模糊环境下基于决策粗糙集的决策方法研究
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摘要
决策环境的复杂性、动态性,以及决策者所具备知识的有限性等都是影响人们作出合理决策所面临的挑战性因素。近些年来,信息与计算机科学相关领域的快速发展和应用,为决策者解决该类不确定性复杂决策问题提供了一种新的思路。决策粗糙集理论作为一种新的处理不确定性决策问题的方法,其特点是基于贝叶斯决策过程,考虑了决策风险对决策结果的影响,可更好为人们决策服务。
从实际决策语义出发,把模糊这一不确定性评估形式引入到决策粗糙集中,既拓宽了决策粗糙集的应用范围,又为该模型中关键要素损失函数的取值提供了新的解决方案。借鉴现有决策理论和粗糙集理论的研究成果,本文选取区间数、三角模糊数、语言变量和犹豫模糊数等四种典型的模糊形式,依次研究相应模糊环境下基于决策粗糙集的理论模型和决策方法。
首先,考虑决策粗糙集中各损失值为区间数的情况,提出了区间数决策粗糙集的基础模型。先基于确定性排序方法和可能度排序方法,探索其决策机制和决策规则。借鉴以上常规分析方法,进一步提出了一种基于区间数决策粗糙集的优化方法。通过实验对比研究,明确了区间数决策粗糙集三种分析方法的适用条件和准则。
其次,考虑决策粗糙集中各损失值为三角模糊数的情况,提出了三角模糊数决策粗糙集的基础模型。先为期望损失选取合适的三角模糊数排序方法,再挖掘出决策规则。进一步,为了确定模型中各损失值,把决策粗糙集中各类损失成功映射到多属性群决策中,这极大促进了该模型的实际应用。与此同时,利用粒子群优化算法通过调节评估刻度,演化群决策的协调过程,以解决群决策中不一致性。
再次,引入语言变量这一定性评估形式,考虑决策粗糙集中条件概率和损失函数两要素,在不同取值类型下构建出一系列新的决策粗糙集模型,从而丰富了原有决策粗糙集的研究内容。为便于模型的实际应用,进一步把决策粗糙集中各类要素成功映射到多属性群决策中,并设计出确定模型中各要素的算法。
最后,考虑决策粗糙集中损失函数为犹豫模糊数这一新型形式,探索出该模型在犹豫模糊环境下的决策机制。进一步,为解决实际决策过程中的资源分配问题,从成本语义出发,利用各对象的风险成本和多目标0-1整数规划设计求解方法,这极大地推动了决策粗糙集在管理决策领域的应用。
本文以决策粗糙集为研究对象,将不确定性模糊理论引入到决策粗糙集中,以损失函数为研究切入点,研究了模糊环境下基于决策粗糙集的决策方法。这不仅拓宽决策粗糙集的应用领域,还为研究基于粗糙集理论的决策分析提供新的方向。
When people want to make a reasonalbe decision, they face many challenges to influence their decisions, e.g. the complexity and the dynamics of decision environment, the limitation of knowledge of the decision makers and so on. In recent years, with the rapid development and application of information technologies and computer science, it provides a new idea to solve these types of uncertainty and complex problems for decision makers. As a new method to solve uncertainty decision problems, decision-theoretic rough sets consider the influence of decision risk to the result based on Bayesian decision process. It can serve to help the decision-making.
In the viewpoint of the practical semantics, we introduce the fuzzy uncertainty formation into the decision-theoretic rough set model. On the one hand, it extends the application ranges of decision-theoretic rough sets. On the other hand, it also provides a new solution for determining the value of loss function presented in decision-theoretic rough sets. In the light of the research results exsited in the available decision theory and rough set theory, this paper chooses four typical fuzzy formations to individually discuss the models and decision-making methods based on decision-theoretic rough sets, including interval-valued, triangular fuzzy number, linguistic variable and hesitant fuzzy number.
