new high resolution scheme for three dimensional nonlinear hyperbolic conservation laws we present a new third order central weighted essentially non oscillatory cweno reconstruction for computations of nonlinear hyperbolic conservation laws in three spatial dimensions the semi discrete central upwind schemes of kurganov et al are extended by giving some simple approximations for the local speeds of the discontinuities to this end the obtained cweno type central upwind scheme i e the extended semi discrete central upwind scheme based on the new high resolution cweno reconstruction is developed straightforwardly to solve 3d systems such as euler equations and magnetohydrodynamics mhd equations the good performance of the resulting method is finally shown in the numerical examples

redundancy optimization problems with uncertainty of combining randomness and fuzziness by using random fuzzy lifetimes as basic parameters three types of system performance expected system lifetime system lifetime and system reliability are presented some random fuzzy simulations are employed to estimate the system performance furthermore a spectrum of random fuzzy models are constructed for redundancy optimization problems in order to solve these models a hybrid intelligent algorithm is used finally some numerical examples are provided for the sake of illustration

the maximum fuzzy weighted matching models and hybrid genetic algorithm a matching of a graph is an independent subset of the edges set and a maximum matching is a matching with as many edges in it as possible the maximum weighted matching problem is to find a maximum matching in a given graph such that the sum of the weights of the edges in it is maximum in this paper the concepts of expected maximum fuzzy weighted matching the maximum fuzzy weighted matching and the most maximum fuzzy weighted matching are initialized according to various decision criteria the maximum fuzzy weighted matching problem is formulated as expected value model chance constrained programming and dependent chance programming by using the credibility theory and the crisp equivalents are also given furthermore a hybrid genetic algorithm is designed for solving the proposed fuzzy programming models finally a numerical example is given

fuzzy random renewal reward process and its applications this paper studies a renewal reward process with fuzzy random interarrival times and rewards under the independence associated with any continuous archimedean t norm the interarrival times and rewards of the renewal reward process are assumed to be positive fuzzy random variables whose fuzzy realizations are independent fuzzy variables under these conditions some limit theorems in mean chance measure are derived for fuzzy random renewal rewards in the sequel a fuzzy random renewal reward theorem is proved for the long run expected reward per unit time of the renewal reward process the renewal reward theorem obtained in this paper can degenerate to that of stochastic renewal theory finally some application examples are provided to illustrate the utility of the result

finite element analysis with uncertain probabilities this paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness within this framework the standard perturbation based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static dynamic and modal analyses general formulae are provided for assessing the fuzzy structural reliability and several typologies of optimization problems reliability based design robust design robust reliability based design are formalized in doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results so that standard optimizers can be adopted to solve the most important design problems it is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider both probabilistic and non probabilistic sources of uncertainties such as randomness vagueness ambiguity and imprecision

interval type 2 credibilistic clustering for pattern recognition this paper presents a new approach to interval type 2 fuzzy clustering in order to consider compactness within the clusters and separation of them simultaneously the objective function of this paper is designed such that it generates both degrees of membership and non membership of each data in each cluster and integrates them using credibility concept also a new approach to separation of clusters is proposed and utilized in designing the objective function in this approach the borders of clusters and therefore their compactness contribute in attaining their separation so the separation of clusters is not assessed only by the distance of their centers the credibility degrees are transformed to interval type 2 form to handle different sources of uncertainty finally a new validity index to characterize the number of clusters based on proposed approach to separation of clusters and choquet integrals are proposed the advantages of paper contributions are illustrated using several examples a new objective function based fuzzy clustering is introduced using credibility concept a new approach to separation of clusters is presented a new validity index is designed by proposed approach to separation and choquet integral the obtained results show that proposed model can handle different types of clusters

some properties of fuzzy random renewal processes fuzzy random variable is a measure function from a probability space to a collection of fuzzy variables based on the fuzzy random theory this paper addresses some properties of fuzzy random renewal processes generated by a sequence of independent and identically distributed iid fuzzy random interarrival times the relationship between the expected value of the fuzzy random renewal variable and the distribution functions of the alpha pessimistic values and alpha optimistic values of the interarrival times is discussed furthermore the fuzzy random style of renewal equation is provided finally fuzzy random blackwell s renewal theorem and smith s key renewal theorem are also given

