考虑后悔规避与匹配意愿的直觉模糊双边匹配方法

针对直觉模糊偏好信息的双边匹配问题,提出一种考虑匹配主体后悔规避心理行为和匹配意愿的双边匹配方法。首先,将双边主体的直觉模糊偏好信息转化为效用值;然后,依据后悔理论的思想,通过一方主体将另一方主体进行两两比较计算每个主体的后悔值和欣喜值,进而计算每个主体的总体后悔欣喜值,构建匹配满意度计算规则,建立双边匹配多目标优化模型,通过分析现有匹配意愿系数确定方法的不足,给出一种新的匹配意愿系数确定方法,在此基础上,考虑双边主体的匹配意愿,采用线性加权法将多目标优化模型转化为单目标规划模型进行求解,获得双边匹配结果;最后,通过一个算例验证了提出方法的可行性和有效性。     

基于语言偏好信息的稳定双边匹配决策方法

针对语言偏好信息下的双边匹配问题,提出一种双边匹配决策方法。首先,将双边主体给出的语言偏好信息转化为三角模糊数;然后,基于去模糊化处理方法将三角模糊数转化为匹配满意度,在此基础上,考虑稳定匹配约束条件,以最大化每方主体的匹配满意度为目标,建立双边匹配多目标优化模型,求解模型,获得双边匹配结果;最后,通过一个算例验证了提出方法的可行性和有效性。     

考虑个体偏好和互惠偏好的双边匹配决策方法研究

针对具有个体偏好和互惠偏好的双边匹配问题,提出了一种考虑稳定性和满意性的决策方法。首先,给出了考虑个体偏好和互惠偏好的双边匹配问题描述;其次,对基于满意度的个体理性匹配、稳定匹配等相关概念进行了界定,并给出了个体满意度、互惠满意度和总体满意度的计算方法;在此基础上,构建了以双边主体总体满意度最大为目标的稳定匹配优化模型,采用基于隶属函数的加权和方法将多目标优化模型转化为单目标优化模型,通过求解单目标优化模型获得双边主体最优稳定匹配方案。最后,通过算例分析说明所提方法的有效性和实用性。     

考虑老年人感知满意度的社区居家养老护理人员调度策略研究

近年来,随着人口老龄化进程不断加快,社区居家养老模式越来越受到社会各界的高度关注。为了向社区居家养老服务中心护理人员调度提供决策支持,研究考虑老年人感知满意度的护理人员调度问题。以社区居家养老预约服务为背景,首先融合前景理论和模糊理论分别从老年人等待时间、老年人对护理人员偏好和老年人对服务价格偏好三个方面建立老年人感知满意度函数;其次确定主要目标为最大化老年人综合感知满意度,次要目标为最小化社区居家养老服务中心运营成本的优化调度问题,并且构建了相应的混合整数非线性规划数学模型;最后综合应用遗传算法和模拟植物生长算法(PGSA)对该模型进行求解,其中遗传算法用于求解护理人员的服务顺序,PGSA用于求解护理人员调度方案,并且利用MATLAB软件进行仿真,同时引入粒子群算法与PGSA进行计算对比,发现PGSA在性能参数和计算时间方面都有明显的优势。通过算例验证分析,结果表明该模型在考虑老年人感知满意度的基础上,能够获得最优的护理人员调度方案,证明了上述优化模型和算法的可行性和有效性。     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

一种考虑评价标准权重和主体满意度的双边匹配决策方法

针对公共文化服务设施建设项目与私人部门之间的匹配问题,提出了一种双边匹配的决策方法。首先,利用基于偏好关系的群决策方法确定匹配双方评价标准权重。由直觉乘法偏好关系到直觉模糊偏好关系的转换公式,得到关联直觉模糊偏好关系矩阵,给出考察其一致性程度的公式,从而获得决策组中各个专家权重,并进一步计算评价标准的权重。接着,利用区间直觉模糊数描述匹配双方的互相评价结果,根据加权算子定义主体加权满意度,引入调节参数,综合考虑双方主体满意度的一致性和互补性,构建了以整体满意度最大为目标的优化模型。最后,通过具体算例说明了所提方法的有效性和合理性。     

基于直觉模糊偏好信息的多阶段双边匹配方法

针对偏好序值难以区分匹配主体偏好强度的缺陷问题,考虑双边匹配的阶段性特征,提出一种多阶段双边匹配方法。首先将匹配主体的直觉模糊偏好信息转化成基本信任分配函数;然后依据直觉模糊相似度构建匹配权重优化模型,使用匹配权重对基本信任分配函数进行修正和证据合成,进一步,基于信任度给出了匹配满意度测度方法,建立双边匹配优化模型;最后通过算例分析验证了提出方法的有效性和可行性。     

