on viewing fuzzy measures as fuzzy subsets we introduce the concept of a fuzzy measure discuss some of their basic properties and look at some notable examples we introduce a correspondence between a fuzzy measure on x and a fuzzy subset over the power set of x these fuzzy subsets are required to have special properties on the space 2x and we refer to these as measure type fuzzy sets we take advantage of this correspondence between a fuzzy measure and a fuzzy set to suggest the formulation of various set operations on fuzzy measures

on line fuzzy modeling via clustering and support vector machines in this paper we propose a novel approach to identify unknown nonlinear systems with fuzzy rules and support vector machines our approach consists of four steps which are on line clustering structure identification parameter identification and local model combination the collected data are firstly clustered into several groups through an on line clustering technique then structure identification is performed on each group using support vector machines such that the fuzzy rules are automatically generated with the support vectors time varying learning rates are applied to update the membership functions of the fuzzy rules the modeling errors are proven to be robustly stable with bounded uncertainties by a lyapunov method and an input to state stability technique comparisons with other related works are made through a real application of crude oil blending process the results demonstrate that our approach has good accuracy and this method is suitable for on line fuzzy modeling

exact results for the critical behaviour of a nienhuis o n model on the square lattice exact results are obtained for a square lattice fifteen vertex model and related o n model recently proposed by nienhuis 1990 the partition function per site and finite size corrections are obtained along with the critical exponents via the temperley lieb equivalent six vertex model the exact exponents nu 4 7 and gamma 6 7 follow in the limit n 0 for even system sizes odd system sizes are also discussed the fifteen vertex model is also the vertex formulation of the anisotropic or q deformed spin 1 biquadratic model

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

on the combination and normalization of interval valued belief structures this paper investigates the issues of combination and normalization of interval valued belief structures within the framework of dempster shafer theory dst of evidence existing approaches are reviewed examined and critically analysed they either ignore the normalization or separate it from the combination process leading to irrational or suboptimal interval valued belief structures a new logically correct optimality approach is developed where the combination and the normalization are optimised together rather than separately numerical examples are provided throughout the paper

on distribution function description of probabilistic sets and its application in decision making the paper deals with some problems of decision making described and solved by the use of the concept of a probabilistic set the distribution function description of probabilistic sets which is important from a theoretical point of view is discussed and its application in decision making is illustrated by means of numerical examples

a hierarchical neural model of matching abstract the issue of matching two fuzzy sets emerges as an essential design aspect in many algorithms of processing fuzzy information including fuzzy controllers pattern classifiers knowledge based systems etc this paper introduces a new model of matching the primordial features of the proposed model involve 1 i matching being carried out with respect to the grades of membership of the discussed fuzzy sets as well as some of their functionals like energy entropy transom 2 ii the concepts of hierarchies of matching in the model leading directly to a straightforward distinction between local and global levels of matching and 3 iii a distributed character of the model that is realized as a logic based neural network with enhanced learning capabilities

the solution of singularly perturbed semilinear elliptic problems by iterative domain decomposition algorithms abstract parallel domain decomposition algorithms for the solution of singularly perturbed semilinear elliptic problems are considered convergence properties and numerical stability of these iterative algorithms are established numerical experiments are provided

diagnosability of fuzzy discrete event systems in this paper discrete event systems dess are reformulated as fuzzy discrete event systems fdess and fuzzy discrete event dynamical systems fdedss these frameworks include fuzzy states events and if then rules in these frameworks all events occur at the same time with different membership degrees fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems such as fault diagnosis applications to measure a diagnoser s fault discrimination ability a fuzzy diagnosability degree is proposed if the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system for any degree less than one researchers should not devote their time to distinguish all possible fault types correctly thus two different diagnosability definitions fdeds and fdes are introduced due to the specialized fuzzy rule base embedded in the fdeds it is capable of representing a class of non linear dynamic system computationally speaking the framework of diagnosability of the fdeds is structurally similar to the framework of diagnosability of a non linear system the crisp des diagnosability has been turned into the term fuzzy diagnosability for the fdes the newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non linear systems in addition a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development finally the potential applications of the proposed method are discussed

