finding p in p q with a given data sequence of q written as q i i 1 2 n based on the concept of zadeh s relative sigma count we formulate the problem as a multi objective optimization with sufficiency and necessity criteria we give explicit formulae of the ideal evidence sequence p 1 and we analyze how the ideal sequence depends on different t norm operations and the parameters specified in the criteria using schweizer and sklar s one parameter family of t norms

finite element approximation of nematic liquid crystal flows using a saddle point structure in this work we propose finite element schemes for the numerical approximation of nematic liquid crystal flows based on a saddle point formulation of the director vector sub problem it introduces a lagrange multiplier that allows to enforce the sphere condition in this setting we can consider the limit problem without penalty and the penalized problem using a ginzburg landau penalty function in a unified way further the resulting schemes have a stable behavior with respect to the value of the penalty parameter a key difference with respect to the existing schemes two different methods have been considered for the time integration first we have considered an implicit algorithm that is unconditionally stable and energy preserving the linearization of the problem at every time step value can be performed using a quasi newton method that allows to decouple fluid velocity and director vector computations for every tangent problem then we have designed a linear semi implicit algorithm i e it does not involve nonlinear iterations and proved that it is unconditionally stable verifying a discrete energy inequality finally some numerical simulations are provided

connections between the real positive semidefinite and distance matrix completion problems abstract though the real symmetric positive semidefinite psd matrices and the euclidean distance matrices are closely related exact relationships between the corresponding completion problems are not apparent we establish strong partial relationships of two types this permits the transfer of some insights from one problem to the other and allows computational tools for the psd problem to be used for the distance problem

possibility versus probability the main objective of this note is to try to indicate that a possibility distribution at least in some applications can be interpreted as a family of probabilities possibly subjective an advantage of the latter interpretation is that subsequent derivations can be made by well proven probabilistic arguments rather than relying on an intuition concerning the properties of possibility distributions which is not well developed multistate reliability theory is given as an example of an area of application where the probabilistic approach seems far superior

the use of a fuzzy decision making method in a large scale computer system choice problem abstract we recently proposed a fuzzy decision making method for multiple objectives problems in an uncertain and ill defined environment this paper presents a real and large scale application of the method the problem is to decide what sort of computer system for research and education should be renewed in the department of computer engineering one member of a renewal committee appears as a decision maker after describing the outline of the fuzzy decision making method the decision analysis process objective hierarchy identification of decision maker s preference structure rating and ranking of alternatives and sensitivity analysis is presented

error estimates of a linear decoupled euler fem scheme for a mass diffusion model we present error estimates of a linear fully discrete scheme for a three dimensional mass diffusion model for incompressible fluids also called kazhikhov smagulov model all unknowns of the model velocity pressure and density are approximated in space by c 0 finite elements and in time an euler type scheme is used decoupling the density from the velocity pressure pair if we assume that the velocity and pressure finite element spaces satisfy the inf sup condition and the density finite element space contains the products of any two discrete velocities we first obtain point wise stability estimates for the density under the constraint lim h k 0 h k 0 h and k being the space and time discrete parameters respectively and error estimates for the velocity and density in energy type norms at the same time afterwards error estimates for the density in stronger norms are deduced all these error estimates will be optimal of order mathcal o h k for regular enough solutions without imposing nonlocal compatibility conditions at the initial time finally we also study two convergent iterative methods for the two problems to solve at each time step which hold constant matrices independent of iterations

a variance inequality ensuring that a pre distance matrix is euclidean we derive a variance inequality on the squares of the pre distances between n objects ensuring that the corresponding pre distance matrix is euclidean the result is discussed in relation with some transformations making a pre distance matrix euclidean

some optimal error estimates for piecewise linear finite element approximations it is shown that the ritz projection onto spaces of piecewise linear finite elements is bounded in the sobolev space wl for 2 p oc this implies that for functions in wf n w2 the error in approximation behaves like 0 h in wp for 2 p oo and like 0 h2 in lp for 2 p oo in all these cases the additional logarithmic factor previously included in error estimates for linear finite elements does not occur

a note on the operativeness of neyman pearson tests with fuzzy information abstract in a previous paper we have studied the extension of the neyman pearson optimality criterion of testing statistical hypotheses when the available experimental information involves fuzzy imprecision this extension usually becomes unmanageable for small samples nevertheless we will verify that when the sample size is large enough the application of the central limit theorem determines an operative extension

