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

fuzzy markovian decision process in this paper a markovian decision process with fuzzy states is considered it is shown that if the markov chain associated with the process of non fuzzy states is irreducible then the corresponding markov chain associated with the fuzzy states is also irreducible the importance of this result lies in the fact that the traditional methods for solving the markovian decision process can be used in the case with fuzzy states also

theory of markov systems with fuzzy states in this paper the theory of fuzzy logic is combined with the theory of markov systems and the concept of a markov system with fuzzy states is introduced for the first time the main objective is to develop a methodology of describing a markov population system with fuzzy states this is an effort to deal with the fact that in real applications one is often faced with fuzzy states this paper investigates the properties of a markov system with states that have imprecise boundaries a full description of a nonhomogeneous markov system with fuzzy states is outlined and the basic parameters of the system are provided more specifically the expected population structure of the system is found and given in a closed analytic form and the asymptotic behaviour of the system is provided under the more realistic assumption of a fuzzy set space

a splitting method for incompressible flows with variable density based on a pressure poisson equation a new fractional time stepping technique for solving incompressible flows with variable density is proposed the main feature of this method is that as opposed to other known algorithms the pressure is determined by just solving one poisson equation per time step which greatly reduces the computational cost the stability of the method is proved and the performance of the method is numerically illustrated

a conservative finite element method for the incompressible euler equations with variable density abstract we construct a finite element discretization and time stepping scheme for the incompressible euler equations with variable density that exactly preserves total mass total squared density total energy and pointwise incompressibility the method uses raviart thomas or brezzi douglas marini finite elements to approximate the velocity and discontinuous polynomials to approximate the density and pressure to achieve exact preservation of the aforementioned conserved quantities we exploit a seldom used weak formulation of the momentum equation and a second order time stepping scheme that is similar but not identical to the midpoint rule we also describe and prove stability of an upwinded version of the method we present numerical examples that demonstrate the order of convergence of the method

reliable mixed h passive control for t s fuzzy delayed systems based on a semi markov jump model approach abstract this paper investigates the problem of the reliable mixed h passive control for takagi sugeno t s fuzzy delayed systems based on a semi markov jump model smjm approach the focus is to design a fuzzy fault tolerant controller such that the resulting closed loop system is stochastically stable with a prescribed mixed h passive performance level even if the actuator failures appear a semi markov process is employed to describe the encountered failures of the actuator by applying the lyapunov krasovskii method in combination with some novel inequalities some conditions on the performance analysis are established where some negative quadratic terms are fully considered to reduce the conservatism based on the conditions an explicit expression for the desired controller is given three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method

asymptotic behavior of nonhomogeneous semi markov systems abstract we study the asymptotic behavior of a nonhomogeneous semi markov system population in discrete time after a series of definitions lemmas and theorems we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi markov chain exists and then find the limit of the basic matrix of the chain q n s in closed form finally the existence of the asymptotic population structure of the nonhomogeneous semi markov system is studied and the limit is provided in closed analytic form

a projection fem for variable density incompressible flows abstract this work describes a new finite element projection method for the computation of incompressible viscous flows of nonuniform density one original idea of the proposed method consists in factorizing the density variable partly outside and partly inside the time evolution operator in the momentum equation to prevent spatial discretization errors in the mass conservation to affect the kinetic energy balance of the fluid it is shown that unconditional stability in the incremental version of the projection method is possible provided two projections are performed per time step in particular a second order accurate bdf projection method is presented and its numerical performance is illustrated by test computations and comparisons

asymptotic behaviour of the survival probabilities in an inhomogeneous semi markov model for the migration process in credit risk abstract we start with the stochastic foundation of the general discrete time market of defaultable bonds we prove that the above market is viable if and only if there exists an equivalent martingale measure from which we construct the forward probability measure and under which the discounted default free bond price is a martingale assuming that the migration process of defaultable bonds evolves as an inhomogeneous semi markov process we study the asymptotic behaviour of survival probabilities we provide a method of estimating real world transition probability sequences for the semi markov process and statistics for testing their homogeneity over time

finite time h control for t s fuzzy descriptor semi markov jump systems via static output feedback abstract this paper is concerned with the finite time static output feedback h controller design problem for a type of nonlinear continuous time descriptor semi markov jump systems s mjss via takagi sugeno t s fuzzy model where the transition rates are time varying and dependent on sojourn time firstly based on the stochastic lyapunov functional sufficient conditions on singular stochastic h finite time boundedness ss h ftb for continuous time t s fuzzy descriptor s mjss are given then in order to design the static output feedback controller easily the closed loop system is represented in an augmented form furthermore based on the lower and upper bounds of the time varying transition rates and by using the matrix inequality decoupling technique a novel linear matrix inequality lmi condition on ss h ftb of closed loop system is presented meanwhile the static output feedback controller is developed in terms of lmis the proposed design method doesn t impose any constraints on system matrices or slack variables which shows less conservative results lastly numerical examples are given to demonstrate the effectiveness of the obtained methods

an energy and helicity conserving finite element scheme for the navier stokes equations we present a new finite element scheme for solving the navier stokes equations that exactly conserves both energy int omega u 2 and helicity int omega u cdot nabla times u in the absence of viscosity and external force we prove stability exact conservation and convergence for the scheme energy and helicity are exactly conserved by using a combination of the usual convective form with the rotational form of the nonlinearity and solving for both velocity and a projected vorticity in a trapezoidal time discretization numerical results are presented that compare the scheme to the usual trapezoidal schemes