the solution of singularly perturbed parabolic problems by parallel algorithms combining crank nicholson scheme and overlapping schwarz methods abstract parallel algorithms combining a time discretization and overlapping domain decomposition methods are applied to the solution of singularly perturbed parabolic problems two domain decomposition methods based on the schwarz alternating procedure are proposed the method with two colour ordering of subdomains and the method with additional correcting problems moreover modifications of the methods are considered using time extrapolation on subdomain interfaces convergence properties of the algorithms are established at the differential level numerical results for a test singularly perturbed problem are presented to confirm the convergence theory and to evaluate the parallel arithmetic complexity of the algorithms

iterative domain decomposition algorithms for the solution of 2 d eddy current problem abstract iterative domain decomposition algorithms are applied to the solution of two dimensional eddy current problem the system of differential equations describing this problem is considered as singularly perturbed problem convergence of these algorithms is established several numerical experiments are presented

surface critical behaviour of an o n loop model related to two manhattan lattice walk problems we find and discuss the scaling dimensions of the branch 0 manifold of the nienhuis o n loop model on the square lattice concentrating on the surface dimensions the results are extracted from a bethe ansatz calculation of the finite size corrections to the eigenspectrum of the six vertex model with free boundary conditions these results are especially interesting for polymer physics at two values of the crossing parameter lambda interacting self avoiding walks on the manhattan lattice at the collapse temperature lambda pi 3 and hamiltonian walks on the manhattan lattice lambda pi 2 are discussed in detail our calculations illustrate the importance of examining both odd and even strip widths when performing finite size correction calculations to obtain scaling dimensions

the relationship of controllability between classical and fuzzy discrete event systems we have known that the controllability of classical discrete event systems has already been extended into fuzzy discrete event systems in this paper firstly we recall some related definitions and results of the controllability for classical and fuzzy discrete event systems respectively secondly we are concerned with the relationship of the controllability between classical and fuzzy discrete event systems in particular we show that there is an equivalence of the controllability between the two systems to some extent some special proofs are also presented finally we use this equivalence to extend some general controllability properties of classical discrete event systems into fuzzy ones

sensitivity of spin glass order to temperature changes by a loop expansion around parisi s mean field theory for an ising spin glass it is shown that the overlap of the magnetization patterns belonging to two different temperatures t and t vanishes to any order si t si t 0 while the correlation overlap sisj t sisj t calculated to first loop order and for technical reasons for dimensions d 8 only is found to decay exponentially with a characteristic length approximately t t 1

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

fuzzy set connectives as combinations of belief structures abstract consonant belief structures provide a representation for fuzzy sets owing to the fact that their plausibility measures are essentially possibility measures we note that two belief structures are equivalent if their plausibility and belief functions are equal this observation leads us to provide a multiple number of equivalent representations for any belief structure commensurate representations can be induced for two different belief structures by forcing the same number of focal elements with the same weights we show that if we represent two consonant belief structures in a commensurate manner then their aggregations are closed with respect to consonance provided that the additional requirement that the underlying probability distributions satisfy a condition of correlation is imposed the results of this work allow us to use belief structure representations for the manipulation of fuzzy subsets under various logical combinations all basic fuzzy set connectives can thus be interpreted in the framework of the theory of evidence