Firstly, considering the values of losses used in decision-theoretic eough sets with intervals, we propose a basic model of interval-valued decision-theoretic rough sets. In the frame of interval-valued decision-theoretic rough sets, we focus on deriving decision rules with the aid of the two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively. Following the above analysis, we further propose an optimization method for interval-valued decision-theoretic rough sets. By the comparsion study of experimental analysis, the criteria for choosing a suitable analysis method to interval-valued decision-theoretic rough sets are generated.
Secondly, considering the values of losses used in decision-theoretic eough sets with triangular fuzzy numbes, we propose a basic model of triangular fuzzy decision-theroetic rough sets. Ranking the expected loss with triangular fuzzy number is analyzed and decision rules are derived. With the aid of multiple attribute group decision making, we further design an algorithm to determine the values of losses used in triangular fuzzy decision-theroetic rough sets. It can promote the applications of triangular fuzzy decision-theroetic rough sets. Meanwhile, we optimize the scales of the linguistic variables with the use of particle swarm optimization, which evolves the negotiation process of experts and produces higher values of consistency.
Thirdly, we introduce the linguistic variable into decision-theoretic rough sets. Considering the two elements of conditional probability and loss function used in decision-theoretic rough sets, a series of novel models are constructed under their different value types. It can enrich the research contents of original decision-theoretic rough sets. For convenience of application, we determine the values of the two elements used in decision-theoretic rough sets with the aid of multi-attribute group decision making and design an adaptive algorithm.
Finally, considering the new expression of evaluation information of hesitant fuzzy number, we introduce hesitant fuzzy number into decision-theoretic rough sets and explore its decision mechanism. In order to solve the resource allocation problems in the decision procedure, we design the associated risks of alternatives and multi-objective0-1integer programming to solve it according to the practical semantics. It greatly promotes the applications of decision-theoretic rough sets in the area of management decision.
The topic of this paper is on the decision-theoretic rough sets. We introduce the fuzzy uncertainty formation into decision-theoretic rough sets and focus on discussing the loss function. Under the fuzzy environment, we study some decision-making methods based on decision-theoretic rough sets. It not only extends the application range of decision-theoretic rough sets, but also provides a new direction for decision analysis in the rough set theory.
从实际决策语义出发,把模糊这一不确定性评估形式引入到决策粗糙集中,既拓宽了决策粗糙集的应用范围,又为该模型中关键要素损失函数的取值提供了新的解决方案。借鉴现有决策理论和粗糙集理论的研究成果,本文选取区间数、三角模糊数、语言变量和犹豫模糊数等四种典型的模糊形式,依次研究相应模糊环境下基于决策粗糙集的理论模型和决策方法。
首先,考虑决策粗糙集中各损失值为区间数的情况,提出了区间数决策粗糙集的基础模型。先基于确定性排序方法和可能度排序方法,探索其决策机制和决策规则。借鉴以上常规分析方法,进一步提出了一种基于区间数决策粗糙集的优化方法。通过实验对比研究,明确了区间数决策粗糙集三种分析方法的适用条件和准则。
其次,考虑决策粗糙集中各损失值为三角模糊数的情况,提出了三角模糊数决策粗糙集的基础模型。先为期望损失选取合适的三角模糊数排序方法,再挖掘出决策规则。进一步,为了确定模型中各损失值,把决策粗糙集中各类损失成功映射到多属性群决策中,这极大促进了该模型的实际应用。与此同时,利用粒子群优化算法通过调节评估刻度,演化群决策的协调过程,以解决群决策中不一致性。
再次,引入语言变量这一定性评估形式,考虑决策粗糙集中条件概率和损失函数两要素,在不同取值类型下构建出一系列新的决策粗糙集模型,从而丰富了原有决策粗糙集的研究内容。为便于模型的实际应用,进一步把决策粗糙集中各类要素成功映射到多属性群决策中,并设计出确定模型中各要素的算法。
最后,考虑决策粗糙集中损失函数为犹豫模糊数这一新型形式,探索出该模型在犹豫模糊环境下的决策机制。进一步,为解决实际决策过程中的资源分配问题,从成本语义出发,利用各对象的风险成本和多目标0-1整数规划设计求解方法,这极大地推动了决策粗糙集在管理决策领域的应用。
本文以决策粗糙集为研究对象,将不确定性模糊理论引入到决策粗糙集中,以损失函数为研究切入点,研究了模糊环境下基于决策粗糙集的决策方法。这不仅拓宽决策粗糙集的应用领域,还为研究基于粗糙集理论的决策分析提供新的方向。
When people want to make a reasonalbe decision, they face many challenges to influence their decisions, e.g. the complexity and the dynamics of decision environment, the limitation of knowledge of the decision makers and so on. In recent years, with the rapid development and application of information technologies and computer science, it provides a new idea to solve these types of uncertainty and complex problems for decision makers. As a new method to solve uncertainty decision problems, decision-theoretic rough sets consider the influence of decision risk to the result based on Bayesian decision process. It can serve to help the decision-making.
