An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia...An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.展开更多
The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interva...The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.展开更多
Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling ...Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.展开更多
Skyline查询是基于位置服务(Location based service,LBS)的一项重要操作,其目的是发现数据集中不被其他点支配的点的集合.移动对象在运动过程中,其位置信息具有不确定性,导致各数据点间的支配关系不稳定,从而影响Skyline操作.本文针对...Skyline查询是基于位置服务(Location based service,LBS)的一项重要操作,其目的是发现数据集中不被其他点支配的点的集合.移动对象在运动过程中,其位置信息具有不确定性,导致各数据点间的支配关系不稳定,从而影响Skyline操作.本文针对以位置不确定移动对象为查询点的Skyline查询进行研究,首先,定义了查询点移动时各对象间支配概率,提出了支配概率和Skyline概率的微元计算方法.在此基础上,提出一种面向不确定移动对象进行连续概率Skyline查询的有效算法UCPSC.该算法首先快速计算初始时刻的p-Skyline集合;然后,定义了两类可能引起p-Skyline变动的事件,通过对这些事件的跟踪计算快速更新p-Skyline集合,无需在移动对象的每一运动时刻去遍历整个数据集,实现了对p-Skyline的连续更新操作,大大减少了算法的查找和计算开销,提高了运算效率;最后,提出一种静态算法USPSC,与UCPSC进行了对比试验,实验结果证明了算法的有效性.展开更多
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
文摘The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.
文摘Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.
文摘Skyline查询是基于位置服务(Location based service,LBS)的一项重要操作,其目的是发现数据集中不被其他点支配的点的集合.移动对象在运动过程中,其位置信息具有不确定性,导致各数据点间的支配关系不稳定,从而影响Skyline操作.本文针对以位置不确定移动对象为查询点的Skyline查询进行研究,首先,定义了查询点移动时各对象间支配概率,提出了支配概率和Skyline概率的微元计算方法.在此基础上,提出一种面向不确定移动对象进行连续概率Skyline查询的有效算法UCPSC.该算法首先快速计算初始时刻的p-Skyline集合;然后,定义了两类可能引起p-Skyline变动的事件,通过对这些事件的跟踪计算快速更新p-Skyline集合,无需在移动对象的每一运动时刻去遍历整个数据集,实现了对p-Skyline的连续更新操作,大大减少了算法的查找和计算开销,提高了运算效率;最后,提出一种静态算法USPSC,与UCPSC进行了对比试验,实验结果证明了算法的有效性.
