军械物资供应系统中的多目标运输问题

建立了军械物资运输问题的模糊多目标线性规划模型，运用一种解模糊函数和一种基于线性隶属函数的模糊规划算法求其调和解。方法简便、有效，可为部队军械物资的运输供应高效化提供科学依据。     

多目标运输问题的Fuzzy线性规划解法

经典运输问题是一类特殊的单目标线性规划问题，可用表上作业法或单纯形法求其最优解。近年来，许多学研究了多目标运输问题，提出了相应的求解算法。本应用Fuzzy线性规划的方法，给出了多目标运输问题的又一求解算法。     

多目标运输问题的区间模型及其算法

主要给出一类目标函数的系数、供应量和需求量均为区间数的多目标运输问题模型,根据参数的实际意义和区间数的序关系,针对所建立模型,利用区间规划的方法,将其转化为确定型的多目标运输问题,最后用模糊规划技术处理等价的多目标运输问题.数值例子表明算法的有效性和可行性.     

多目标指派问题在潜艇兵力配置中的应用

运用模糊数学的思想，首先将各目标下的属性值矩阵转化为模糊关系矩阵，再将模糊关系合成矩阵与解决传统指派问题的匈牙利法相结合，提出一种求解多目标指派问题的综合方法：模糊匈牙利法，并结合优化潜艇兵力配置问题进行了应用分析。     

运输问题的模糊聚类分析求解

通过对传统模糊聚类经验公式的改进和对最后两类排序的确定,提出了一种基 于模糊聚类分析的运输问题简单快速的求解方法．编出了通用程序,并给除了实例和计算 结果．该算法既是模糊聚类分析应用的扩展,又是对运筹学知识的补充和完善．     

含直觉模糊弹性约束的多目标模糊线性规划求解

基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的多目标模糊线性规划问题.通过引入模糊数的加权特征数,定义了一种序关系并拓展了Verdegay的模糊线性规划方法,将上述多目标模糊线性规划问题转化成两个等价含参数约束条件的清晰多目标线性规划模型,并应用一种线性加权函数法给出了此类线性规划模型的对比最优可行解.最后通过一个数值实例来说明此类问题的一般求解方法.     

具有模糊报酬的多目标马尔可夫决策规划

给出一种模糊多目标马尔可夫决策规划的定义,即当报酬是模糊函数时的多目标马尔可夫决策规划,并解决求解这种规划的最优策略的方法以及这种多目标规划最优解的判决问题。     

偏好信息为模糊互反判断矩阵的模糊多属性决策法

研究只有部分权重信息且决策者对方案的偏好信息以模糊互反判断矩阵形式给出的模糊多属性决策问题。提出了一种基于目标规划模型的模糊多属性决策方法。该法首先基于模糊互反判断矩阵，利用转换函数将决策信息一致化，建立了一个目标规划模型．通过求解该模型确定属性的权重，然后运用加性加权法求出各方案的模糊综合属性值，并利用已有的三角模糊数排序公式求得决策方案的排序。文章最后把该法应用于解决风险投资领域中的项目评估问题。     

物流运输网络多目标最短路问题的模糊满意解

本文对物流运输网络多目标最短路问题进行了研究。提出了一种求解多目标最短路问题的目标集成方法和对集成后目标函数求解的扩展标号法。在将多目标转化为单目标时,综合考虑了每个目标的边缘评价和所有目标的整体评价因素,通过对每个目标的权重分配将决策者的偏好充分体现到决策过程中,采用广义的模糊目标集成算子形成了相应的折衷规划模型。最后,通过实例对本文所提方法进行了说明。     

多目标模糊系数规划

在单目标模糊系数规划的理论基础上，对多目标模糊系数规划进行讨论，在以目标间的协调程度尽可能大为最优性条件的要求下提出多目标模糊系数规划最优解的定义，并给出一种可行的求解方法。     

Multi-objective multi-item solid transportation problem in fuzzy environment

A multi-objective multi-item solid transportation problem with fuzzy coefficients for the objectives and constraints, is modeled and then solved by two different methods. A defuzzification method based on fuzzy linear programming is applied for fuzzy supplies, demands and conveyance capacities, including the condition that both total supply and conveyance capacity must not fall below the total demand. First, expected values of the fuzzy objective functions are considered to derive crisp values. Another method based on the concept of “minimum of fuzzy number” is applied for the objective functions that yields fuzzy values instead of particular crisp values for the fuzzy objectives. Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives. A numerical example is solved using above mentioned methods and corresponding results are compared.     