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

the cone of distance matrices abstract the geometry of the cone of euclidean distance matrices edms is analyzed using a new characterization of an edm the facial structure and the angle that edms of embedding dimension one make with the center ray are found this result follows from a complete analysis of the critical points of the distance function in frobenius norm from the matrix e consisting of zero diagonal and ones elsewhere to the edms of embedding dimension one

a fuzzy decision making method and its application to a company choice problem abstract we propose a fuzzy decision making method for multiobjective decision problems its main features are the use of fuzzy connectives to represent the decision maker s preference structure and fuzzy probability to express imprecise and uncertain outcomes the preference structure is extracted through interaction between the decision maker and a computer the fuzzy connectives adopted here are zimmermann s operation and its two extensions the extended operations describe the preference structure better than the operation the proposed method consists of the following five steps 1 1 identification of the problem 2 2 a questionnaire process 3 3 parameter identification 4 4 evaluations of alternatives 5 5 aggregated rating and ranking of alternatives finally an application of this method to a company choice problem is presented

aggregation of fuzzy opinions an axiomatic approach abstract the importance of fuzzy valuations in diagnostics is mentioned the problem of aggregation of fuzzy opinions obtained from a group of experts in answer to the question has an object the property labeled a and no property labeled 1a is formulated the set of fung and fu s 10 aggregation axioms is shortly described the idea of weighting expert s opinions is formalized then a new set of aggregation axioms is presented and an aggregating operator is introduced a posteriori weighting of opinions in aggregation is examined

an extended rule based inference for general decision making problems complex decision making problems are usually modeled in terms of a number of decisive variables that are related hierarchically pieces of evidence are aggregated in a bottom up way to determine the final decision goal for dealing with such problems ishizuka et al 5 6 developed a rule based inference procedure by using fuzzy sets to represent imprecise data and employed the dempster shafer theory to aggregate evidence for structural damage assessment this paper highlights the necessity of applying the rules with all possible consequent clauses in the procedure with the considerations of information quality and quantity when applying the procedure to more general decision making problems the use of such rules can provide high quality information which contains much less ignorance in the resultant information also it can afford more information due to the decrease in total ignorance a simple example with two cases is used to compare the results based on the two different presentations of rules in the inference procedure for illustrating the importance of considering the rules proposed in this paper

finite element approximations of the ericksen leslie model for nematic liquid crystal flow the ericksen leslie model describes dynamics of low molar mass nematic liquid crystals where the spatiotemporal distribution of defects defining texture is represented by the director unit vector field bf d omega t rightarrow mathbb s 2 it consists of the navier stokes equations with an extra viscous stress tensor and a convective harmonic map heat flow equation to govern the dynamics of the director field two fully discrete finite element methods for a regularized system using the ginzburg landau regularization and for the limiting ericksen leslie model are proposed and well posedness and related discrete energy laws are established for the regularized model unconditional convergence of finite element solutions towards weak solutions of the continuum model as well as convergence towards measure valued solutions of the limiting ericksen leslie model are verified when the mesh parameters and the regularization parameter successively tend to zero computational experiments are also presented to show the importance of balancing numerical and regularization parameters to compare regularized and direct approaches and to show numerically the finite time formation annihilation and evolution of point defects

a new fuzzy multiple attributive group decision making methodology and its application to propulsion manoeuvring system selection problem in this paper a new fuzzy multiple attribute decision making fmadm method which is suitable for multiple attributive group decision making gdm problems in fuzzy environment is proposed to deal with the problem of ranking and selection of alternatives since the subjectivity imprecision and vagueness in the estimates of a performance rating enter into multiple attribute decision making madm problems fuzzy set theory provides a mathematical framework for modelling vagueness and imprecision in the proposed approach an attribute based aggregation technique for heterogeneous group of experts is employed and used for dealing with fuzzy opinion aggregation for the subjective attributes of the decision problem the propulsion manoeuvring system selection as a real case study is used to demonstrate the versatility and potential of the proposed method for solving fuzzy multiple attributive group decision making problems the proposed method is a generalised model which can be applied to great variety of practical problems encountered in the naval architecture from propulsion manoeuvring system selection to warship requirements definition

fuzzy rule generation methods for high level computer vision abstract in many decision making systems involving multiple sources the decisions made may be considered as the result of a rule based system in which the decision rules are usually enumerated by experts or generated by a learning process in this paper we discuss the various issues involved in the generation of fuzzy rules automatically from training data for high level computer vision features are treated as linguistic variables that appear in the antecedent clauses of the rules we present methods to generate the corresponding linguistic labels values and their membership functions rules are generated by constructing a minimal approximate fuzzy aggregation network and then training the network using gradient descent methods several examples are given