fuzzy based robust structural optimization robust optimization is conventionally defined as the collection of the possible problem solutions that can ensure acceptable performances and sufficient immunity against the effects of uncertain parameter variability methods proposed until now use a probabilistic way to model uncertainty and to quantify the final sensitivity in this work a fuzzy uncertainty modellization is adopted for structural engineering in particular to define solution performance scattering the fuzzy entropy is used as a global measure of variable dispersion the final formulation of the problem deals with two antithetical objective functions the fuzzy expected value of structural performance and its fuzzy entropy this fuzzy based approach in robust design is able to give a set of pareto optimal solutions in terms of structural efficiency and sensitivities regarding uncertainty and represents a suitable tool in supporting the decision maker finally different applications have been developed to demonstrate the applicability of the proposed method

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

on the specificity of a possibility distribution abstract the specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation as such it is a measure of amount of uncertainty or information we investigate a number of issues related to specificity measures we discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution we describe unifying view for constructing specificity measures we look at the relationship of the specificity of a distribution and its negation we consider the case where the base set is continuous

solving linear programming problems under fuzziness and randomness environment using attainment values in this paper the author presents a model to measure attainment values of fuzzy numbers fuzzy stochastic variables these new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem numerical comparisons are provided to illustrate the effectiveness of the proposed method

a new ranking method to fuzzy data envelopment analysis due to its wide practical use data envelopment analysis dea has been adapted to many fields to deal with problems that have occurred in practice one adaptation has been in the field of ranking decision making units dmus most methods of ranking dmus assume that all input and output data are exactly known but in real life the data cannot be precisely measured thus this paper will carry out some researches to dea under fuzzy environment a fuzzy comparison of fuzzy variables is defined and the ccr model is extended to be a fuzzy dea model based on credibility measure in order to rank all the dmus a full ranking method will be given since the ranking method involves a fuzzy function a fuzzy simulation is designed and embedded into the genetic algorithm to establish a hybrid intelligent algorithm however it is shown to be possible to avoid some of the need for dealing with these nonlinear problems by identifying conditions under which they can be replaced by linear problems finally we will provide a numerical example to illustrate the fuzzy dea model and the ranking method

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

regular fuzzy measure and representation of comonotonically additive functional this paper discusses the functional i defined on the class of continuous functions which is comonotonically additive and monotone the notion of regular fuzzy measure is proposed and the uniqueness theorem of regular fuzzy measure is shown it is also shown that i can be represented by the difference of two choquet integrals with respect to regular fuzzy measures when the universal set x is a locally compact hausdorff space and that i can be represented by one choquet integral with respect to a regular fuzzy measure when x is a compact hausdorff space

natural continuous extensions of runge kutta methods the present paper develops a theory of natural continuous extensions nces for the discrete approximate solution of an ode given by a runge kutta process these nces are defined in such a way that the continuous solutions furnished by the one step collocation methods are included

on the problem of possibilistic optimization abstract this paper is a continuation on the author s investigation on possibilistic optimization problems which are considered from general methodological positions of possibility theory and managing uncertainty as well to tackle optimization tasks under uncertainty a calculus for possibilities is developed leading to classic and interval valued optimization

fuzzy and stochastic programming abstract fuzzy mathematical programming is considered on the basis of the concept of fuzzy variable 5 that is one of the most complete patterns of fuziness statements of problems under consideration are analogous to those in stochastic programming equivalent precise analogues are derived for these problems the relationship between fuzzy programming and stochastic programming is determined

a note on chance constrained programming with fuzzy coefficients this paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives we also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints finally a fuzzy simulation based genetic algorithm is employed to solve a numerical example

