二元联系数A+Bi的理论基础与基本算法及在人工智能中的应用

二元联系数4＋Bi的特点是把确定性测度与不确定测度联系在一起,基本思想是把一个确定集与一个不确定集联系在一起去研究同一个客观对象,其理论基础是集对论,概率、模糊隶属度、区间数可以转换成二元联系数,基本算法简明实用,因而可用于不同不确定性问题的处理．     

一种基于区间规则的条件证据网络推理决策方法

针对证据网络推理方法无法对区间规则进行表示和推理的问题, 提出一种基于区间规则的条件证据网络推理决策方法. 该方法针对模糊规则的条件概率或信度为不确定区间的情况, 可同时表达不确定性和模糊性; 并将区间不确定规则转化为区间条件信度函数作为证据网络的结点参数, 通过条件推理和证据融合得到条件证据网络中各结点幂集空间中焦元的随机分布作为决策依据. 最后, 通过空中目标态势评估实例, 验证了所提出方法的有效性.

     

单自由度不确定滞回系统振动响应的区间分析方法

利用区间理论并结合求解不确定非线性结构动力学响应的泰勒方法的二阶展开,推导出求解由滞回环本身的不确定性引起的、单自由度不确定滞回系统响应的有效数值方法,得到了系统响应的上下界.并与概率分析方法求得的系统响应进行比较分析,其计算结果与概率方法结果基本相吻合.当求解由滞回环本身的不确定性引起的非线性振动系统的不确定响应问题,而滞回环本身的不确定性统计信息较少概率方法无法适用时,利用本文所推导的区间方法可为工程实际提供参考.     

过程系统在线鲁棒优化控制方法

生产过程系统优化控制的主要任务是迅速地跟踪过程系统最优操作条件的变化[1].然而 由于实际过程系统的模型以及测量信息具有不确定性,因而研究具有鲁棒性的优化控制方法 具有一定的价.为此提出了基于一定长度优化序列以及不确定区间最优化的优化控制方 法.     

证据理论中基于区间概率的不确定测度

在证据理论的应用中,不确定测度作为一种新的评价准则,可以对知识进行量化评价.相关研究者对证据不确定测度进行了研究,但现有不确定测度在应用中存在一定的局限性,尤其是对信任函数的变化不够敏感.针对现有不确定测度对证据变化不够敏感问题,从信度区间的角度提出了一种新的证据不确定性测度.首先基于证据理论和概率论之间的关系,将证据理论中基本概率赋值函数转化为单元素子集上的信度区间,区间的上下界分别为似然函数和信任函数,然后结合证据理论中的不一致性和不精确性,定义了一种新的不确定测度SU,并通过数值算例对SU的计算过程和数学性质进行了分析,最后对SU在证据组合中的应用进行了验证.算例结果表明,在其他不确定测度无法辨别不同证据的不确定性时,SU仍能较好反映不同证据间不确定性的差异,而且对于参数化的基本概率赋值函数,SU对参数变化比较敏感.可见,考虑了区间数中值和区间长度的不确定测度SU可以很好地对证据不确定性进行度量;而且,当所有焦元都为单元素子集时,SU退化为香农熵的形式,证据不确定性的最大值与辨识框架中元素的个数有关,这在实际应用中更具意义.     

证据理论中基于区间概率的不确定测度

在证据理论的应用中,不确定测度作为一种新的评价准则,可以对知识进行量化评价.相关研究者对证据不确定测度进行了研究,但现有不确定测度在应用中存在一定的局限性,尤其是对信任函数的变化不够敏感.针对现有不确定测度对证据变化不够敏感问题,从信度区间的角度提出了一种新的证据不确定性测度.首先基于证据理论和概率论之间的关系,将证据理论中基本概率赋值函数转化为单元素子集上的信度区间,区间的上下界分别为似然函数和信任函数,然后结合证据理论中的不一致性和不精确性,定义了一种新的不确定测度SU,并通过数值算例对SU的计算过程和数学性质进行了分析,最后对SU在证据组合中的应用进行了验证.算例结果表明,在其他不确定测度无法辨别不同证据的不确定性时,SU仍能较好反映不同证据间不确定性的差异,而且对于参数化的基本概率赋值函数,SU对参数变化比较敏感.可见,考虑了区间数中值和区间长度的不确定测度SU可以很好地对证据不确定性进行度量;而且,当所有焦元都为单元素子集时,SU退化为香农熵的形式,证据不确定性的最大值与辨识框架中元素的个数有关,这在实际应用中更具意义.     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

概率不确定语言熵及其多属性群决策

针对概率不确定语言集的多个不确定语言术语和其概率各不相同的特点,提出基于概率不确定语言熵的多属性决策方法。定义四种新的概率不确定语言熵：模糊熵、犹豫熵、不完全信息熵和总熵,以分别测量概率不确定语言集的模糊性、犹豫性、信息不完全性和整体不确定性。给出了四种熵测度的公理化定义和表达式,根据概率不确定语言集的四种熵,构建能够解决属性权重未知的多属性决策模型,并通过案例和对比分析验证了该模型的有效性和合理性。     

金氰化浸出过程的自优化控制

针对湿法冶金金氰化浸出过程的实时优化问题,提出一个自优化控制方案.基于系统的参数不确定模型,选择并求解输出变量的线性组合为被控变量,在反馈控制器作用下跟踪其恒定设定值,实现浸出过程在不确定性扰动下的自优化控制.仿真结果验证了该控制方案的有效性:扰动产生时,系统的经济指标在常规控制作用下得到改善,并最终运行于真实的最优点附近,提高了浸出过程的生产效益.     