optimal encoding of graph homomorphism energy using fuzzy information aggregation operators abstract the attributed relational graph matching arg strategy is a well known approach to object pattern recognition in the past for the parallel solution of arg matching problem an overall objective function was constructed using linearly weighted information aggregation function and one set of parameter values was chosen for all models by trial and error for the parameters in the function in this paper the compatibility between every pair of model and scene attributes is interpreted as a fuzzy value and subsequently the nonlinear fuzzy information aggregation operators are used to fuse the information captured in the chosen attributes to learn the parameters in the fuzzy information aggregation operators the learning from samples strategy is used the learning of weight parameters is formulated as an optimisation problem and solved using the gradient projection algorithm based learning procedure the learning procedure implicitly evaluates ambiguity robustness and discriminatory power of the relational attributes chosen for graph matching and assigns weights appropriately to the chosen attributes the learning procedure also enables us to compute a distinct set of optimal parameters for every model to reflect the characteristics of the model so that the homomorphic arg matching problem can be optimally encoded in the energy function for the model experimental results are presented to illustrate effectiveness and necessity of the parameter estimation and learning procedures

mixed formulation approximation and decoupling algorithm for a penalized nematic liquid crystals model a linear fully discrete mixed scheme using c 0 finite elements in space and a semi implicit euler scheme in time is considered for solving a penalized nematic liquid crystal model of the ginzburg landau type we prove 1 unconditional stability and convergence towards weak solutions and 2 first order optimal error estimates for regular solutions but without imposing the well known global compatibility condition for the initial pressure in the navier stokes framework these results are valid in a general connected polygon or in a lipschitz polyhedral domain without any constraints on its angles finally since the scheme couples the unknowns we propose several algorithms for decoupling the computation of these unknowns and establish their rates of convergence in convex domains when the mesh size is sufficiently small compared to the time step

computationally efficient active rule detection method algorithm and architecture in this paper a new active rule detection algorithm is proposed which is efficiently implemented in dedicated fuzzy processors here its advantages are analytically attested a novel realization architecture is proposed that has higher performance and uses lower hardware resources in comparison to the other reported architectures the structure of the proposed active rule detection unit is scalable in terms of the number of inputs the number of membership functions and their bit widths the proposed architecture is flexible in term of membership function shape as well

properties of the aggregation operators related with fuzzy relations abstract the problem of information generalization in multicriteria decision making is considered in this paper the information is unified by fuzzy relations and the generalization is realized with the help of aggregation operators some of the most oftenly used operators are presented and their properties depending on the properties of the fuzzy relations which they aggregate are proved the sensitivity of the operators with respect to variations in their arguments is investigated the numerical example deciding the problem of alternatives ranking is given as well

an interactive fuzzy programming system abstract an interactive system is introduced which supports a decision maker in solving programming models with crisp or fuzzy constraints and crisp or fuzzy goals one part of the system is the determination of membership functions representing goals to this purpose fuzzy extreme solutions are computed and are presented to the decision maker these and each of the proposed compromise solutions are fuzzy efficient

basic concepts for a theory of evaluation hierarchical aggregation via autodistributive connectives in fuzzy set theory abstract the aggregative operator introduced by combi 1982 in his analysis of basic concepts for a theory of evaluation in this journal is based on the axioms of associativity continuity and monotonicity in this paper an alternative approach is given where associativity is replaced by another axiom viz autodistributivity implying a kind of hierarchical aggregation instead of the former horizontal one the new set of properties yields a general class of operators for connecting fuzzy sets which are formally similar to the aggregative operators but are purely compensative in a strong sense moreover this modified approach generalizes a recent approach based on generalized means as compensative connectives it appears to be similar to expected utility approaches in decision making under uncertainty and seems to be a very promising tool to handle representation problems as they grow from other fields of human decision making e g of multicriteria analysis and of welfare theory