object tracking from image sequences using adaptive models in fuzzy particle filter this paper describes a vision based system for tracking objects from image sequences the proposed system has the standard architecture with a particle filter which is a popular algorithm to track objects in real time many tracking algorithms have a great difficulty in tracking objects robustly by reason of complex background and rapid changes under a real complex environment such as a traffic road to make a robust algorithm for object tracking we propose the method that uses the adaptive autoregressive model as a state transition model and the adaptive appearance mixture model as an observation model but in case of changing the state of a tracked object suddenly the adaptive models may not make the optimal parameters for accurate states at current time because the noise variance of the adaptive models in this case is larger than that in normal case it has an effect on the accuracy of an object tracking algorithm thus we propose a fuzzy particle filter to overcome problems from the occurrence of the unexpected improper variances due to several causes in this paper as the process noises and the observation noises in a fuzzy particle filter are considered as fuzzy variables by using the possibility theory a fuzzy particle filter with fuzzy noises is used to manage uncertainty in various noise models also we make possibility measure as using the fuzzy relation equation which is defined by these fuzzy variables and then the states are estimated by using a fuzzy expected value operator also because the proposed algorithm applies several functions to improve the accuracy of tracking an object the performance of tracking speed deteriorates to resolve this problem to some extent we consider the fact that a fuzzy particle filter has a little bit of an effect on the number of particles consequently we propose the method which can adjust the number of particles by using the result from a measurement step in order to improve the speed for an object tracking in the proposed algorithm the experiments of this paper show that the proposed method is efficient and has many advantages for an object tracking in real environments

fuzzy optimization an appraisal abstract this paper takes a general look at core ideas that make up the burgeoning body of fuzzy mathematical programming emphasizing the methodological view although fuzzy mathematical programming has enjoyed a rapidly increasing acceptance within the scientific community some technical hurdles exist to hinder a unanimity reasons for this as well as possible ways for improvement are also discussed

the fuzzy quadratic assignment problem with penalty new models and genetic algorithm the assignment problem is to find the total costs optimal jobs assignment schedule where n jobs are allocated to n workers and each worker receives exactly just one job such that the total cost is optimal the quadratic assignment problem with penalty takes three types of costs into consideration direct cost interactive cost an penalty in this paper the fuzzy quadratic assignment problem with penalty is formulated as expected value model chance constrained programming and dependent chance programming according to various decision criteria and the crisp equivalents are given furthermore hybrid genetic algorithm is designed for solving the proposed fuzzy programming models

possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems abstract in this paper several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems interval and triangular possibility distributions are used to express the non interactive cases between the fuzzy decision variables and exponential possibility distributions are used to represent the interrelated cases possibilistic linear programming problems based on exponential possibility distributions become non linear optimization problems in order to solve optimization problems easily algorithms for obtaining center vectors and distribution matrices in sequence are proposed by the proposed algorithms the possibility distribution of fuzzy decision variables can be obtained

a new credibilistic clustering algorithm abstract this paper focuses on credibilistic clustering approach a data clustering method partitions unlabeled data sets into clusters and labels them for various goals such as computer vision and pattern recognition there are different models for objective function based fuzzy clustering such as fuzzy c means fcm possibilistic c mean pcm and their combinations credibilistic clustering is a new approach in this field in this paper a new credibilistic clustering model is introduced in which credibility measure is applied instead of possibility measure in possibilistic clustering also in objective function the separation of clusters is considered in addition to the compactness within clusters the steps of clustering are designed based on this approach finally the main issues about model are discussed and the results of computational experiments are presented to show the efficiency of the proposed model

random fuzzy renewal process abstract this paper attempts to discuss a random fuzzy renewal process based on random fuzzy theory the interarrival times are characterized as nonnegative random fuzzy variables which is a more reasonable consideration in the real world under this setting the rate of the random fuzzy renewal process is discussed and a random fuzzy elementary renewal theorem is presented furthermore the expected value of renewals in an arbitrary interval is investigated and blackwell s theorem in random fuzzy sense is also established

the interest rate for saving as a possibilistic risk abstract the paper is concerned with a saving model in which the interest rate risk is a fuzzy number our model can be seen as a possibilistic variant of a saving model due to rothschild and stiglitz in which the interest rate risk is a random variable a notion of possibilistic precautionary saving is defined as a measure of the optimal saving variation when moving from a certain model to the possibilistic interest rate risk model a first result of the paper characterizes the possibilistic precautionary saving i e generating extra saving by an inequality in which the relative prudence index associated with the consumer s utility function appears a second result compares the level of optimal saving from the rothschild and stiglitz with the level of optimal saving from the possibilistic model from the paper finally two propositions on the approximate calculation of possibilistic optimal saving are proved the two approximate calculation procedures are illustrated for particular cases of utility functions and fuzzy numbers

maximum entropy membership functions for discrete fuzzy variables due to the deficiency of information the membership function of a fuzzy variable cannot be obtained explicitly it is a challenging work to find an appropriate membership function when certain partial information about a fuzzy variable is given such as expected value or moments this paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints a genetic algorithm is designed to solve the general maximum entropy model for discrete fuzzy variables which is illustrated by some numerical experiments

