fuzzy quality and analysis on fuzzy probability abstract the paper puts forward the fuzzy attribute of quality and the way of a qualified handling of fuzzy quality it brings to light the transition and consistency between clear quality and fuzzy quality and advances the concept of fuzzy qualification and puts forward its corresponding computing formula the paper also develops the concept of fuzzy process capability and puts forward the computing formula of fuzzy process capability index by which fuzzy process can be controlled

a theory of independent fuzzy probability for system reliability fuzzy fault trees provide a powerful and computationally efficient technique for developing fuzzy probabilities based on independent inputs the probability of any event that can be described in terms of a sequence of independent unions intersections and complements may be calculated by a fuzzy fault tree unfortunately fuzzy fault trees do not provide a complete theory many events of substantial practical interest cannot be described only by independent operations thus the standard fuzzy extension based on fuzzy fault trees is not complete since not all events are assigned a fuzzy probability other complete extensions have been proposed but these extensions are not consistent with the calculations from fuzzy fault trees we propose a new extension of crisp probability theory our model is based on n independent inputs each with a fuzzy probability the elements of our sample space describe exactly which of the n input events did and did not occur our extension is complete since a fuzzy probability is assigned to every subset of the sample space our extension is also consistent with all calculations that can be arranged as a fault tree our approach allows the reliability analyst to develop complete and consistent fuzzy reliability models from existing crisp reliability models this allows a comprehensive analysis of the system computational algorithms are provided both to extend existing models and develop new models the technique is demonstrated on a reliability model of a three stage industrial process

the cauchy problem for the generalized imbq equation in ws p rn in this paper the existence and the uniqueness of the global strong solution and the global classical solution for the cauchy problem of the multidimensional generalized imbq equation are proved the nonexistence of the global solution for the cauchy problem of the generalized imbq equation is discussed

fuzzy process control construction of control charts with fuzzy numbers this paper presents the construction of fuzzy control charts for a process with fuzzy outcomes derived from the subjective quality ratings provided by a group of experts the proposed fuzzy process control fpc methodology comprises an off line stage and an on line stage in the off line stage experts assign quality ratings to products based on a numerical scale the individual numerical ratings are then aggregated to form collective opinions expressed in the form of fuzzy numbers the collective knowledge applied by the experts when conducting the quality rating process is acquired through a process of fuzzy regression analysis performed by a neural network in the on line stage the product dimensions are measured and the fuzzy regression model is employed to automate the experts judgments by mapping the measured dimensions to appropriate fuzzy quality ratings the fuzzy quality ratings are then plotted on fuzzy control charts whose construction and out of control conditions are developed using possibility theory the developed control charts not only monitor the central tendency of the process but also indicate its degree of fuzziness

using fuzzy sets in operational research abstract during the last four decades a large number of mainly mathematical tools have been developed in and for operational research they are primarily devices to find optimal solutions after a problem has been modelled formally hardly any new tools have been developed for proper modelling of problems which are not well structured and which can not easily be cast into classical mathematical models fuzzy set theory as proposed by l zadeh in 1965 promises to bridge part of this gap it is much more adaptable to different problem structures and better suited to model human evaluation and decision making processes than classical mathematics this paper will primarily focus attention on four questions why fuzzy sets in or what are fuzzy sets where can they be used and how are they being used

extension of the concept of mappings using fuzzy sets abstract in this paper we develop a new method of extending the concept of ordinary mappings from ordinary sets to ordinary sets to mapping from sets to fuzzy sets by constructing corresponding mappings from original ordinary mappings we also compare this method with other similar methods including zadeh s extension

construction of p charts using degree of nonconformity control charts are among the simplest of on line statistical process control techniques when the quality characteristic is a variable the p chart takes time to react to shifts in the production process because of its weak response to small variations in the process mean and variance in this paper instead of considering an item to be either conforming or nonconforming the degree of nonconformity based on fuzzy concepts is defined and a fuzzy p chart based on the mean degree of nonconformity is constructed it is shown that this chart has a better response to variations in both the mean and the variance of the process

a review and comparison of six reasoning methods abstract five fuzzy reasoning methods are reviewed and their performance is compared with respect to a fuzzy control system model developed by an objective method based on three sets of real life data it is found from the investigation that the reasoning precision the calculation time and the number of possible input states to which a given reasoning method responds differ according to each reasoning method generally the point valued reasoning methods which are based on the assumption that connectives are crisp give better precision and shorter calculation time when the connectives are assumed to be linguistic reasoning with interval valued fuzzy sets are more appropriate to represent linguistic uncertainty for this reason type ii fuzziness generated with interval valued fuzzy sets are better handled with interval valued reasoning methods