Fuzzy goal programming for multiobjective transportation problems

Several fuzzy approaches can be considered for solving multiobjective transportation problem. This paper presents a fuzzy goal programming approach to determine an optimal compromise solution for the multiobjective transportation problem. We assume that each objective function has a fuzzy goal. Also we assign a special type of nonlinear (hyperbolic) membership function to each objective function to describe each fuzzy goal. The approach focuses on minimizing the negative deviation variables from 1 to obtain a compromise solution of the multiobjective transportation problem. We show that the proposed method and the fuzzy programming method are equivalent. In addition, the proposed approach can be applied to solve other multiobjective mathematical programming problems. A numerical example is given to illustrate the efficiency of the proposed approach.     

Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost

In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP). In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic) membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.     

Editorial

Linear programming problems with fuzzy parameters are formulated by fuzzy functions. The ambiguity considered here is not randomness, but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership. Parameters on constraint and objective functions are given by fuzzy numbers. In this paper, our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters. This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential.     

Uncertain solid transportation problems

The solid transportation problem arises when bounds are given on three item properties. Usually, these properties are source, destination and type of product or mode of transport, and often are given in a uncertain way. This paper deals with two of the ways in which uncertainty can appear in the problem: Interval solid transportation problem and fuzzy solid transportation problem. The first arises when data problem are expressed as intervals instead of point values, and the second when the nature of the information is vague. Both models are treated in the case in which the uncertainty affects only the constraint set. For interval case, an auxiliary problem is obtained in order to find a solution. This auxiliary problem is a standard solid transportation problem which can be solved with the efficient methods existing. For fuzzy case, a parametric approach which makes it possible to find a fuzzy solution to the former problem is used.     

两阶段模糊运输期望值模型及其逼近方法

基于可信性理论和两阶段模糊优化方法,提出一类带有模糊参数的两阶段运输期望值模型.由于提出运输问题包含带有无限支撑的模糊变量系数,因此它是一个无限堆的优化问题.然后,讨论两阶段模糊运输期望值问题的逼近方法并且将逼近方法嵌套到遗传算法中产生一个基于遗传算法的逼近方法求解提出的两阶段模糊运输期望值问题.最后,给出一个数值例子...     

A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems

In this paper, we introduce a fuzzy mathematical programming with generalized fuzzy number as objective coefficients. We also examine a transportation problem with additional restriction. There is an additional entropy objective function in the transportation problem besides transportation cost objective function. Using new fuzzy mathematical programming, this multi-objective entropy transportation problem with generalized trapezoidal fuzzy number costs has been reduced to a primal geometric programming problem. Pareto optimal solution of the transportation model is found. Numerical examples have been provided to illustrate the problem.     

A class of multiobjective linear programming model with fuzzy random coefficients

The aim of this paper is to deal with a multiobjective linear programming problem with fuzzy random coefficients. Some crisp equivalent models are presented and a traditional algorithm based on an interactive fuzzy satisfying method is proposed to obtain the decision maker’s satisfying solution. In addition, the technique of fuzzy random simulation is adopted to handle general fuzzy random objective functions and fuzzy random constraints which are usually hard to be converted into their crisp equivalents. Furthermore, combined with the techniques of fuzzy random simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy random multiobjective programming problem. Finally, illustrative examples are given in order to show the application of the proposed models and algorithms.     

A simple approach to fuzzy critical path analysis in project networks

This paper develops a simple approach to critical path analysis in a project network with activity times being fuzzy numbers. The idea is based on the linear programming (LP) formulation and fuzzy number ranking method. The fuzzy critical path problem is formulated as an LP model with fuzzy coefficients of the objective function, and then on the basis of properties of linearity and additivity, the Yager’s ranking method is adopted to transform the fuzzy LP formulation to the crisp one which can be solved by using the conventional streamlined solution methods. Consequently, the critical path and total duration time can be obtained from the derived optimal solution. Moreover, in this paper we also define the most critical path and the relative path degree of criticality, which are theoretically sound and easy to use in practice. An example discussed in some previous studies illustrates that the proposed approach is able to find the most critical path, which is proved to be the same as that derived from an exhausted comparison of all possible paths. The proposed approach is very simple to apply, and it is not require knowing the explicit form of the membership functions of the fuzzy activity times.     

On fuzzy random multiobjective quadratic programming

In this paper, a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered. First, we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. At the end, numerical examples are illustrated in the support of the obtained results.