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

manhattan lattice theta point exponents from kinetic growth walks and exact results from the nienhuis o n model kinetic growth walks kgw on the manhattan lattice have previously been shown to be equivalent to the static problem of interacting self avoiding walks on that lattice at the theta temperature here we illustrate how a complete set of exponents for the static problem including the crossover exponent phi and surface exponents at the ordinary and special transition points may be obtained from simulations of kinetic walks in the process we find that phi m 0 430 or 0 006 which encompasses the conjectured value 3 7 approximately 0 42857 for the theta point on an isotropic lattice our numerics confirm a predicted set of exponents for both the bulk and surface transitions in addition to results such as the exact internal energy at the bulk transition furthermore we point out that a recently examined variant of the nienhuis o n model can be mapped onto theta point walks on the manhattan lattice which allows identification of the scaling dimensions for that problem and thereby provides a method for proving all the numerical conjectures

an evidential network approach to support uncertain multiviewpoint abductive reasoning the paper proposes an approach to support human abductive reasoning in the diagnosis of a multiviewpoint system the novelty of this work lies on the capability of the approach to treat the uncertainty held by the agent performing the diagnosis to do so we make use of evidential networks to represent and propagate the uncertain evidence gathered by the agent using forward and backward propagation of the information the impact of the evidence over the different symptoms and causes of failure is quantified the agent can then make use of this information as additional hints in an iterative diagnosis process until a desired degree of certainty is obtained the model is compared with a deterministic one in which evidence is represented by binary states that is a symptom is either observed or not

rough set based conflict analysis model and method over two universes rough set theory as a new mathematical tool to handle uncertainty decision making problems was used to study conflict analysis decision making in late90 s and then the pawlak conflict analysis model was established the approach of rough set provides a new perspective and also gives an effective tool to deal with conflict analysis decision making both theoretically and practically in this paper we propose a new rough set model of conflict analysis a conflict analysis decision model based on rough set theory over two universes it is a natural extension of the pawlak conflict analysis model subsequently we define the conflict matrix and a consistent disagreement matrix on the basis of the model proposed in this paper then we can find the intrinsic reasons for conflict and attain a feasible strategy for a conflict situation furthermore we define a positive alliance matrix and a negative alliance matrix for a conflict situation these can help us analyze the opinions of different agents in the conflict situation moreover we develop a matrix approach for a conflict analysis model based on rough set theory over two universes which provides a convenient way to analyze and solve the conflict situation comparing to the pawlak conflict analysis model our proposed model not only could reveal the core causes for a conflict situation but also can find a possible optimal feasible consensus strategy to solve the conflict situation which satisfies the agents as much as possible finally we illustrate the idea and the basic principles established in this paper by analyzing a conflict decision making scenario

surface operator content of the al face models abstract a set of fixed boundary weights for both the critical dense and dilute a l face models is constructed from the known boundary weights of the related loop model the surface operator content and the conformal partition functions then follow from the results obtained via the bethe equations

critical exponents of manhattan hamiltonian walks in two dimensions from potts and o n models we consider a set of hamiltonian circuits filling a manhattan lattice i e a square lattice with alternating traffic regulation we show that the generating function with fugacityz of this set is identical to the critical partition function of aq state potts model on an unoriented square lattice withq1 2 z the set of critical exponents governing correlations of hamiltonian circuits is derived using a coulomb gas technique these exponents are also found to be those of an o n vector model in the low temperature phase withn q1 2 z the critical exponents in the limitz 0 are then those of spanning trees q 0 and of dense polymers n 0 t tc corresponding to a conformal theory with central chargec 2 this shows that the manhattan orientation and the hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of hamiltonian walks

representation similarity measures and aggregation methods using fuzzy sets for content based recommender systems representation of features of items and user feedback and reasoning about their relationships are major problems in recommender systems this is because item features and user feedback are subjective imprecise and vague the paper presents a fuzzy set theoretic method ftm for recommender systems that handles the non stochastic uncertainty induced from subjectivity vagueness and imprecision in the data and the domain knowledge and the task under consideration the research further advances the application of fuzzy modeling for content based recommender systems initially presented by ronald yager the paper defines a representation method similarity measures and aggregation methods as well as empirically evaluates the methods performance through simulation using a benchmark movie data ftm consist of a representation method for items features and user feedback using fuzzy sets and a content based algorithm based on various fuzzy set theoretic similarity measures the fuzzy set extensions of the jaccard index cosine proximity or correlation similarity measures and aggregation methods for computing recommendation confidence scores the maximum minimum or weighted sum fuzzy set theoretic aggregation methods compared to the baseline crisp set based method csm presented the empirical evaluation of the ftm using the movie data and simulation shows an improvement in precision without loss of recall moreover the paper provides a guideline for recommender systems designers that will help in choosing from a combination of one of the fuzzy set theoretic aggregation methods and similarity measures