fuzzy importance in fault tree analysis abstract in fault tree analysis system success or failure can be described by the state of the top event which is usually defined by a so called structure function in this paper we attempt to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function using fuzzy sets theory furthermore it is shown that the importance of each basic event can be evaluated through fuzzy operations the method proposed herein is demonstrated by some examples with respect to the failure analysis of structures

fuzzy system reliability analysis by interval of confidence abstract the use of fuzzy number over interval of confidence instead of probability and possibilitic considerations for evaluating the range value and interval of the fuzzy reliability is proposed this approach of evaluating fuzzy system reliability by interval arithmetic and cuts has a considerable advantage we can calculate reliability problems easily by the use of derive and mathcad packages through theoretical analysis an illustrative example and computational results we show that the proposed approach is more general and simplified

bayesian reliability analysis for fuzzy lifetime data lifetime data are important in reliability analysis classical reliability estimation is based on precise lifetime data it is usually assumed that observed lifetime data are precise real numbers however some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers thus it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers bayesian methods have proved to be very useful when the sample size is small there is little study on bayesian reliability estimation based on fuzzy lifetime data most of the reported works in this area is limited to single parameter lifetime distributions in this paper we propose a new method to determine the membership function of the estimates of the parameters and the reliability function of multi parameter lifetime distributions an artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction the genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level this method can be used to determine the membership functions of the bayesian estimates of multi parameter distributions the effectiveness of the proposed method is illustrated with normal and weibull distributions

global existence and asymptotics of solutions of the cahn hilliard equation abstract this paper is concerned with the cauchy problem of the cahn hilliard equation u t u 2 u 0 x r n t 0 u t 0 u 0 x x r n first we construct a local smooth solution u t x to the above cauchy problem then by combining some a priori estimates sobolev s embedding theorem and the continuity argument the local smooth solution u t x is extended step by step to all t 0 provided that the smooth nonlinear function u satisfies a certain local growth condition at some fixed point u r and that u 0 x u l 1 r n is suitably small secondly we show that the global smooth solution u t x satisfies the following temporal decay estimates d k u t x u l p r n c 1 t k 4 n 4 1 1 p t 0 k 0 1 here p 1 c 0 is a constant depending on and 0 is any positive constant which can be chosen sufficiently small at last we show that under a strong assumption on the growth of the nonlinear function u at u u the asymptotics of solutions of the above cauchy problem is described by u 0 t n 4 g x t 4 here 0 r n u 0 x u d x g x r n exp 4 i x d

on modeling possibilistic uncertainty in two state reliability theory in this paper we show how a possibilistic uncertainty model can be used to represent and manipulate uncertainty about the states of a system and of its components at the same time we present a thorough study of the incorporation of this possibilistic uncertainty model in classical two state reliability theory the possibilistic reliability of a component or system is introduced and studied furthermore we introduce the important notion of a possibilistic structure function based upon the concept of a classical two valued structure function under certain conditions of possibilistic independence it allows us to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components finally we give straightforward methods for determining a possibilistic structure function from its classical two valued counterpart in this way we intend to show that a possibilistic uncertainty model in two state reliability theory is formally analogous to and certainly not more complicated than a probabilistic uncertainty model

covariant schrodinger operator we analyse the schrodinger operator for a quantum scalar particle in a curved spacetime which is fibred over absolute time and is equipped with given spacelike metric gravitational field and electromagnetic field we approach the schrodinger operator in three independent ways in terms of covariant differentials induced by the quantum connection via a quantum lagrangian and directly by the only requirement of general covariance in particular in the flat case our schrodinger operator coincides with the standard one

fuzzy estimation for process capability indices process capability indices are summary statistics which measure the actual or the potential performance of process characteristics relative to the target and specification limits in most traditional methods precise estimation is used to assess the capability of manufacturing processes in this paper we introduce an algorithm based on buckley s estimation approach and use a family of confidence intervals to estimate process capability indices c p c p k and c p m the estimators of these indices thus obtained are triangular shaped fuzzy numbers we also present and illustrate method for the comparison of estimated process capability indices numerical examples are given to show the performance of the method