scaling radial basis functions via euclidean distance matrices a radial basis function approximation is typically a linear combination of shifts of a radially symmetric function possibly augmented by a polynomial of suitable degree that is it takes the forms x k 1nc k f x x k p x x din the mid 1980s micchelli building on pioneering work of schoenberg in the 1930s and 1940s provided simple sufficient conditions on that imply radial basis functions can interpolate scattered data however when the data density varies locally several authors such as hon and kansa 1 have suggested scaling the translates in other words it can be advantageous to replace the euclidean norm by some more general distance functional d that iss x k 1nc k f d x x k p x x dthis distance functional a need not be a metric but we shall require that d be symmetric and satisfy d g g 0 for all g d unfortunately the micchelli schoenberg theory does not obviously apply in this more general setting but some papers have observed that interpolation is well defined if the distance functional is a sufficiently small perturbation of the euclidean norm however in this study we follow a different approach which returns to the roots of schoenberg s work specifically we use schoenberg s classification of euclidean distance matrices to provide a simple technique which given a suggested distance functional d calculates a perturbed distance functional d for which the underlying interpolation matrix is invertible when the function q is strictly positive definite i e a mercer kernel or strictly conditionally positive or negative definite of order one as a simple by product of this method we can also apply the narcowich ward 2 norm estimate results easily since the minimum distance between points is now under our control via d

simultaneous classification and multidimensional scaling with external information for the exploratory analysis of a matrix of proximities or dis similarities between objects one often uses cluster analysis ca or multidimensional scaling mds solutions resulting from such analyses are sometimes interpreted using external information on the objects usually the procedures of ca mds and using external information are carried out independently and sequentially although combinations of two of the three procedures ca and mds or multidimensional scaling and using external information have been proposed in the literature the present paper offers a procedure that combines all three procedures in one analysis using a model that describes a partition of objects with cluster centroids represented in a low dimensional space which in turn is related to the information in the external variables a simulation study is carried out to demonstrate that the method works satisfactorily for data with a known underlying structure also to illustrate the method it is applied to two empirical data sets

nonlinear eigenvector algorithms for local optimization in multivariate data analysis abstract many multivariate statistical procedures such as principal component canonical correlation correspondence and discriminant analysis are based on the solution of a certain matrix approximation problem one of the most important being the reduced rank approximation its solution hinges on the singular value or the eigendecomposition of a certain matrix therefore numerical techniques to determine eigenvalues and eigenvectors play an important role in these statistical applications furthermore various modifications generalizations or refinements of the classical methods lead to some sort of nonlinear eigenproblem with no immediate unique solution however the nonlinear eigenvector approach has proved to be quite effective in solving these types of constrained optimization problems in diverse fields of multivariate data analysis since a general analysis of the properties and performance of the nonlinear eigenvector algorithm seems to be long overdue this paper collects the common features in the applications mentioned above and gives an overview from a superior perspective it unifies the treatment by contrasting the nonlinear eigenvector algorithm with the well known inverse iteration iteratively reweighted least squares and majorization algorithms extracts the mathematical tools basically from convex analysis and matrix algebra needed for the convergence proofs and discusses convergence properties

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

the efficacy of fuzzy representations of uncertainty advocates of the theory of fuzzy sets as a system for representing uncertainty have based their case on five basic arguments these are 1 the reality hypothesis which holds that imprecision is an inherent property of the world external to an observer 2 the subjectivity hypothesis which holds that probability is an exclusively objective measure of uncertainty and that therefore subjective uncertainty can only be represented with fuzzy sets 3 the behaviorist hypothesis which claims that uncertainty systems should emulate rather than prescribe human behavior in the face of uncertainty 4 the probability as fiction hypothesis which claims that probability does not comprise a field of study in its own right and 5 the superset hypothesis which holds that fuzzy set theory includes probability as a special case and thus provides a richer uncertainty modeling environment we discuss and criticize all five we then criticize the argument that fuzziness represents a type of uncertainty distinct from probability and also the inordinate complexity of fuzzy methods we present a method for assessing the efficacy of fuzzy representations of uncertainty and apply this method in three examples

vagueness and bayesian probability this paper is a response to michael laviolette and john w seaman jr s ibid vol 2 no 1 p 4 1994 position paper the efficacy of fuzzy representations of uncertainty which criticizes fuzzy representations of uncertainty and suggests that bayesian probability can do better the commenter argues that the author s make some misleading comments about bayesian probability and he briefly discusses the problem of giving a satisfactory interpretation of membership functions

comparison of empirical and computed values of fuzzy conjunction abstract the necessity for further experiments such as in 4 for the foundation of fuzzy sets theory is shown generality of the experimental results on fuzzy conjunction in the paper by thole zimmermann and zisno 1979 4 for the other objects and language is verified for other conditions usually the minimum the product and the restricted sum operators are used as an intersection conjunction of fuzzy sets in fuzzy optimization f optimization on the basis of experiments it is shown that these operators are correct for f optimization their correctness is founded on the stability of the extremal point a decision in bellman zadeh s scheme under a positive linear mapping it is shown that these mappings exist between empirical conjunction and considered operators as a statistical result of linear regression analysis