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

approximation based fuzzy multi objective models with expected objectives and chance constraints application to earth rock work allocation in this paper we introduce a measure me which is more suitable for real life decision making problems under fuzzy environments then we establish a general fuzzy multi objective model with expected objectives and chance constraints ecm based on the me to handle the model and obtain solutions we propose two approximation models by dividing the fuzzy feasible region using rough set theory in particular we focus on a linear ecm and several properties and two equivalent models are presented finally as an illustration we apply the proposed models and approaches to an earth rock work allocation problem at the longfeng hydropower construction project

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

a multi objective portfolio selection model with fuzzy value at risk ratio considering nonstatistical uncertainties and or insufficient historical data in security return forecasts fuzzy set theory has been applied in the past decades to build portfolio selection models meanwhile various risk measurements such as variance entropy and value at risk have been proposed in fuzzy environments to evaluate investment risks from different perspectives sharpe ratio also known as the reward to variability ratio which measures the risk premium per unit of the nonsystematic risk asset deviation has received great attention in modern portfolio theory in this study the sharpe ratio in fuzzy environments is introduced whereafter a fuzzy value at risk ratio is proposed compared with sharpe ratio value at risk ratio is an index with dimensional knowledge that reflects the risk premium per unit of the systematic risk the greatest loss under a given confidence level on the basis of the two ratios a multi objective model is built to evaluate their joint impact on portfolio selection then the proposed model is solved by a fuzzy simulation based multi objective particle swarm optimization algorithm where the global best of each iteration is determined by an improved dominance times based method finally the algorithm superiority is justified via comparing with existing solvers on benchmark problems and the model effectiveness is exemplified by using three case studies on portfolio selection

fuzzy multi product constraint newsboy problem in this paper we consider the multi product newsboy problem with fuzzy demands under budget constraint since the demands of products are often fuzzy in real life the profit of the newsboy is fuzzy too we develop three types of models under different criteria evm model dcp model and ccp model in these models the objective functions are to maximize the expected profit of newsboy the chance of achieving a target profit and the profit which satisfies some chance constraints with at least some given confidence level respectively furthermore the hybrid intelligent algorithm based on genetic algorithm and fuzzy simulation is designed for these models and some illustrating examples are given in order to show the application of these proposed models and algorithm

dependent chance programming with fuzzy decisions dependent chance programming dcp is a new type of stochastic programming and has been extended to the area of fuzzy programming this paper provides a spectrum of dcp and dependent chance multiobjective programming dcmop as well as dependent chance goal programming dcgp models with fuzzy rather than crisp decisions the terms of uncertain environment event chance function and induced constraints are discussed in the case of fuzzy decisions a technique of fuzzy simulation is also designed for computing chance functions finally we present a fuzzy simulation based genetic algorithm for solving these models and illustrate its effectiveness by some numerical examples

fuzziness and randomness in an optimization framework abstract a semi infinite approach for linear programming in the presence of fuzzy random variable coefficients is described as a byproduct a way for dealing with optimization problems including both fuzzy and random data is obtained numerical examples are provided for the sake of illustration

facility location allocation problem in random fuzzy environment using α β cost minimization model under the hurewicz criterion facility location allocation fla which has been proved to be a valuable method in siting service facility is widely used in real life such as emergency service systems telecommunication net works public services etc many researchers have studied the fla problem in a deterministic stochastic or fuzzy environment however those models cannot satisfy various customers demands in some cases thus this paper considers the fla problem under random fuzzy environment using a b cost minimization model under the hurwicz criterion it will be proved that this model can deal with various fla problems in random fuzzy and random fuzzy environments by varying the value l it can balance the optimistic level of the decision makers for solving the random fuzzy model efficiently the simplex algorithm random fuzzy simulation and genetic algorithm are integrated to produce a hybrid intelligent algorithm finally a numerical example is presented for illustration

