模糊多属性决策方法及其在制造业中的应用研究
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摘要
汽车传动器生产厂的半自动生产线上工位绩效评估、零部件的海外订购策略选择和集装箱港口的落场集装箱堆存位置选择是当前我国制造业中的重要问题，多属性决策方法可以用于解决这些问题。为处理实际多属性决策问题中包含的不确定性因素，以及决策者主观判断的含糊性，候选方案的评价值可以表达为模糊集、直觉模糊集、区间值直觉模糊集、语言信息或模糊变量。通过模糊量可以更贴切地反映评估结果中所包含的不确定信息。进一步采用聚合算子和排序方法，便可以得到决策问题的最佳候选方案。
对于直觉模糊环境下的集装箱堆存场地选择问题，本文证明了由所有直觉模糊数或区间值直觉模糊数组成的集合关于序关系均构成完备分配格，并且它们关于交、并、加法、乘法四种运算都构成幺交换半群结构；提出了基于直觉模糊数对应参数优化模型的排序方法和基于无记忆性多次投票模型的排序方法；为了处理更复杂的决策问题，本文提出了广义区间值直觉模糊数的概念及其数乘运算规则，并且将它们应用于解决港口集装箱堆放场地选择的问题。建立了模糊多属性决策中的保序属性约简理论，给出保序属性约简和保序属性约简核的计算方法，考虑了约简方法在港口集装箱堆存场地选址问题中的应用。
针对汽车传动器厂海外订购策略的决策问题中包含未知权重信息的问题，提出了同时考虑决策专家态度、认知不协调程度和决策者置信水平的综合定权模型，使得决策结果符合决策者态度，并且最小化决策过程中产生的认知不协调程度。
在使用模糊TOPSIS方法解决汽车传动器生产厂半自动生产线上工位评估问题时，发现了不能区分的现象，研究了不能区分的条件，利用额外的判定指标，提出了改进的TOPSIS方法，并且证明了新方法在模糊环境中可以对候选方案进行完全区分；对基于模糊变量的多属性决策问题，提出了三类模糊优势关系模型和基于距离的模糊变量比较方法，并且引入了直觉模糊变量的概念和比较方法；还将这些方法应用于解决半自动生产线上工位评估的决策问题。
There are several essential components in the area of operations management inmanufacturing, including the allocation of container yards in a container-terminal, theperformance evaluation of the production systems, and the oversea parts ordering in aautomobile transfer case manufacturing company. Multiple attribute decision makingmodels established in dealing with these issues could help the enterprise make moreprofits and save costs. However, in actual decision processes, where there are complexsituations and combinations of subjective judgments from the decision makers with theobjective circumstances at scene, it is more appropriate to represent the evaluations inthe decision making problems as in the form of fuzzy sets, intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy sets or even linguistic information, fuzzy variables,etc. Through various forms of fuzzy sets, decision experts’ subjective thoughts andattitudes, which are of uncertain information, could be reflected in a more accurate way.Then aggregation operators and ranking methods based on fuzzy quantities could beemployed to derive the final ranking order of the original MADM problem.
First of all, in the container yards allocation problems under intuitionistic fuzzynumber and the interval-valued intuitionistic fuzzy number settings, the sets of thesegeneralized fuzzy numbers are proved to be of the construction of a completedistributive lattices with respect to the order relations, and they form commutativesemi-groups with identity with respect to union, intersection, addition andmultiplication operations, respectively. In the ranking problems with intuitionistic fuzzynumbers, two innovative approaches are developed, one of which applies anoptimization model in setting the ideal weight vector of the attributes, the other methodis based upon a memory-less revote process model. In order to deal with the morecomplex uncertainty contained in MADM problems, in this thesis, generalized(interval-valued) intuitionistic fuzzy numbers and their fundamental operations areproposed. Furthermore, these fuzzy quantities are applied to solve the container yardsallocation problems.
Secondly, in order to deal with the incomplete attribute weight problems from themodel of oversea parts ordering strategy problem, a framework is introduced which consists of three aspects, the magnitude of optimistic attitude of the decision expert, theconfidence level of the decision maker and the dissonance of the expert during thedecision process. This framework is dedicated to design an optimal attribute weightvector in order to approximate the decision maker’s thought and minimize the degree ofdissonance during decision making.
Thirdly, compared with knowledge reduction methods in rough set theory,algorithms for deriving order-preserving attribute reductions and order-preservingattribute core are developed in fuzzy MADM counterpart within the module ofcontainer yards allocation problem. Meanwhile, a comparative study betweengeneralized rough sets and several topological structures is conducted.
Besides, a revised fuzzy TOPSIS method is developed in the production systemevaluation module, since a partial order has been detected in the ranking order ofalternatives. Several extra functions are introduced to help fuzzy TOPSIS method todistinguish each pair of different alternatives under fuzzy environment.