In the viewpoint of the practical semantics, we introduce the fuzzy uncertainty formation into the decision-theoretic rough set model. On the one hand, it extends the application ranges of decision-theoretic rough sets. On the other hand, it also provides a new solution for determining the value of loss function presented in decision-theoretic rough sets. In the light of the research results exsited in the available decision theory and rough set theory, this paper chooses four typical fuzzy formations to individually discuss the models and decision-making methods based on decision-theoretic rough sets, including interval-valued, triangular fuzzy number, linguistic variable and hesitant fuzzy number.
Firstly, considering the values of losses used in decision-theoretic eough sets with intervals, we propose a basic model of interval-valued decision-theoretic rough sets. In the frame of interval-valued decision-theoretic rough sets, we focus on deriving decision rules with the aid of the two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively. Following the above analysis, we further propose an optimization method for interval-valued decision-theoretic rough sets. By the comparsion study of experimental analysis, the criteria for choosing a suitable analysis method to interval-valued decision-theoretic rough sets are generated.
Secondly, considering the values of losses used in decision-theoretic eough sets with triangular fuzzy numbes, we propose a basic model of triangular fuzzy decision-theroetic rough sets. Ranking the expected loss with triangular fuzzy number is analyzed and decision rules are derived. With the aid of multiple attribute group decision making, we further design an algorithm to determine the values of losses used in triangular fuzzy decision-theroetic rough sets. It can promote the applications of triangular fuzzy decision-theroetic rough sets. Meanwhile, we optimize the scales of the linguistic variables with the use of particle swarm optimization, which evolves the negotiation process of experts and produces higher values of consistency.
Thirdly, we introduce the linguistic variable into decision-theoretic rough sets. Considering the two elements of conditional probability and loss function used in decision-theoretic rough sets, a series of novel models are constructed under their different value types. It can enrich the research contents of original decision-theoretic rough sets. For convenience of application, we determine the values of the two elements used in decision-theoretic rough sets with the aid of multi-attribute group decision making and design an adaptive algorithm.
Finally, considering the new expression of evaluation information of hesitant fuzzy number, we introduce hesitant fuzzy number into decision-theoretic rough sets and explore its decision mechanism. In order to solve the resource allocation problems in the decision procedure, we design the associated risks of alternatives and multi-objective0-1integer programming to solve it according to the practical semantics. It greatly promotes the applications of decision-theoretic rough sets in the area of management decision.
The topic of this paper is on the decision-theoretic rough sets. We introduce the fuzzy uncertainty formation into decision-theoretic rough sets and focus on discussing the loss function. Under the fuzzy environment, we study some decision-making methods based on decision-theoretic rough sets. It not only extends the application range of decision-theoretic rough sets, but also provides a new direction for decision analysis in the rough set theory.
引文
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