复杂产品开发项目调度问题的模糊优化算法

对具有不确定时间参数的复杂产品开发项目调度问题,提出一种有效的模糊优化调度算法-基于预测的模糊BoP项目调度算法.首先,用模糊数表示不确定的时间参数,并构造相应的模糊数运算方法,对适合于确定性调度问题的BoP算法进行扩展,使其能处理模糊性时间参数.其次,修正了BoP算法中子项目调度方法,提高了算法的调度性能,降低了计算复杂度.大量的数值仿真实验表明,与基于启发式规则的调度算法相比,模糊BoP算法更适合于具有不确定时间参数的复杂产品开发项目调度问题.     

有色冶金过程建模与优化的若干问题及挑战

有色金属工业发展正面临资源、能源与环境的严重制约, 而有色冶金过程建模与优化是实现有色冶金生产节能降耗减排的关键技术之一. 论文从有色冶金过程的特点出发,首先探讨了有色冶金过程的机理建模、 连续搅拌釜式反应器(Continuous stirred tank reactor, CSTR)模型和智能集成建模的理论与方法,提出了智能集成建模的描述方法, 归纳了模型的集成形式,给出了工业应用上的几类智能集成模型; 然后围绕有色冶金过程工程优化,讨论了操作模式优化、软约束调整满意优化、 多目标智能优化等方法,并阐述了大型湿法炼锌电解过程的综合优化控制技术; 最后探讨了有色冶金过程建模与优化所面临的新挑战.     

Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.     

Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.     

基于专家知识的字典序优化决策方法及工业应用

为有效实现有色冶金配料过程的实时优化,首先根据氧化铝配料过程特点,建立一种字典序区间目标规划模型;然后通过整理长期积累的专家经验知识,构建了具有优先级的分类知识库;接着基于专家知识库的分类结构,提出一种字典序专家推理策略,以实现区间约束条件下的多质量指标的优化控制．工业应用结果表明,所提出的方法能够很好地实现生料浆质量的优化控制,为其他有色冶金工业配料过程的控制提供了一种优化模式．     

一类复杂生产调度问题的基于符号演绎的调度方法

针对带有时问不确定件的复杂生产过程调度问题,提出一种基于符号演绎的调度方法.首先将时间的不确定性信息看作符号型数据,并提出一种用于处理这些符号型数据的基于不确定区间的符号演绎方法;然后将此符号演绎方法与遗传算法相结合,提出一种预排调度计划与实时调度规则相结合的调度方法来求解上述复杂生产调度问题.实验表明,将基于符号演绎的调度方法用于求解带有时间不确定性的复杂生产过程调度问题,能够取得较好的调度效果.     

全局优化视角下的有色冶金过程建模与控制

为提高生产效率、降低能源消耗、减少环境污染,需要对有色冶金过程进行建模,在系统模型的基础上,通过控制与优化技术,使过程系统运行在最优工况.本文以几个典型有色冶金过程为背景,阐述有色冶金过程建模、控制与优化三者之间的内在关联;从科学研究层次的角度上指出建模、控制与优化分属于不同层次的问题,且从方法论的角度指出建模、控制分两步进行:选择模型结构和估计模型参数、选择控制器结构和整定控制器参数,有色冶金过程系统模型、控制器的结构和参数确定问题均可以看成是非凸优化问题;探讨了全局优化视角下,建模、控制问题转化为优化问题以及在求解优化问题过程中存在的难点,提出解决这些难点的一些可行方案.     

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.     

A two-stage programming approach for water resources management under randomness and fuzziness

In this study, a fuzzy stochastic two-stage programming (FSTP) approach is developed for water resources management under uncertainty. The concept of fuzzy random variable expressed as parameters’ uncertainties with both stochastic and fuzzy characteristics was used in the method. FSTP has advantages in uncertainty reflection and policy analysis. FSTP integrates the fuzzy robust programming, chance-constrained programming and two-stage stochastic programming (TSP) within a general optimization framework. FSTP can incorporate pre-regulated water resources management policies directly into its optimization process. Thus, various policy scenarios with different economic penalties (when the promised amounts are not delivered) can be analyzed. FSTP is applied to a water resources management system with three users. The results indicate that reasonable solutions were generated, thus a number of decision alternatives can be generated under different levels of stream flows, α-cut levels and different levels of constraint-violation probability. The developed FSTP was also compared with TSP to exhibit its advantages in dealing with multiple forms of uncertainties.     

A robust critical path in an environment with hybrid uncertainty

In this article, we consider the project critical path problem in an environment with hybrid uncertainty. In this environment, the duration of activities are considered as random fuzzy variables that have probability and fuzzy natures, simultaneously. To obtain a robust critical path with this kind of uncertainty a chance constraints programming model is used. This model is converted to a deterministic model in two stages. In the first stage, the uncertain model is converted to a model with interval parameters by alpha-cut method and distribution function concepts. In the second stage, the interval model is converted to a deterministic model by robust optimization and min-max regret criterion and ultimately a genetic algorithm with a proposed exact algorithm are applied to solve the final model. Finally, some numerical examples are given to show the efficiency of the solution procedure.     

Robust H/sub /spl infin// control for fuzzy systems with Frobenius norm-bounded uncertainties

In this paper, we investigate the problem of robust H/sub /spl infin// performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H/sub /spl infin// control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H/sub /spl infin// problems involving uncertainty and standard uncertainty-free H/sub /spl infin// problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.