Last but not least, three fuzzy dominance models are introduced in order tofully distinguish each pair of different triangular fuzzy variables. Then anotherapproach in ranking fuzzy variables is developed through a new distancebetween two fuzzy variables. Finally, the conception of intuitionistic fuzzyvariable is introduced in order to represent the uncertain information existed inthe production system evaluation process, which is the extension of ordinaryfuzzy variables. And the ranking methods of intuitionistic fuzzy variables aredemonstrated with numerical examples of the manul performance evaluation in theproduction systems.
对于直觉模糊环境下的集装箱堆存场地选择问题，本文证明了由所有直觉模糊数或区间值直觉模糊数组成的集合关于序关系均构成完备分配格，并且它们关于交、并、加法、乘法四种运算都构成幺交换半群结构；提出了基于直觉模糊数对应参数优化模型的排序方法和基于无记忆性多次投票模型的排序方法；为了处理更复杂的决策问题，本文提出了广义区间值直觉模糊数的概念及其数乘运算规则，并且将它们应用于解决港口集装箱堆放场地选择的问题。建立了模糊多属性决策中的保序属性约简理论，给出保序属性约简和保序属性约简核的计算方法，考虑了约简方法在港口集装箱堆存场地选址问题中的应用。
针对汽车传动器厂海外订购策略的决策问题中包含未知权重信息的问题，提出了同时考虑决策专家态度、认知不协调程度和决策者置信水平的综合定权模型，使得决策结果符合决策者态度，并且最小化决策过程中产生的认知不协调程度。
在使用模糊TOPSIS方法解决汽车传动器生产厂半自动生产线上工位评估问题时，发现了不能区分的现象，研究了不能区分的条件，利用额外的判定指标，提出了改进的TOPSIS方法，并且证明了新方法在模糊环境中可以对候选方案进行完全区分；对基于模糊变量的多属性决策问题，提出了三类模糊优势关系模型和基于距离的模糊变量比较方法，并且引入了直觉模糊变量的概念和比较方法；还将这些方法应用于解决半自动生产线上工位评估的决策问题。
There are several essential components in the area of operations management inmanufacturing, including the allocation of container yards in a container-terminal, theperformance evaluation of the production systems, and the oversea parts ordering in aautomobile transfer case manufacturing company. Multiple attribute decision makingmodels established in dealing with these issues could help the enterprise make moreprofits and save costs. However, in actual decision processes, where there are complexsituations and combinations of subjective judgments from the decision makers with theobjective circumstances at scene, it is more appropriate to represent the evaluations inthe decision making problems as in the form of fuzzy sets, intuitionistic fuzzy sets,interval-valued intuitionistic fuzzy sets or even linguistic information, fuzzy variables,etc. Through various forms of fuzzy sets, decision experts’ subjective thoughts andattitudes, which are of uncertain information, could be reflected in a more accurate way.Then aggregation operators and ranking methods based on fuzzy quantities could beemployed to derive the final ranking order of the original MADM problem.
First of all, in the container yards allocation problems under intuitionistic fuzzynumber and the interval-valued intuitionistic fuzzy number settings, the sets of thesegeneralized fuzzy numbers are proved to be of the construction of a completedistributive lattices with respect to the order relations, and they form commutativesemi-groups with identity with respect to union, intersection, addition andmultiplication operations, respectively. In the ranking problems with intuitionistic fuzzynumbers, two innovative approaches are developed, one of which applies anoptimization model in setting the ideal weight vector of the attributes, the other methodis based upon a memory-less revote process model. In order to deal with the morecomplex uncertainty contained in MADM problems, in this thesis, generalized(interval-valued) intuitionistic fuzzy numbers and their fundamental operations areproposed. Furthermore, these fuzzy quantities are applied to solve the container yardsallocation problems.
Secondly, in order to deal with the incomplete attribute weight problems from themodel of oversea parts ordering strategy problem, a framework is introduced which consists of three aspects, the magnitude of optimistic attitude of the decision expert, theconfidence level of the decision maker and the dissonance of the expert during thedecision process. This framework is dedicated to design an optimal attribute weightvector in order to approximate the decision maker’s thought and minimize the degree ofdissonance during decision making.
Thirdly, compared with knowledge reduction methods in rough set theory,algorithms for deriving order-preserving attribute reductions and order-preservingattribute core are developed in fuzzy MADM counterpart within the module ofcontainer yards allocation problem. Meanwhile, a comparative study betweengeneralized rough sets and several topological structures is conducted.
Besides, a revised fuzzy TOPSIS method is developed in the production systemevaluation module, since a partial order has been detected in the ranking order ofalternatives. Several extra functions are introduced to help fuzzy TOPSIS method todistinguish each pair of different alternatives under fuzzy environment.
Last but not least, three fuzzy dominance models are introduced in order tofully distinguish each pair of different triangular fuzzy variables. Then anotherapproach in ranking fuzzy variables is developed through a new distancebetween two fuzzy variables. Finally, the conception of intuitionistic fuzzyvariable is introduced in order to represent the uncertain information existed inthe production system evaluation process, which is the extension of ordinaryfuzzy variables. And the ranking methods of intuitionistic fuzzy variables aredemonstrated with numerical examples of the manul performance evaluation in theproduction systems.
引文
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