conditional probability fuzzy sets and possibility a unifying view we propose an interpretation of fuzzy set theory both from a semantic and a syntactic point of view in terms of conditional events and coherent conditional probabilities during past years a large number of papers has been devoted to support either the thesis that probability theory is all that is required for reasoning about uncertainty or the negative view maintaining that probability is inadequate to capture what is usually treated by fuzzy theory in this paper we emphasize the role of conditioning in a proper framework i e de finetti s coherence to get rid of many controversial aspects moreover we introduce suitable operations between fuzzy subsets looked on as corresponding operations between conditional events endowed with the relevant conditional probability finally we show how the concept of possibility function naturally arises as a coherent conditional probability

energy stable and momentum conserving hybrid finite element method for the incompressible navier stokes equations a hybrid method for the incompressible navier stokes equations is presented the method inherits the attractive stabilizing mechanism of upwinded discontinuous galerkin methods when momentum advection becomes significant equal order interpolations can be used for the velocity and pressure fields and mass can be conserved locally using continuous lagrange multiplier spaces to enforce flux continuity across cell facets the number of global degrees of freedom is the same as for a continuous galerkin method on the same mesh different from our earlier investigations on the approach for the navier stokes equations the pressure field in this work is discontinuous across cell boundaries it is shown that this leads to very good local mass conservation and for an appropriate choice of finite element spaces momentum conservation also a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed even in the absence of a pointwise solenoidal velocity field mass conservation momentum conservation and global energy stability are proved for the time continuous case and for a fully discrete scheme the presented analysis results are supported by a range of numerical simulations

semi markov migration process in a stochastic market in credit risk abstract in the present the idea of stochastic market environment comes into play to express the changes in general economy which affects any industry in small or great amounts of turbulence we model the evolution of the market among its possible states as an f inhomogeneous semi markov process this idea leads us to modeling the migration process of defaultable bonds as different f inhomogeneous semi markov process the survival probabilities of a defaultable bond in every credit grade are found the asymptotic behaviour of the survival probabilities is established under certain conditions also it is proved under what conditions the convergence is geometrically fast the stochastic foundation of the general stochastic discrete time market is provided by proving that the market is viable if and only if there exists an equivalent martingale measure from which we construct the forward probability measure and under which the discounted default free bond price process for all possible states of the market is a martingale the term structure of credit spread and the change of real world probability measure to forward probability measure are studied in the form of a theorem it is proved that under certain conditions changing the real probability measure to a forward probability measure does not affect the inhomogeneous semi markov process modeling the migration of defaultable bonds that is it is proved that it only changes the basic parameters and we provide a relation among the transition probabilities under the two measures finally parameter estimation and calibration of the inhomogeneous semi markov chain in stochastic environment is being provided

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

a second order projection method for variable density flows this paper describes a second order projection method for variabledensity incompressible flows the method is suitable for both finite amplitude density variations and for fluids that are modeled using a boussinesq approximation it is based on a second order fractional step scheme in which diffusion convection terms are advanced without enforcing the incompressibility condition and the resulting intermediate velocity field is then projected onto the space of discretely divergencefree vector fields the nonlinear convection terms are treated using a godunov type procedure that is second order for smooth flow and remain stable and non oscillatory for nonsmooth flows with low fluid viscosities the method is described for finite amplitude density variation and the simplifications for a boussinesq approximation are sketched numerical results are presented that validate the convergence properties of the method and demonstrate its performance on more realistic problems

discussion probability theory and fuzzy logic are complementary rather than competitive the relationship between probability theory and fuzzy logic has long been an object of discussion and some controversy the position articulated in this article is that probability theory by itself is not sufficient for dealing with uncertainty and imprecision in real world settings to enhance its effectiveness probability theory needs an infusion of concepts and techniques drawn from fuzzy logic especially the concept of a linguistic variable and the calculus of fuzzy if then rules in the final analysis probability theory and fuzzy logic are complementary rather than competitive

a new fuzzy support vector machine to evaluate credit risk due to recent financial crises and regulatory concerns financial intermediaries credit risk assessment is an area of renewed interest in both the academic world and the business community in this paper we propose a new fuzzy support vector machine to discriminate good creditors from bad ones because in credit scoring areas we usually cannot label one customer as absolutely good who is sure to repay in time or absolutely bad who will default certainly our new fuzzy support vector machine treats every sample as both positive and negative classes but with different memberships by this way we expect the new fuzzy support vector machine to have more generalization ability while preserving the merit of insensitive to outliers as the fuzzy support vector machine svm proposed in previous papers we reformulate this kind of two group classification problem into a quadratic programming problem empirical tests on three public datasets show that it can have better discriminatory power than the standard support vector machine and the fuzzy support vector machine if appropriate kernel and membership generation method are chosen

regularized moving least square method and regularized improved interpolating moving least square method with nonsingular moment matrices abstract the moving least square mls method has been popular applied in surface construction and meshless methods however the moment matrix in mls method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult to overcome this problem a regularized moving least square method with nonsingular moment matrix is proposed the shape functions obtained from the regularized mls method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized mls based meshless method to overcome this problem a regularized improved interpolating moving least square iimls method based on the iimls method is also proposed compared with the regularized mls method the regularized iimls not only has nonsingular moment matrices but also obtains shape functions with delta function property shape functions of the proposed methods are compared in 1d and 2d cases and the methods have been applied in curve fitting surface fitting and meshless method in numerical examples

on the limiting behaiour of a nonhomogeneour markov chain model in manpower systems summary we study the limiting structure of an expanding manpower system where the nonhomogeneous markov chain model proposed by young vassiliou 1974 is applicable the limiting structure and the relative limiting structure exist under certain conditions which are easily met in practical situations finally the problem of weak ergodicity in the above manpower systems is studied necessary and sufficient conditions are provided for weak ergodicity