mean semivariance models for fuzzy portfolio selection this paper discusses portfolio selection problem in fuzzy environment in the paper semivariance is originally presented for fuzzy variable and three properties of the semivariance are proven based on the concept of semivariance of fuzzy variable two fuzzy mean semivariance models are proposed to solve the new models in general cases a fuzzy simulation based genetic algorithm is presented in the paper in addition two numerical examples are also presented to illustrate the modelling idea and the effectiveness of the designed algorithm

a cweno type central upwind scheme for ideal mhd equations a simple fourth order central upwind scheme based on central weighted essentially non oscillatory cweno reconstruction is proposed in this paper for computing the approximate solutions of one and two dimensional ideal magnetohydrodynamics mhd equations with high resolution since the non uniform width of the different local riemann fans is calculated more accurately the central upwind schemes enjoy a much smaller numerical viscosity as well as the staggering between two neighboring sets of grids is avoided due to the central upwind scheme is combined with the fourth order cweno reconstruction the scheme we present has the non oscillatory behavior the numerical results show the desired accuracy high resolution and robustness of our method

a numerical integration based simulation algorithm for expected values of strictly monotone functions of ordinary fuzzy variables fuzzy simulation is used to approximate the expected values of functions of fuzzy variables which plays an important role in the solution algorithms of fuzzy optimization problems the traditional discretization based simulation algorithms fail to return a satisfactory approximation within an acceptable computation time which hinders the applications of fuzzy optimization methods in large size or even middle size problems in this paper we first prove some equivalent formulas for the expected values of strictly monotone functions of ordinary fuzzy variables then we propose a new fuzzy simulation algorithm based on the numerical integration technique finally we present some numerical examples to make comparisons between the traditional approach and our approach the results show that our approach has higher performances on the reliability stability and computation time

on fuzzy set interpretation of possibility theory a revised fuzzy set interpretation of possibility theory is introduced in this paper contrary to the standard fuzzy set interpretation of possibility theory which is coherent only for normal fuzzy sets the revised interpretation is shown to be coherent for all fuzzy sets it is also argued that the revised interpretation which coincides with the standard one for normal fuzzy sets is more meaningful on intuitive grounds prior to the introduction of the revised interpretation previous efforts to overcome the well known difficulties of the standard interpretation are critically examined and it is demonstrated that none of them results in a coherent and meaningful interpretation of possibility theory

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

fuzzy quadratic minimum spanning tree problem in this paper a fuzzy quadratic minimum spanning tree problem is formulated as expected value model chance constrained programming and dependent chance programming according to different decision criteria then the crisp equivalents are derived when the fuzzy costs are characterized by trapezoidal fuzzy numbers furthermore a simulation based genetic algorithm using prufer number representation is designed for solving the proposed fuzzy programming models as well as their crisp equivalents finally a numerical example is provided for illustrating the effectiveness of the genetic algorithm

dependent chance programming in fuzzy environments dependent chance programming is a new type of stochastic programming this paper provides a framework of dependent chance programming as well as dependent chance multiobjective programming and dependent chance goal programming in fuzzy environment as opposed to stochastic environment we also extend the concepts of uncertain environments events chance functions and induced constraints from stochastic to fuzzy cases finally a fuzzy simulation based genetic algorithm is illustrated by some numerical examples of dependent chance programming models

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

chance constrained programming with fuzzy parameters this paper extends chance constrained programming from stochastic to fuzzy environments analogous to stochastic programming some crisp equivalents of chance constraints in fuzzy environments are presented we also propose a technique of fuzzy simulation for the chance constraints which are usually hard to be converted to their crisp equivalents finally a fuzzy simulation based genetic algorithm is designed for solving this kind of problems and some numerical examples are discussed

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

an information axiom based decision making approach under hybrid uncertain environments this paper aims to develop a decision making approach based on the information axiom under hybrid uncertain environments in these environments fuzziness and randomness co exist to model the hybrid uncertainties the design range and system range of an evaluation criterion are expressed as a fuzzy variable and a random variable respectively calculating the information contents for these criteria would involve integrals whose bounds are fuzzy variables to calculate these integrals an expected information content model eicm is proposed based upon the credibility theory to reflect the designer s risk appetite accurately the confidence levels are introduced and a credibility information content model cicm based on the chance constrains programming model is constructed two algorithms based on fuzzy simulation methods and genetic algorithm are developed for these two models finally a case study is illustrated to highlight the effectiveness and accuracy of the proposed approach

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra