关于语言信息聚合算子的研究

发布时间：2018-02-26 23:06

本文关键词： 模糊多属性群决策聚合算子二元语言变量不确定语言变量幂平均算子 Hero平均算子　出处：《浙江理工大学》2016年硕士论文　论文类型：学位论文

【摘要】：近年来,多属性决策理论与应用成为应用数学,管理科学与决策科学,计算机科学等领域的研究热点之一,其中语言形式给出的多属性群决策问题的研究尤其受到关注,这类问题不仅具有重要的理论意义,而且具有广阔的应用前景.解决这类决策问题的关键之一在于选择合适的基于语言信息的聚合算子.文献中已经提出一些语言型聚合算子,比如,二元语言聚合算子,不确定语言聚合算子等,并将之应用于多属性决策问题的研究之中.但是,语言信息环境下的多属性决策问题是相当复杂的,其理论与应用研究中仍然存在一些问题需要解决,比如,对于同一决策问题采用不同的聚合算子所得到的决策结果是否一致,是否能找到针对复杂的多属性决策问题带参数的聚合算子,针对同一决策问题,当聚合算子参数变化时,对决策结果情况的分析与参数的优选等.本文就是在上述背景下,对现存的一些语言型聚合算子的性质进行研究,并且在此基础上提出新的语言聚合算子,同时讨论这些算子所具有的性质,进而提出新的语言信息环境下的多属性群决策方法,并且通过实际的多属性群决策问题展示所提出决策方法的实用性.本文的主要研究工作与结果如下：基于二元语言环境和幂平均算子,提出了二元语言广义幂混合平均算子,并且验证了它具有一些理想的性质,如有界性,单调性,幂等性,交换性等,同时它还以一些重要的聚合算子为特例.与现存的二元语言聚合算子相比,它具有明显的优势.我们还分别提出了基于t-模和t-余模的二元语言加权平均算子,在模糊逻辑和模糊决策之间建立了有机的联系.基于不确定语言环境和Hero平均算子,提出了不确定语言Hero几何平均算子,讨论了它具有的性质和一些特例.最后,提出了基于新算子的语言环境下的多属性群决策方法,并将之应用于实际的多属性群决策问题中,并且讨论基于不同的语言聚合方法所得决策结果的差异,从而给出一些有意义的结论.
[Abstract]:In recent years, the theory and application of multi-attribute decision making have become one of the research hotspots in the fields of applied mathematics, management science and decision science, computer science and so on. This kind of problem not only has important theoretical significance, but also has broad application prospect. One of the key points to solve this kind of decision problem is to select suitable aggregation operator based on linguistic information. Some linguistic aggregation operators have been proposed in the literature. For example, binary language aggregation operator, uncertain language aggregation operator and so on, are applied to the study of multi-attribute decision making problem. However, the multi-attribute decision making problem in language information environment is quite complex. There are still some problems to be solved in the theoretical and applied research, for example, whether the decision results obtained by using different aggregation operators for the same decision problem are consistent or not. Whether we can find the aggregation operator with parameters for complex multi-attribute decision making problems, and for the same decision problem, when the parameters of the aggregation operator change, the analysis of the decision results and the optimal selection of the parameters are given in this paper. The properties of some existing linguistic aggregation operators are studied, and on this basis, new language aggregation operators are proposed, and the properties of these operators are discussed, and then a new multi-attribute group decision making method under the new language information environment is proposed. The main work and results of this paper are as follows: based on binary language environment and power averaging operator, a binary language generalized power mixed averaging operator is proposed. It is proved that it has some ideal properties, such as boundedness, monotonicity, idempotent, commutativity, etc. At the same time, it takes some important aggregation operators as special cases. We also propose a binary language weighted averaging operator based on tmodules and tcomodules, which establishes an organic relationship between fuzzy logic and fuzzy decision making. Based on the uncertain language environment and the Hero averaging operator, In this paper, an uncertain language Hero geometric averaging operator is proposed, and its properties and some special cases are discussed. Finally, the method of multi-attribute group decision making based on the new operator is proposed and applied to the practical multi-attribute group decision making problem. The differences of decision results based on different linguistic aggregation methods are discussed, and some meaningful conclusions are given.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O159;O225

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