an alternative approach to fuzzy control charts direct fuzzy approach the major contribution of fuzzy set theory lies in its capability of representing vague data fuzzy logic offers a systematic base to deal with situations which are ambiguous or not well defined in the literature there exist few papers on fuzzy control charts which use defuzziffication methods in the early steps of their algorithms the use of defuzziffication methods in the early steps of the algorithm makes it too similar to the classical analysis linguistic data in those works are transformed into numeric values before control limits are calculated thus both control limits as well as sample values become numeric in this paper some contributions to fuzzy control charts based on fuzzy transformation methods are made by the use of a cut to provide the ability of determining the tightness of the inspection the higher the value of a the tighter inspection a new alternative approach direct fuzzy approach dfa is also developed in this paper in contrast to the existing fuzzy control charts the proposed approach is quite different in the sense it does not require the use of the defuzziffication this prevents the loss of information included by the samples it directly compares the linguistic data in fuzzy space without making any transformation we use some numeric examples to illustrate the performance of the method and interpret its results

fuzzy human reliability analysis on the chernobyl accident abstract this paper compares the result of fuzzy reliability analysis using error possibility with that of probabilistic analysis on the accident at the chernobyl nuclear power plant the case study shows that fuzzy reliability analysis gives information from more points of view than probabilistic analysis

fuzzy system reliability analysis using fuzzy number arithmetic operations abstract this paper presents a new method to analyze fuzzy system reliability using fuzzy number arithmetic operations where the reliability of each system component is represented by a triangular fuzzy number because the proposed method uses simplified fuzzy arithmetic operations of fuzzy numbers rather than the complicated interval arithmetic operations of fuzzy numbers mentioned by cheng and mon in fuzzy sets and systems 56 1993 29 35 or the complicated extended algebraic operations of fuzzy numbers mentioned by singer in fuzzy sets and systems 34 1990 145 155 its execution is faster than the ones presented by cheng and mon and singer

stable patterns in a viscous diffusion equation we consider a pseudoparabolic regularization of a forward backward nonlinear diffusion equation ut a f u vut motivated by the problem of phase separation in a viscous binary mixture the function f is nonmonotone so there are discontinuous steady state solutions corresponding to arbitrary arrangements of phases we find that any bounded measurable steady state solution u x satisfying f u constant f u x 0 a e is dynamically stable to perturbations in the sense of convergence in measure in particular smooth solutions may achieve discontinuous asymptotic states furthermore stable states need not correspond to absolute minimizers of free energy thus violating gibbs principle of stability for phase mixtures

structure functions with fuzzy states systems are modeled in reliability theory by means of structure functions which show how the system state of performance depends on the state of all its components in this paper we consider that the space of states allowed for both the system and its components is an appropriate family of fuzzy numbers basic concepts in classical crisp binary and multistate models in reliability theory are in this way generalized some particular consequences relative to component importance are also analyzed

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

a covariant approach to the quantization of a rigid body this paper concerns the quantization of a rigid body in the framework of covariant quantum mechanics on a curved spacetime with absolute time we consider the configuration space of n classical particles as the n fold product of the configuration space of one particle then we impose a rigid constraint and the resulting space is dealt with as a configuration space of a single abstract particle this classical framework turns out to be suitable for the formulation of covariant quantum mechanics according to this scheme thus we quantize such a particle accordingly this scheme can model e g the quantum dynamics of extremely cold molecules we provide a new mathematical interpretation of two valued wavefunctions on so 3 in terms of single valued sections of a new non trivial quantum bundle these results have clear analogies with spin

the schrodinger operator as a generalized laplacian the schrodinger operators on the newtonian spacetime are defined in a way which make them independent of the class of inertial observers in this picture the schrodinger operators act not on functions on the spacetime but on sections of a certain one dimensional complex vector bundle the schrodinger line bundle this line bundle has trivializations indexed by inertial observers and is associated with an u 1 principal bundle with an analogous list of trivializations the schrodinger principal bundle if an inertial frame is fixed the schrodinger bundle can be identified with the trivial bundle over spacetime but as there is no canonical trivialization inertial frame these sections interpreted as wavefunctions cannot be viewed as actual functions on the spacetime in this approach the change of an observer results not only in the change of actual coordinates in the spacetime but also in a change of the phase of wavefunctions for the schrodinger principal bundle a natural differential calculus for wave forms is developed that leads to a natural generalization of the concept of the laplace beltrami operator associated with a pseudo riemannian metric the free schrodinger operator turns out to be the laplace beltrami operator associated with a naturally distinguished invariant pseudo riemannian metric on the schrodinger principal bundle the presented framework does not involve any ad hoc or axiomatically introduced geometrical structures it is based on the traditional understanding of the schrodinger operator in a given reference frame which is supported by producing right physics predictions and it is proven to be strictly related to the frame independent formulation of analytical newtonian mechanics and hamilton jacobi equations that makes a bridge between the classical and quantum theory