modeling vague beliefs using fuzzy valued belief structures abstract this paper presents a rational approach to the representation and manipulation of imprecise degrees of belief in the framework of evidence theory we adopt as a starting point the non probabilistic interpretation of belief functions provided by smets transferable belief model as well as previous generalizations of evidence theory allowing to deal with fuzzy propositions we then introduce the concepts of interval valued and fuzzy valued belief structures defined respectively as crisp and fuzzy sets of belief structures verifying hard or elastic constraints we then proceed with a generalization of various concepts of dempster shafer theory including those of belief and plausibility functions combination rules and normalization procedures most calculations implied by the manipulation of these concepts are based on simple forms of linear programming problems for which analytical solutions exist making the whole scheme computationally tractable we discuss the application of this framework in the areas of decision making under uncertainty and classification of fuzzy data

overlapping schwarz methods for a singularly perturbed semilinear elliptic problem and their parallel implementation domain decomposition algorithms based on the schwarz alternating method are applied to the numerical solution of a singularly perturbed semilinear elliptic problem the emphasis is given to the description of the algorithms multidomain schwarz alternating method and two level schwarz method as well as their computer realization on a distributed memory multiprocessor computer numerical experiments related to a model problem illustrate the performance of the algorithms on parallel environment as well as their behavior with respect to the critical parameters such as the perturbation parameter the amount of overlapping and sizes of subdomains application of the two level schwarz method to a model semiconductor problem is also discussed

maximal confidence intervals of the interval valued belief structure and applications an unsolved problem in the interval valued belief structure is the existence of maximal confidence intervals referring to the credible and maximal interval valued beliefs assigned to focal elements in which every point can be reached by a combination rule in this study the existence of maximal confidence intervals of the interval valued belief structure was investigated and validated in addition some applications of the maximal confidence interval in constructing valid and normalized interval valued belief structures are discussed a numerical experiment was conducted to illustrate the existence of maximal confidence intervals several propositions and a theorem were further proposed to demonstrate the validity of the maximal confidence interval by using the concept of the maximal confidence interval a procedure was proposed to construct valid and normalized interval valued belief structures and some meaningful guidance for assigning interval valued beliefs was also suggested to the experts finally a series of well designed examples was presented as applications of the maximal confidence interval the proposed procedure and the suggestions they indicated that valid and normalized interval valued belief structures can be achieved accurately and efficiently in practical applications with the proposed procedure and guidance on the basis of the concept of the maximal confidence interval

exact solution and surface critical behaviour of an o n model on the honeycomb lattice the authors obtain the exact bethe ansatz solution of an o n model on the honeycomb lattice with open boundaries across a finite strip several quantities relevant to the surface critical behaviour of the o n model are derived from this solution the exact surface critical exponents are in agreement with those obtained by cardy 1987 and by duplantier and saleur 1986 based on conformal invariance arguments

boundary critical behavior of d 2 self avoiding walks on correlated and uncorrelated vacancies in this paper we present exact results for the critical exponents of interacting self avoiding walks with ends at a linear boundary effective interactions are mediated by vacancies correlated and uncorrelated on the dual lattice by choosing different boundary conditions several ordinary and special regimes can be described in terms of clusters geometry and of critical and lowtemperature properties of the mathcal o n 1 model in particular the problem of boundary exponents at the point is fully solved and implications for point universality are discussed the surface crossover exponent at the special transition of noninteracting self avoiding walks is also interpreted in terms of percolation dimensions