基于对偶犹豫模糊偏好信息的双边稳定匹配决策方法

针对基于对偶犹豫模糊偏好信息的双边稳定匹配问题,提出了一种新的匹配方法.首先,给出了基于对偶犹豫模糊偏好信息的双边稳定匹配问题的描述;然后,依据双边主体给出的偏好信息构造对偶犹豫模糊偏好矩阵,使用投影技术将对偶犹豫模糊偏好矩阵转化为满意度矩阵;接着,以双方主体满意度最大化为目标,考虑稳定匹配的约束条件,构建了匹配模型;进而,运用组合满意度分析方法,将多目标优化模型转化为单目标优化模型,通过模型求解得到最优的匹配方案;最后,实例分析说明了所提方法的实用性和有效性.     

不确定风险偏好下的直觉模糊匹配决策方法

针对匹配信息为直觉模糊偏好关系的双边匹配问题,给出一种考虑主体风险偏好态度的决策方法.首先,定义了加性一致性直觉模糊偏好关系;然后,综合考虑主体给定的偏好关系以及风险偏好参数,建立并求解一种一致性偏差最小的非线性规划模型,从而获得最优排序向量;进而将其作为相应匹配对象的匹配度信息.在此基础上,构建最大化双方匹配度之和的多目标匹配模型,使用极大极小法转化为单目标线性规划模型,求解模型得到匹配结果;最后,通过一个算例表明所提方法的可行性与有效性.     

考虑模糊交货期的柔性作业车间动态调度研究

针对柔性作业车间调度在机器故障扰动情况下的动态性,采用基于事件与周期混合驱动的滚动窗口再调度策略进行动态调度.对于工件交货期模糊的情况采用梯形交货期窗口表示,并运用字典序多目标规划的方法,以平均流经时间最小、能耗最小、客户满意度最大为目标,建立多目标柔性作业车间动态调度模型,并设计了改进的自适应免疫遗传算法,在对种群进行初始化时,将初始化机器、初始化工序及随机初始化结合在一起,并对模型进行求解.将算例仿真结果与遗传算法所得的结果进行对比,验证算法的有效性.     

Fuzzy optimality based decision making under imperfect information without utility

In the realm of decision making under uncertainty, the general approach is the use of the utility theories. The main disadvantage of this approach is that it is based on an evaluation of a vector-valued alternative by means of a scalar-valued quantity. This transformation is counterintuitive and leads to loss of information. The latter is related to restrictive assumptions on preferences underlying utility models like independence, completeness, transitivity etc. Relaxation of these assumptions results into more adequate but less tractable models. In contrast, humans conduct direct comparison of alternatives as vectors of attributes’ values and don’t use artificial scalar values. Although vector-valued utility function-based methods exist, a fundamental axiomatic theory is absent and the problem of a direct comparison of vectors remains a challenge with a wide scope of research and applications. In the realm of multicriteria decision making there exist approaches like TOPSIS and AHP to various extent utilizing components-wise comparison of vectors. Basic principle of such comparison is the Pareto optimality which is based on a counterintuitive assumption that all alternatives within a Pareto optimal set are considered equally optimal. The above mentioned mandates necessity to develop new decision approaches based on direct comparison of vector-valued alternatives. In this paper we suggest a fuzzy Pareto optimality (FPO) based approach to decision making with fuzzy probabilities representing linguistic decision-relevant information. We use FPO concept to differentiate “more optimal” solutions from “less optimal” solutions. This is intuitive, especially when dealing with imperfect information. An example is solved to show the validity of the suggested ideas.     

On the calculation of a membership function for the solution of a fuzzy linear optimization problem

In the present paper the fuzzy linear optimization problem (with fuzzy coefficients in the objective function) is considered. Recent concepts of fuzzy solution to the fuzzy optimization problem based on the level-cut and the set of Pareto optimal solutions of a multiobjective optimization problem are applied. Chanas and Kuchta suggested one approach to determine the membership function values of fuzzy optimal solutions of the fuzzy optimization problem, which is based on calculating the sum of lengths of certain intervals. The purpose of this paper is to determine a method for realizing this idea. We derive explicit formulas for the bounds of these intervals in the case of triangular fuzzy numbers and show that only one interval needs to be considered.     