approximation of liquid crystal flows the numerical solution of the flow of a liquid crystal governed by a particular instance of the ericksen leslie equations is considered convergence of finite element approximations is established under appropriate regularity hypotheses and numerical experiments exhibiting the interaction of singularities and the coupling of the director and momentum equations are presented

compensatory fuzzy multiple level decision making abstract fuzzy set theory has been shown to be an effective tool to overcome the computational difficulties encountered in solving large multiple level programming problems shih et al 1996 in this paper compensatory operators are introduced for adjusting the decision making process between the different levels and also between the decision makers of the same level after a brief consideration of the bi level and three level systems the large decentralized organizations with both equal and unequal goals are investigated various numerical examples are given to compare the influences of compensation and to illustrate the approaches

existence of solutions for the ericksen leslie system we study the general ericksen leslie system which describes the flow of liquid crystal materials the dissipation property of the system is established and is used to prove the global existence of weak solutions we also study the existence of classical solutions and the asymptotic stability of the solutions

additive hybrid networks for fuzzy logic abstract evidence aggregation networks based on multiplicative fuzzy hybrid operators were introduced by krishnapuram and lee they have been used for image segmentation pattern recognition and general multicriteria decision making one of the drawbacks of these networks is that the training is complex and quite time consuming we have recently modified these aggregation networks to implement additive fuzzy hybrid connectives these new networks have similar excellent properties for decision making under uncertainty as do their multiplicative precursors and have the advantage that training is easier since the additive operators are not as complex in form in earlier work trainable neural networks have been used to perform inference in a fuzzy logic system fixed architecture networks of fuzzy operators and standard neural networks have been utilized the additive hybrid operators are extremely flexible and so are excellent candidates for nodes in a network structure for fuzzy logic inference the purpose of this paper is to demonstrate the capability of networks of additive hybrid nodes to learn appropriate functional relationships for fuzzy logic an added advantage of these networks is that they are transparent i e after training the individual nodes can be analyzed as a collection of mini rules

the best euclidian fit to a given distance matrix in prescribed dimensions abstract in this paper we determine the euclidean distance matrix which is closest to a given not necessarily euclidian one we admit a wide class of appropriate matrix norms as measures of closeness majorization results on sums of eigenvalues of symmetric matrices serve as basic tools

the weak solutions to the evolution problems of harmonic maps on demontre l existence de solutions faibles globales a des problemes d evolution des applications harmoniques de varietes de riemann compactes sans bord dans des spheres

applications of fuzzy set theory to mathematical programming mathematical programming is one of the areas to which fuzzy set theory has been applied extensively primarily based on bellman and zadeh s model of decision in fuzzy environments models have been suggested which allow flexibility in constraints and fuzziness in the objective function in traditional linear and nonlinear programming in integer and fractional programming and in dynamic programming these models in turn have been used to offer computationally efficient approaches for solving vector maximum problems this paper surveys major models and theories in this area and offers some indication on future developments which can be expected

multi criteria decision making in german automotive industry using fuzzy logic abstract in recent years fuzzy logic technologies have been widely applied to control applications in engineering where they are now considered an enabling technology for intelligent control systems fuzzy logic expedites the design of complex systems by allowing heuristic control strategies to be formulated by natural language rules rather than mathematical models hence the essence of fuzzy logic is its ability to put engineering expertise right into an algorithm the domain of such a technology is not limited to control engineering it can also be applied to incorporate complex decision making and the analysis of numerical data into non control systems this paper covers such an application realized at mercedes benz in germany for the optimization of the design process of truck components such as gear boxes the maturity of a current component development needs to be evaluated the objective is to reduce the amount of existing data of the development project to a single parameter describing the overall maturity of the design

introduction to a new weighting method hierarchy consistency analysis abstract this paper proposes a new methodology hierarchy consistency analysis hca the approach to this methodology was developed owing to the fact that in the analysis of large scale problems a different viewpoint or specific points emphasis will result in different hierarchy structures on the basis of different structures being created the methodology is designed to combine these different structures and estimate their compromised criterion weights so that all different hierarchy structures will have the same aggregated index the hca methodology will thus provide us with a comprehensive framework for solving hierarchy evaluation problems its merits include amongst others providing a simpler method for calculating the weight of criteria providing a consistency index for monitoring dm judgment consistency and delivering more types of hierarchy structure schemata to aid the decision maker in understanding and auditing the performance status of systems