fuzzy nonlinear programming approach for evaluating and ranking process yields with imprecise data abstract process yield the percentage of processed product units passing inspection is a standard numerical measure of process performance in the manufacturing industry on the basis of the process yield expression an index s p k was developed to provide an exact measure of process yield for normally distributed processes most traditional studies measuring process capability are based on crisp estimates in which the output process measurements are precise however it is common that the measurements of process quality characteristics are insufficiently precise traditional approaches for evaluating process yield become unreliable in such cases therefore this study formulates fuzzy numbers to describe the quality characteristic measurements and applies two methods to construct the fuzzy estimation for s p k a nonlinear programming approach is provided to solve the level sets of the estimator and a testing procedure is presented for making decisions finally this concept is illustrated with an example and extended to solve the ranking problem of multiple yield indices

on the geometric quantization of jacobi manifolds the geometric quantization of jacobi manifolds is discussed a natural cohomology termed lichnerowicz jacobi on a jacobi manifold is introduced and using it the existence of prequantization bundles is characterized to do this a notion of contravariant derivatives is used in such a way that the procedure developed by vaisman for poisson manifolds is naturally extended a notion of polarization is discussed and the quantization problem is studied the existence of prequantization representations is also considered

an efficient method combining active learning kriging and monte carlo simulation for profust failure probability abstract for more and more complicated engineering structures it is a challenge to efficiently estimate the profust failure probability based on the probability inputs and fuzzy state assumption by combining active learning kriging with monte carlo simulation ak mcs an efficient method is proposed to estimate the profust failure probability firstly the profust failure probability is transformed into an integral of the classical failure probability by introducing a variable related to the fuzzy state assumption this integral is further reorganized as a weighted sum of a series of classical failure probabilities by gaussian quadrature and the series of the classical failure probabilities have the similar limit state function constructions constrained by different thresholds secondly mcs is used according to the probability input distribution to generate the sample pool in which the active learning kriging is used to establish the surrogates of the series of similar limit state functions with different thresholds an improved learning function is proposed by minimizing the u learning function minima corresponding to all limit state functions so that the candidate with the largest effect on the surrogating quality of all limit states can be selected as a training point to update the kriging model once the updating process of the kriging model converges all limit state functions can be identified by the kriging model and the profust failure probability can be estimated by using the kriging model without any extra model evaluation several examples are used to demonstrate the feasibility of the proposed strategy for estimating the profust failure probability

q scale measures of fuzzy sets abstract in an attempt to generalize nahmias scale measure to apply to fuzzy sets in this paper we introduce the notion of q scale measure a q scale measure is slightly different from a crisp valued possibility measure in several ways we use a number of examples to demonstrate the validity of the notion of q scale measure in various circumstances and give preliminary discussions on basic properties of q scale measure induced q scale measure semigroup of q scale measures q scale measure of probabilistic sets and q scale measure of l fuzzy sets

system failure engineering and fuzzy methodology an introductory overview abstract system failure engineering may encompass reliability safety security maintainability risk and quality control in this paper we pay a unified view i e a failure oriented view to system failure engineering the notion of failure can be represented in terms of fuzzy sets and widely interpreted we then discuss various application aspects of fuzzy methodology in system failure engineering which include fuzzy methodology in fault diagnosis in probist systems in structural reliability in software reliability in human reliability in safety engineering in security engineering in risk engineering and in quality control as well as profust posbist and posfust reliability theories engineering case studies and mathematical problems raised by applications of fuzzy methodology in system failure engineering are also addressed in this paper

potential applications of fuzzy sets in industrial safety engineering abstract this paper discusses potential applications of fuzzy set theory to risk analysis in the area of industrial safety engineering vagueness and imprecision in mathematical quantification of risk are equated with fuzziness rather than randomness the concept of risk evaluation using linguistic representation of the likelihood of the occurrence of a hazardous event exposure and possible consequences of that event is proposed the approximate reasoning technique based on fuzzy logic is used to derive fuzzy values of risk

qualitative analysis of a nonlinear viscous diffusion equation abstract we study the cauchy problem of multidimensional viscous diffusion equations by using an equivalent integral equation we first give the existence of local solutions then under some assumptions we obtain the global existence of solutions