Multi-objective algorithm for the design of prediction intervals for wind power forecasting model

A composite forecasting framework is designed and implemented successfully to estimate the prediction intervals of wind speed time series simultaneously through machine learning method embedding a newly proposed optimization method (multi-objective salp swarm algorithm). In this study, data pre-process strategy based on feature extraction is served for reducing the fluctuations of wind power generation and select appropriate input forms of wind speed datasets for the sake of improving the overall performance. Besides, fuzzy set theory selection technique is used to determine the best compromise solutions from Pareto front set deriving from the optimization phase. To test the effectiveness of the proposed composite forecasting framework, several case studies based on different time-scale wind speed datasets are conducted. The corresponding results present that the proposed framework significantly outperforms other benchmark methods, and it can provide very satisfactory results in both goals between high coverage and small width.     

Fuzzy Optimization Problems Based on Ordering Cones

The solution concepts of the fuzzy optimization problems using ordering cone (convex cone) are proposed in this paper. We introduce an equivalence relation to partition the set of all fuzzy numbers into the equivalence classes. We then prove that this set of equivalence classes turns into a real vector space under the settings of vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. Therefore, the optimality notions in the set of equivalence classes (in fact, a real vector space) can be naturally elicited by using the similar concept of Pareto optimal solution in vector optimization problems. Given an optimization problem with fuzzy coefficients, we introduce its corresponding (usual) optimization problem. Finally, we prove that the optimal solutions of its corresponding optimization problem are the Pareto optimal solutions of the original optimization problem with fuzzy coefficients.     

Conflict resolution in fuzzy environment

Conflict resolution methodology is discussed with fuzzified Pareto frontier. Four solution concepts, namely, the Nash solution, the generalized Nash solution, the Kalai-Smorodinsky concept, and a solution method based on a special bargaining process are examined. The solutions are also fuzzy, the corresponding payoff values are fuzzy numbers, the membership functions of which are determined. Three particular cases are considered in the paper. Linear, quadratic, and general nonlinear Pareto frontiers with known shape are examined.     

Pareto Simulated Annealing for Fuzzy Multi-Objective Combinatorial Optimization

The paper presents a metaheuristic method for solving fuzzy multi-objective combinatorial optimization problems. It extends the Pareto simulated annealing (PSA) method proposed originally for the crisp multi-objective combinatorial (MOCO) problems and is called fuzzy Pareto simulated annealing (FPSA). The method does not transform the original fuzzy MOCO problem to an auxiliary deterministic problem but works in the original fuzzy objective space. Its goal is to find a set of approximately efficient solutions being a good approximation of the whole set of efficient solutions defined in the fuzzy objective space. The extension of PSA to FPSA requires the definition of the dominance in the fuzzy objective space, modification of rules for calculating probability of accepting a new solution and application of a defuzzification operator for updating the average position of a solution in the objective space. The use of the FPSA method is illustrated by its application to an agricultural multi-objective project scheduling problem.     

Variable and large neighborhood search to solve the multiobjective set covering problem

In this paper, we study the multiobjective version of the set covering problem. To our knowledge, this problem has only been addressed in two papers before, and with two objectives and heuristic methods. We propose a new heuristic, based on the two-phase Pareto local search, with the aim of generating a good approximation of the Pareto efficient solutions. In the first phase of this method, the supported efficient solutions or a good approximation of these solutions is generated. Then, a neighborhood embedded in the Pareto local search is applied to generate non-supported efficient solutions. In order to get high quality results, two elaborate local search techniques are considered: a large neighborhood search and a variable neighborhood search. We intensively study the parameters of these two techniques. We compare our results with state-of-the-art results and we show that with our method, better results are obtained for different indicators.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

Solving the multiobjective possibilistic linear programming problem

In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM), who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed. In this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters (FP-MOLP), whose possibility distributions are given by fuzzy numbers, estimated from the information provided by the DM. As the parameters, intervening in the model, are fuzzy the solutions will be also fuzzy. We propose a new Pareto Optimal Solution concept for fuzzy multiobjective programming problems. It is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem. The method relies on α-cuts of the fuzzy solution to generate its possibility distributions. These ideas are illustrated with a numerical example.     

Applying fuzzy weighted average approach to evaluate office layouts with Feng–Shui consideration

Office layout is an important issue, especially in China and the Asian countries, where the Feng–Shui theory frequently plays a vital role. Yet, in the literature, Feng–Shui theory has seldom been discussed. Another problem is the imprecise or vague satisfaction level of the linguistic expression used in this theory. In this article, the fuzzy set theory is applied to deal with this aspect of the problem. Using an improved and efficient fuzzy weighted average (EFWA) algorithm, which has been shown to be more advantageous than the existing FWA algorithms, an empirical study of an office-layout design problem with the consideration of Feng–Shui is presented to illustrate the EFWA approach. The results and the criteria developed, based on the interpretation of the Form school concept of the Feng–Shui are reported.