approximation by matrices positive semidefinite on a subspace abstract we obtain the best approximation to a matrix by matrices positive semidefinite on a subspace as a by product we present two new characterizations of euclidean distance matrices

fuzzy mcdm based on ideal and anti ideal concepts this paper presents a novel fuzzy multiple criteria decision making mcdm based on the concepts of ideal and anti ideal points the concepts of fuzzy set theory and hierarchical structure analysis are used to develop a weighted suitability decision matrix to evaluate the weighted suitability of different alternatives versus various criteria the distance of different alternatives versus positive ideal solution and negative ideal solution are then obtained by using the proposed ranking method finally the relative approximation values of various alternatives versus positive ideal solution are ranked to determine the best alternative

decisions and evaluations by hierarchical aggregation of information usually in preparing a decision a hierarchy of criteria for evaluating alternatives can he agreed upon by the decision makers the problem addressed in this paper is the appropriate modelling of such evaluations and their aggregation in order to arrive at a proper overall evaluation function by which the decision alternatives can be ordered easily representing the criteria subjective categories by fuzzy sets it is possible to use aggregation operators as models for the amalgamation of those criteria in the framework of an empirical research project a hierarchy of criteria was developed for the evaluation of credit worthiness of customers 50 credit applications were evaluated by a number of credit managers of banks and their judgement could be appropriately modelled by a four level hierarchy of criteria

computing the nearest euclidean distance matrix with low embedding dimensions euclidean distance embedding appears in many high profile applications including wireless sensor network localization where not all pairwise distances among sensors are known or accurate the classical multi dimensional scaling cmds generally works well when the partial or contaminated euclidean distance matrix edm is close to the true edm but otherwise performs poorly a natural step preceding cmds would be to calculate the nearest edm to the known matrix a crucial condition on the desired nearest edm is for it to have a low embedding dimension and this makes the problem nonconvex there exists a large body of publications that deal with this problem some try to solve the problem directly and some are the type of convex relaxations of it in this paper we propose a numerical method that aims to solve this problem directly our method is strongly motivated by the majorized penalty method of gao and sun for low rank positive semi definite matrix optimization problems the basic geometric object in our study is the set of edms having a low embedding dimension we establish a zero duality gap result between the problem and its lagrangian dual problem which also motivates the majorization approach adopted numerical results show that the method works well for the euclidean embedding of network coordinate systems and for a class of problems in large scale sensor network localization and molecular conformation

numerical solution of the ericksen leslie dynamic equations for two dimensional nematic liquid crystal flows a finite difference method for solving nematic liquid crystal flows under the effect of a magnetic field is developed the dynamic equations of nematic liquid crystals given by the ericksen leslie dynamic theory are employed these are expressed in terms of primitive variables and solved employing the ideas behind the gensmac methodology tome and mckee 1994 tome et al 2002 38 41 these equations are nonlinear partial differential equations consisting of the mass conservation equation and the balance laws of linear and angular momentum by employing fully developed flow assumptions an analytic solution for steady 2d channel flow is found the resulting numerical technique was then in part validated by comparing numerical solutions against this analytic solution convergence results are presented to demonstrate the capabilities of the numerical method the flow of a nematic liquid crystal through various complex geometries are then simulated results are obtained for l shaped channels and planar 4 1 contraction for several values of reynolds and ericksen numbers

a spectrum of compromise aggregation operators for multi attribute decision making in many decision making problems a number of independent attributes or criteria are often used to individually rate an alternative from an agent s local perspective and then these individual ratings are combined to produce an overall assessment now in cases where these individual ratings are not in complete agreement the overall rating should be somewhere in between the extremes that have been suggested however there are many possibilities for the aggregated value given this this paper systematically explores the space of possible compromise operators for such multi attribute decision making problems specifically we axiomatically identify the complete spectrum of such operators in terms of the properties they should satisfy and show the main ones that are widely used namely averaging operators uninorms and nullnorms represent only three of the nine types we identify for each type we then go onto analyse their properties and discuss how specific instances can actually be developed finally to illustrate the richness of our framework we show how a wide range of operators are needed to model the various attitudes that a user may have for aggregation in a given scenario bidding in multi attribute auctions