Solving linear programming problems under fuzziness and randomness environment using attainment values

In this paper, the author presents a model to measure attainment values of fuzzy numbers/fuzzy stochastic variables. These new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem. Numerical comparisons are provided to illustrate the effectiveness of the proposed method.     

Solving fuzzy (stochastic) linear programming problems using superiority and inferiority measures

In this paper, the author presents a model to measure the superiority and inferiority of fuzzy numbers/fuzzy stochastic variables. Then, the new measures are used to convert the fuzzy (stochastic) linear program into the corresponding deterministic linear program. Numerical examples are provided to illustrate the effectiveness of the proposed method.     

Stochastic simulation-based genetic algorithm for chance constraint programming problems with continuous random variables

In this article, we present a stochastic simulation-based genetic algorithm for solving chance constraint programming problems, where the random variables involved in the parameters follow any continuous distribution. Generally, deriving the deterministic equivalent of a chance constraint is very difficult due to complicated multivariate integration and is only possible if the random variables involved in the chance constraint follow some specific distribution such as normal, uniform, exponential and lognormal distribution. In the proposed method, the stochastic model is directly used. The feasibility of the chance constraints are checked using stochastic simulation, and the genetic algorithm is used to obtain the optimal solution. A numerical example is presented to prove the efficiency of the proposed method.     

Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables

Solution procedure consisting of fuzzy goal programming and stochastic simulation-based genetic algorithm is presented, in this article, to solve multiobjective chance constrained programming problems with continuous random variables in the objective functions and in chance constraints. The fuzzy goal programming formulation of the problem is developed first using the stochastic simulation-based genetic algorithm. Without deriving the deterministic equivalent, chance constraints are used within the genetic process and their feasibilities are checked by the stochastic simulation technique. The problem is then reduced to an ordinary chance constrained programming problem. Again using the stochastic simulation-based genetic algorithm, the highest membership value of each of the membership goal is achieved and thereby the most satisfactory solution is obtained. The proposed procedure is illustrated by a numerical example.     

上层含约束条件且具有模糊决策变量的二层多随从线性规划

提出并研究了一类上层含约束条件且具有模糊决策变量的二层多随从线性规划模型,利用结构元理论证明了该模型最优解等价于上层含约束条件的二层多随从线性规划模型最优解,利用Kuhn-Tucker方法得到了该模型最优解,并通过数值算例验证了该方法的可行性。     

矿山产能分配的变量模糊线性规划模型

针对矿山资源开采过程中产能不确定的分配问题,引入了模糊结构元素理论。将产能用结构元表示,并利用结构元加权序将模糊数比较转化为单调函数比较,将含有模糊变量的线性规划问题等价转化为经典线性规划问题。以某矿山为例,建立矿山产能分配的变量模糊线性规划模型,并进行求解。结果表明：实现了将实际问题中的模糊事件进行精确表达,原问题的求解更简便。得到矿山产能取得最大可能利润时的可能分配。应用结构元加权序求解的线性规划模型优于结构元元序的。     

A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.     

改进RWP移动模型结合线性规划的无线网络能量均衡算法

针对无线网络中大多数现有方法不能很好地兼顾能量效率和能量均衡的问题,提出了基于改进随机路点移动模型(random waypoint mobility models,RWP)结合线性规划(linear programming, LP)的无线网络能量平衡模型。首先,使用方形网络拓扑和RWP生成移动性场景;然后,在最优路由条件下建模网络行为并构建了一种LP架构;最后,利用优化问题的全局知识获得了该架构的高效解。数值分析结果表明,移动性对无线节点的能量耗散趋势具有显著影响,移动性可提高能量平衡达到某一级别,但极端的移动性可能会导致无线网络能量平衡的劣化。     

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.     

Optimal linear filtering and extrapolation of realizations of a vector random function observed with errors

A solution to an optimal linear filtering and extrapolation problem is proposed. The investigation object is a realization of multidimensional random function, which is measured with random errors. The solution method does not put any essential constraints on the investigated random fimction, measurment error characteristics, and on the character of relations between them. The solution is based on Pugachov’s canonical decomposition of the investigated random function, and its form is convenient for use with a computer. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 125–132, July–August, 2000.