动态模糊规划模型的构建及应用

常规规划模型通常存在如下两种缺陷:首先,它的目标系数及约束条件都是在硬性限制下的确定值,因而在建模方面弹性小、硬度大;其次,它的目标系数与时间无关,因此不能有效地刻划时时刻刻变化着的目标系数,而动态模糊规划模型可以有效地解决上述缺陷.首先应用模糊动态AHP确定目标系数;然后根据L-R模糊数的强序关系准则,将动态模糊规划模型分解为最优与最劣两个模糊规划模型;再根据以α水平截集为基础的求解方法,将上述两个模型进行相应的转换,建立具有风险分析功能的动态模糊规划模型;最后将其应用到一个实际算例中,收到较好的结果.     

含直觉模糊弹性约束的广义模糊变量线性规划

本文基于模糊结构元方法建立并讨论了一类含有直觉模糊弹性约束的广义模糊变量线性 规划问题。首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析。然后,通过选取风险中立型决策态度来定义序关系并拓展Verdegay模糊线性规划方法,将新型模糊变量线性规划问题转化为两个含一般模糊弹性约束的模糊变量线性规划模型,给出了此类规划最优直觉模糊解的求法。最后,通过数值算例进一步说明该方法的有效性。     

Fuzzy linear programming under interval uncertainty based on IFS representation

The equivalence between the interval-valued fuzzy set (IVFS) and the intuitionistic fuzzy set (IFS) is exploited to study linear programming problems involving interval uncertainty modeled using IFS. The non-membership of IFS is constructed with three different viewpoints viz., optimistic, pessimistic, and mixed. These constructions along with their indeterminacy factors result in S-shaped membership functions in the fuzzy counterparts of the intuitionistic fuzzy linear programming models. The solution methodology of Yang et al. [45], and its subsequent generalization by Lin and Chen [33] are used to compute the optimal solutions of the three fuzzy linear programming models.     

Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations

This paper proposes linear goal programming models for deriving intuitionistic fuzzy weights from intuitionistic fuzzy preference relations. Novel definitions are put forward to define additive consistency and weak transitivity for intuitionistic fuzzy preference relations, followed by a study of their corresponding properties. For any given normalized intuitionistic fuzzy weight vector, a transformation formula is furnished to convert the weights into a consistent intuitionistic fuzzy preference relation. For any intuitionistic fuzzy preference relation, a linear goal programming model is developed to obtain its intuitionistic fuzzy weights by minimizing its deviation from the converted consistent intuitionistic fuzzy preference relation. This approach is then extended to group decision-making situations. Three numerical examples are provided to illustrate the validity and applicability of the proposed models.     

A new method for solving fully fuzzy linear programming problems

Lotfi et al. [Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33 (2009) 3151–3156] pointed out that there is no method in literature for finding the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints. In this paper, a new method is proposed to find the fuzzy optimal solution of same type of fuzzy linear programming problems. It is easy to apply the proposed method compare to the existing method for solving the FFLP problems with equality constraints occurring in real life situations. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.     

Matrix Games with Fuzzy Goals and Fuzzy Linear Programming Duality

A two person zero-sum matrix game with fuzzy goals is shown to be equivalent to a primal-dual pair of fuzzy linear programming problems. Further certain difficulties with similar studies reported in the literature are also discussed.     

Possibilistic Linear Programming with Fuzzy If-Then Rule Coefficients

In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.     

模糊环境下批量制造业提前/拖期交货的生产计划

描述了基于客户需求为模糊量的批量生产提前/拖期交货的生产计划,并建立了模糊环境下的三个模型.为了有效求解优化模型,我们将模糊模拟和遗传算法相结合给出了混合智能算法.最后通过数值例子说明算法的有效性.     

Note on “Some models for deriving the priority weights from interval fuzzy preference relations”

Deriving accurate interval weights from interval fuzzy preference relations is key to successfully solving decision making problems. Xu and Chen (2008) proposed a number of linear programming models to derive interval weights, but the definitions for the additive consistent interval fuzzy preference relation and the linear programming model still need to be improved. In this paper, a numerical example is given to show how these definitions and models can be improved to increase accuracy. A new additive consistency definition for interval fuzzy preference relations is proposed and novel linear programming models are established to demonstrate the generation of interval weights from an interval fuzzy preference relation.     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.