properties of nonlinear schrodinger equations associated with diffeomorphism group representations the authors recently derived a family of nonlinear schrodinger equations on r3 from fundamental considerations of generalized symmetry ih cross delta t psi h cross 2 2m del 2 psi f psi psi psi ih cross d del 2 psi mod del psi mod 2 mod psi mod 2 psi where f is an arbitrary real functional and d a real continuous quantum number these equations descriptive of a quantum mechanical current that includes a diffusive term correspond to unitary representations of the group diff m parametrized by d where m r3 is the physical space in the present paper we explore the most natural ansatz for f which is labelled by five real coefficients we discuss the invariance properties describe the stationary states and some non stationary solutions and determine the extra dissipative terms that occur in the ehrenfest theorem we identify an interesting galilean invariant subfamily whose properties we investigate including the case where the dissipative terms vanish

asymptotic behavior of a nonisothermal viscous cahn hilliard equation with inertial term we consider a differential model describing nonisothermal fast phase separation processes taking place in a three dimensional bounded domain this model consists of a viscous cahn hilliard equation characterized by the presence of an inertial term tt being the order parameter which is linearly coupled with an evolution equation for the relative temperature the latter can be of hyperbolic type if the cattaneo maxwell heat conduction law is assumed the state variables and the chemical potential are subject to the homogeneous neumann boundary conditions we first provide conditions which ensure the well posedness of the initial and boundary value problem then we prove that the corresponding dynamical system is dissipative and possesses a global attractor moreover assuming that the nonlinear potential is real analytic we establish that each trajectory converges to a single steady state by using a suitable version of the eojasiewicz simon inequality we also obtain an estimate of the decay rate to equilibrium

constraints reduction and quantization theorems are proved that establish the unitary equivalence of the extended and reduced phase space quantizations of a constrained classical system with symmetry several examples are presented

fuzzy system reliability analysis for components with different membership functions abstract this paper addresses the fuzzy system reliability analysis for components with different membership functions conventionally it is not always easy to obtain a system reliability for components with different individual failure probability density functions p d f due to the necessary but complicated combination and integration of various p d f s for such a problem and considering fuzzy environment and data imprecision in the real life we now apply fuzzy set theory to solve the inadequacy of the conventional probability in accounting and processing of built in uncertainties in the probabilistic data therefore we will use fuzzy distributions instead of the classical probability distribution for the components and calculate the functions of fuzzy numbers to solve for the fuzzy system reliability via non linear programming techniques where the commercial packages are available to use this solution procedure will be described in conjunction with an example used to illustrate the analysis algorithm and computation of this proposed method

repairable consecutive k out of n f system with fuzzy states in this paper we study a repairable consecutive k out of n f system with fuzzy states the maintenance of the system is carried out by r repairmen or repair facilities the system is either circular or linear it is assumed that the working time and the repair time of each component in the system are both exponentially distributed and every component after repair is as same as new each component is classified as either a key component or an ordinary one according to its priority role to the system s repair when the system displays a gradual degradation of its performance its reliability is then analyzed in terms of fuzzy failure and success states the difference between fuzzy reliability theory and the conventional reliability theory is highlighted

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

a general formal approach for fuzzy reliability analysis in the possibility context abstract in this paper we focus on the fuzzy reliability analysis in the posbist reliability theory in accordance with this theory the system failure state is defined precisely and the system failure and repair behaviour is fully characterized in the context of possibility measures to formalize the reliability analysis in the posbist theory we propose a general approach on the basis of a system of functional equations the solution of the system allows us to obtain fuzzy reliability characteristics of the arbitrary repairable and unrepairable systems to illustrate the construction and application of the system of functional equations various examples are given

a fuzzy set approach for event tree analysis the traditional event tree analysis uses a single probability to represent each top event however it is unrealistic to evaluate the occurrence of each event by using a crisp value without considering the inherent uncertainty and imprecision a state has the fuzzy set theory is universally applied to deal with this kind of phenomena the main purpose of this study is to construct an easy method to evaluate human errors and integrate them into event tree analysis by using fuzzy concepts a systematic fuzzy event tree analysis algorithm is developed to evaluate the risk of a large scale system a practical example in a nuclear power plant is used to demonstrate this procedure

an approach to human reliability on man machine systems using error possibility abstract this paper is concerned with proposing the concept error possibility instead of the error rate and presenting a method of fault tree analysis of human errors based on this concept the dependence between consecutive human tasks is considered as a fuzzy causal relation human reliability is defined as the evaluation of the error possibility from several points of view 1 the likelihood of error which gives the maximal grade of membership 2 potentiality for error 3 fuzziness of error possibility and 4 importance of a basic event as an illustrative example the emergency tasks in blackout at a pwr plant are shown and the fault tree concerning the error of these tasks is analyzed it is shown that the proposed method gives us information as well