A survey of credibility theory

This paper provides a survey of credibility theory that is a new branch of mathematics for studying the behavior of fuzzy phenomena. Some basic concepts and fundamental theorems are introduced, including credibility measure, fuzzy variable, membership function, credibility distribution, expected value, variance, critical value, entropy, distance, credibility subadditivity theorem, credibility extension theorem, credibility semicontinuity law, product credibility theorem, and credibility inversion theorem. Recent developments and applications of credibility theory are summarized. A new idea on chance space and hybrid variable is also documented.  

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.  

模糊批量生产计划问题的机会约束规划

描述了模糊单位利润、模糊生产能力以及模糊需求下的批量生产计划,并应用模糊机会约束规划规划建立了模型.当模糊变量是梯形模糊数时,我们将模糊模型转化为确定意义下的模型.为了求解优化模型,我们设计了基于模糊模拟的遗传算法.最后,通过一个数值例子说明算法的有效性.  

Mean-variance-skewness model for portfolio selection with fuzzy returns

Numerous empirical studies show that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same. In order to measure the asymmetry of fuzzy portfolio return, a concept of skewness is defined as the third central moment in this paper, and its mathematical properties are studied. As an extension of the fuzzy mean-variance model, a mean-variance-skewness model is presented and the corresponding variations are also considered. In order to solve the proposed models, a genetic algorithm integrating fuzzy simulation is designed. Finally, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm.  

模糊批量生产计划问题的可信性规划模型与算法

描述模糊单位利润、模糊生产能力以及模糊需求下的批量生产计划,并应用可信性规划建立了模型.当模糊变量是梯形模糊数时,我们将模糊模型转化为确定意义下的模型.为了求解优化模型,我们设计了基于模糊模拟的遗传算法.最后,通过一个数值例子说明算法的有效性.  

基于模糊随机变量的结构可靠性分析

研究了广义应力和广义强度同时具有模糊性和随机性时的结构可靠度计算问题,基于模糊随机变量和模糊随机事件的理论,建立了结构模糊可靠度的计算模型.最后通过一算例,验证了该方法的有效性和合理性.  

基于可信度模糊费用多设施选址模型和算法

设施选址在整个物流网络中是一个十分重要的决策问题，它决定了整个物流系统的模式，结构和形状。设施选址方法尤其是多设施选址方法的研究已经成为一个备受人们关注的研究领域。本文首先介绍了设施选址的重要性，然后在模糊环境中根据不同的决策标准，建立了三种不同类型的模型，并设计了一个遗传算法来解决其中一个模型。最后给出了一个数值例子。  

The Further Study of Safety Stock under Uncertain Environment

Corresponding to stochastic variable, it is a better choice to describe the market demand uncertainty of innovative products with fuzzy variable because no historical data is available. Traditionally, possibility measure is regarded as the parallel concept of probability measure. However, it is, in fact, the credibility measure that plays the role of probability measure! Based on the credibility theory, this paper studies how to evaluate the safety stock of enterprise given desired product availability when the node enterprise market demand of supply chain is described by Gauss fuzzy variable. Thereinafter, the authors discuss the impact of required product availability and demand uncertainty on safety stock, compare the correlative issues with stochastic demand, and get some useful results.  

Fuzzy BCC Model for Data Envelopment Analysis

Fuzzy Data Envelopment Analysis (FDEA) is a tool for comparing the performance of a set of activities or organizations under uncertainty environment. Imprecise data in FDEA models is represented by fuzzy sets and FDEA models take the form of fuzzy linear programming models. Previous research focused on solving the FDEA model of the CCR (named after Charnes, Cooper, and Rhodes) type (FCCR). In this paper, the FDEA model of the BCC (named after Banker, Charnes, and Cooper) type (FBCC) is studied. Possibility and Credibility approaches are provided and compared with an -level based approach for solving the FDEA models. Using the possibility approach, the relationship between the primal and dual models of FBCC models is revealed and fuzzy efficiency can be constructed. Using the credibility approach, an efficiency value for each DMU (Decision Making Unit) is obtained as a representative of its possible range. A numerical example is given to illustrate the proposed approaches and results are compared with those obtained with the -level based approach.  

Fuzzy turnover rate chance constraints portfolio model

One concern of many investors is to own the assets which can be liquidated easily. Thus, in this paper, we incorporate portfolio liquidity in our proposed model. Liquidity is measured by an index called turnover rate. Since the return of an asset is uncertain, we present it as a trapezoidal fuzzy number and its turnover rate is measured by fuzzy credibility theory. The desired portfolio turnover rate is controlled through a fuzzy chance constraint. Furthermore, to manage the portfolios with asymmetric investment return, other than mean and variance, we also utilize the third central moment, the skewness of portfolio return. In fact, we propose a fuzzy portfolio mean–variance–skewness model with cardinality constraint which combines assets limitations with liquidity requirement. To solve the model, we also develop a hybrid algorithm which is the combination of cardinality constraint, genetic algorithm, and fuzzy simulation, called FCTPM.