random set framework for multiple instance learning multiple instance learning mil is a technique used for learning a target concept in the presence of noise or in a condition of uncertainty while standard learning techniques present the learner with individual samples mil alternatively presents the learner with sets of samples although sets are the primary elements used for analysis in mil research in this area has focused on using standard analysis techniques in the following a random set framework for multiple instance learning rsf mil is proposed that can directly perform analysis on sets the proposed method uses random sets and fuzzy measures to model the mil problem thus providing a more natural mathematical framework a more general mil solution and a more versatile learning tool comparative experimental results using rsf mil are presented for benchmark data sets rsf mil is further compared to the state of the art in landmine detection using ground penetrating radar data

solvable lattice models labelled by dynkin diagrams an equivalence between generalized restricted solid on solid models associated with sets of graphs and multi colour loop models is established as an application the authors consider solvable loop models and in this way obtain new solvable families of critical rsos models these families can all be classified by the dynkin diagrams of the simply laced lie algebras for one of the rsos models labelled by the lie algebra pair al al and related to the c2 1 vertex model they give an off critical extension which breaks the z2 symmetry of the dynkin diagrams

combining uncertainty and imprecision in models of medical diagnosis the paper presents a unified fuzzy probabilistic framework for modeling processes of medical diagnosis the two basic concepts of the dempster shafer theory i e focal elements and a basic probability assignment correspond to disease symptoms and the significance of an individual symptom in the diagnosis respectively the belief computation is related to diagnostic inference the final conclusion of the inference is the diagnosis with the greatest belief value fuzzy sets are used to describe focal elements it is shown how their membership functions and basic probability assignments are estimated on the basis of experimental data the interpretation of focal elements as fuzzy sets along with individual consideration of evidence imprecision and uncertainty of diagnosis are the essential new aspects of the presented method experimental studies have demonstrated the superiority of the proposed approach over some other modeling alternatives

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

collapse of a polymer in two dimensions abstract we numerically investigate the influence of self attraction on the critical behaviour of a polymer in two dimensions by means of an analysis of finite size results of transfer matrix calculations the transfer matrix is constructed on the basis of the o n loop model in the limit n 0 it yields finite size results for the magnetic correlation length of systems with a cylindrical geometry a comparison with the predictions of finite size scaling enables us to obtain information about the phase diagram as a function of the chemical potential of the loop segments and the strength of the attractive potential results for the magnetic scaling dimension can be interpreted in terms of known universality classes in particular when the attractive potential is increased we observe the crossover between the polymer critical behaviour of the self avoiding walk type to behaviour described earlier for the theta point

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

mass function derivation and combination in multivariate data spaces in this paper we consider the problem of how to derive mass functions systematically from data samples we also consider the ensuing problem of how to combine different mass functions derived in this way we show that a mass function can be efficiently and systematically derived from multivariate data we also demonstrate that combining mass functions obtained in this manner can be done easily the way of deriving and combining mass functions is illustrated with a simple example

the solution of singularity perturbed huge problems via domain decomposition abstract this paper deals with iterative algorithms for domain decomposition suitable for singular perturbation problems convergence results are established for one dimensional and two dimensional problems decomposition into subdomains is accompanied via singular perturbation character of problems numerical examples are presented the developed parallel iterative algorithm is compared with the schwarz alternating procedure

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

surface free energy of the critical six vertex model with free boundaries the bethe ansatz equations are derived for the six vertex model with general boundary weights on a lattice in a diagonal orientation these are solved in the thermodynamic limit finite size corrections to the free energy for a restricted class of boundary weights including those corresponding to a potts model with free boundaries are calculated in the critical region the first order term gives the surface free energy of the model the second order term is found to be pi okt tan pi nu 2 mu c 48n 2 where c 1 6 mu 2 pi 2 pi mu is the conformal anomaly this can be compared to pi kt sin pi nu mu c 6n 2 for a calculation on the lattice in the standard orientation and with periodic boundary conditions this difference can be explained geometrically using conformal invariance

efficiencies of two stage systems with fuzzy data two stage dea data envelopment analysis models show the performance of individual processes and thus are more informative than the conventional one stage models for making decisions this paper extends this approach from deterministic to uncertain situations where the observations are represented by fuzzy numbers the extension principle is utilized to develop a pair of two level mathematical programs to calculate the lower and upper bounds of the a cut of the fuzzy efficiency by enumerating various values of a the membership functions of fuzzy efficiencies are constructed numerically it is found that the property of the system efficiency being equal to the product of the two process efficiencies which holds for the deterministic case also holds for the fuzzy case this property can be generalized to series systems with more than two processes an example of non life insurance companies in taiwan is used to explain how to calculate the system and process efficiencies and how to derive their relationship when the data is fuzzy

two level parallel schwarz methods for singularly perturbed semilinear elliptic problems abstract two level domain decomposition methods based on the schwarz alternating procedure are proposed for the numerical solution of singularly perturbed semilinear elliptic problems convergence properties of the two level schwarz methods are established numerical experiments for a test problem illustrate the behaviour of the methods with respect to the critical parameters such as the perturbation parameter the amount of overlapping and sizes of subdomains application of one of the two level schwarz methods to a model semiconductor problem is also discussed

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

on some optimization problems under uncertainty abstract the last ten years show a diversification of the approaches for handling uncertainties in optimization problems by certain relaxations or on the contrary seeking a more conservative solution in this paper we present some new results and points of view in nonlinear inexact and fuzzy mathematical programming possible applications to capital budgeting of interrelated projects and to production planning are also discussed

possibility and necessity in optimization abstract we employ possibility and necessity in fuzzy programming and in other optimization problems that traditionally use random variables the possibility approach to multiobjective programming produces the same results as fuzzy programming a detailed example is presented to illustrate the use of possibility and necessity in optimization problems that usually employ random variables to describe uncertainty

comparison of parallel implementation of some multi level schwarz methods for singularly perturbed parabolic problems abstract parallel multi level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems two methods based on the schwarz alternating procedure are considered a two level method with auxiliary correcting subproblems as well as a three level method with auxiliary predicting and correcting subproblems moreover modifications of the methods using time extrapolation on subdomain interfaces are investigated the emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer numerical experiments illustrate the performance of the algorithms on parallel environment and their behaviour with respect to the critical parameters such as the perturbation parameter and the size of the auxiliary subdomains

exact solution and surface critical behaviour of open cyclic sos lattice models we consider the l state cyclic solid on solid lattice models under a class of open boundary conditions the integrable boundary face weights are obtained by solving the reflection equations functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions the eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic bethe ansatz for a special case of crossing parameter the finite size corrections to the eigenspectra of the critical models are obtained from which the corresponding conformal dimensions follow the calculation of the surface free energy away from criticality yields two surface specific heat exponents and where coprime to l these results are in agreement with the scaling relations and

universal distance ratios for interacting two dimensional polymers we present the hypothesis that at the theta temperature of a single interacting polymer in two dimensions a particular combination of universal distance amplitude ratios is given exactly by a simple formula in terms of critical indices only this generalizes a similar claim for noninteracting self avoiding walks which was derived from conformal invariance considerations we support our hypothesis with a series analysis of interacting self avoiding walks on the square lattice high precision simulations of interacting self avoiding walks on the manhattan lattice at the exact theta point and similar simulations of interacting trails on the square lattice

critical behaviour of the fully packed loop model on the square lattice we investigate the critical behaviour of the fully packed o n loop model on the square lattice in which each vertex is visited once by a loop a transfer matrix analysis shows that this model can be interpreted as a superposition of a low temperature o n model and an solid on solid sos model as for the fully packed model on the honeycomb lattice however not all of the critical exponents are the same for both lattices in contrast the fully packed model on the triangular lattice appears to behave as a pure low temperature o n model

computer aided fuzzy medical diagnosis this paper describes a fuzzy approach to computer aided medical diagnosis in a clinical context it introduces a formal view of diagnosis in clinical settings and shows the relevance and possible uses of fuzzy cognitive maps and fuzzy logic a constraint satisfaction method is introduced which uses the temporal uncertainty in symptom durations that may occur with particular diseases together with fuzzy symptom descriptions the method results in an estimate of the stage of a disease if the temporal constraints of the disease in relation to the occurrence of the symptoms are satisfied the approach is evaluated through simulation experiments showing the effects of symptom ordering temporal uncertainty and symptom strengths on the diagnosis efficiency the method is effective and can be developed further using second order type 2 fuzzy logic to better represent uncertainty in the clinical context thus improving differential diagnosis accuracy

extracting easily interpreted diagnostic rules abstract diagnosis support systems are often disregarded because of their high costs complicated inference and inability to modify the knowledge base the aim of this work is to propose a method that helps to resolve these problems by extracting diagnostic rules that can be easily interpreted and verified by experts the rules can be obtained from data even if the latter are imperfect which is usual in medical databases next intuitively clear reasoning is suggested to elaborate on the diagnosis rules are focal elements in the framework of the dempster shafer theory they include fuzzy sets in their premises thus a measure of imprecision as a fuzzy membership function and a measure of uncertainty as the basic probability value are used moreover a rule selection algorithm and a rule evaluation method that prevent some of the imperfections of the existing methods are proposed particular attention is paid to the evaluation of the extracted rule set according to its reliability and clarity for a human user experimental results obtained for popular medical data sets demonstrate the advantages of the proposed approach for each data set simple and readable rule sets are determined they provide comparable or better results than the approaches published so far

fuzzy integrals on l fuzzy sets abstract the fuzzy measures and fuzzy integrals for zadeh s fuzzy sets were studied by qiao and wang 5 6 7 12 in this paper we consider the real valued fuzzy measures and fuzzy integrals for l fuzzy sets where l is a pseudocomplemented infinitely distributive complete lattice on a fuzzy algebra of l fuzzy sets the concepts of fuzzy measure and fuzzy integral are introduced some equivalent forms of fuzzy integrals on l fuzzy sets are given moreover we discuss several properties of fuzzy integrals on l fuzzy sets and prove some convergence theorems for a sequence of fuzzy integrals on l fuzzy sets

singularly perturbed problems in partial differential equations a survey this survey paper contains a surprisingly large amount of material on singularly perturbed partial differential equations and indeed can serve as an introduction to some of the ideas and methods of the singular perturbation theory starting from prandtl s work a large amount of work has been done in the area of singular perturbations this paper limits its coverage to some standard singular perturbation models considered by various workers and the methods developed by numerous researchers after 1980 2000 in this review we have covered singularly perturbed partial differential equations about odes the survey has already been done by us see m k kadalbajoo k c patidar appl math comput 130 2002 457 510

advanced fuzzy inference engines in situation aware computing we focus on the very important family of context aware applications context aware computing relies on tasks like capturing sensing environmental parameters e g lightness location classifying context and inferring further knowledge about that context determine the situation the user is currently in however the relevant applications have to deal with the inherent imperfection of context sensing for decision making we propose an extension of context representation and inference for situation aware applications our model relies on fuzzy set theory to accommodate the imperfection of sensed context based on this model we have developed three fuzzy inference engines which rely on advanced semantics specialization mereological and compatibility relations we have evaluated the proposed engines through a series of experiments involving real users our findings indicate the strong points of the proposed context classification and inference processes

a possibilistic argument for irreversibility abstract our aim is to explicate the idea of irreversibility by a mathematical representation of irreversible processes occurring in possibilistic dynamical systems with this in mind solutions of the cauchy problem in the space of fuzzy points are examined to meet the correspondence argument solutions of the cauchy problem in the space of concentrated points are examined too

alternative second order cone programming formulations for support vector classification this paper presents two novel second order cone programming socp formulations that determine a linear predictor using support vector machines svms inspired by the soft margin svm formulation our first approach x socp svm proposes a relaxation of the conic constraints via a slack variable penalizing it in the objective function the second formulation r socp svm is based on the lp svm formulation principle the bound of the vc dimension is loosened properly using the l norm and the margin is directly maximized the proposed methods have several advantages the first approach constructs a flexible classifier extending the benefits of the soft margin svm formulation to second order cones the second method obtains comparable results to the socp svm formulation with less computational effort since one conic restriction is eliminated experiments on well known benchmark datasets from the uci repository demonstrate that our approach accomplishes the best classification performance compared to the traditional socp svm formulation lp svm and to standard linear svm

parallel schwarz methods for convection dominated semilinear diffusion problems parallel two level schwarz methods are proposed for the numerical solution of convection diffusion problems with the emphasis on convection dominated problems two variants of the methodology are investigated they differ from each other by the type of boundary conditions dirichlet or neumann type posed on a part of the second level subdomain interfaces convergence properties of the two level schwarz methods are experimentally compared with those of a variant of the standard multi domain schwarz alternating method numerical experiments performed on a distributed memory multiprocessor computer illustrate parallel efficiency of the methods

generalization of the dempster shafer theory a fuzzy valued measure the dempster shafer theory dst may be considered as a generalization of the probability theory which assigns mass values to the subsets of the referential set and suggests an interval valued probability measure there have been several attempts for fuzzy generalization of the dst by assigning mass probability values to the fuzzy subsets of the referential set the interval valued probability measures thus obtained are not equivalent to the original fuzzy body of evidence in this paper a new generalization of the dst is put forward that gives a fuzzy valued definition for the belief plausibility and probability functions over a finite referential set these functions are all equivalent to one another and to the original fuzzy body of evidence the advantage of the proposed model is shown in three application examples it can be seen that the proposed generalization is capable of modeling the uncertainties in the real world and eliminate the need for extra preassumptions and preprocessing

computational method for a singular perturbation problem via domain decomposition and its parallel implementation abstract in this paper a computation method for the nonlinear problem with a small perturbation parameter via domain decomposition is presented we apply a combination of the two approaches to solving the problem iterative algorithms for domain decomposition and a grid refinement technique on subdomains two iterative algorithms are examined the first one is the schwarz alternating procedure and the second algorithm is highly suitable for parallel computing numerical examples are provided

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application

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

the evidential reasoning approach for mada under both probabilistic and fuzzy uncertainties abstract many multiple attribute decision analysis mada problems are characterised by both quantitative and qualitative attributes with various types of uncertainties incompleteness or ignorance and vagueness or fuzziness are among the most common uncertainties in decision analysis the evidential reasoning er approach has been developed in the 1990s and in the recent years to support the solution of mada problems with ignorance a kind of probabilistic uncertainty in this paper the er approach is further developed to deal with mada problems with both probabilistic and fuzzy uncertainties in this newly developed er approach precise data ignorance and fuzziness are all modelled under the unified framework of a distributed fuzzy belief structure leading to a fuzzy belief decision matrix a utility based grade match method is proposed to transform both numerical data and qualitative fuzzy assessment information of various formats into the fuzzy belief structure a new fuzzy er algorithm is developed to aggregate multiple attributes using the information contained in the fuzzy belief matrix resulting in an aggregated fuzzy distributed assessment for each alternative different from the existing er algorithm that is of a recursive nature the new fuzzy er algorithm provides an analytical means for combining all attributes without iteration thus providing scope and flexibility for sensitivity analysis and optimisation a numerical example is provided to illustrate the detailed implementation process of the new er approach and its validity and wide applicability

fuzzy inference relation based on the theory of falling shadows abstract in this paper we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows the main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication we shall show that the formulae of fuzzy inference relation given by ukasiewicz zadeh and the probability formula are consequences of our definition under three different correlations of the propositions