基于犹豫模糊信息群决策问题的集结算子的研究

发布时间：2018-06-20 21:19

本文选题：多准则群决策 + 区间直觉犹豫模糊集　；参考：《沈阳工业大学》2017年硕士论文

【摘要】：多准则决策(Multiple criteria decision making,MCDM)问题存在于现代社会的方方面面,其本质是:针对已给出的决策信息,通过一些方法对每组备选方案进行择优或排序,从而选出最优方案。在现实生活中,由于决策者自身的局限性及目标本身的不确定性,决策者很难给出精准评价,总是在若干个数值之间徘徊,为了解决这一问题,Torra提出了犹豫模糊集。至今,关于犹豫模糊环境下的决策问题许多专家已进行了细致研究,但研究的评价始终都是精确值。现实生活中,人们对于评价对象很难赋予精确数值,为了更细致的刻画决策者的偏好,区间信息引起人们的强烈关注。虽然区间直觉犹豫模糊集的理论和方法已得到了系统性研究,但基于区间直觉犹豫信息的模糊多准则群决策问题的决策方法仍有待完善。首先介绍了多准则群决策问题、犹豫模糊信息和基于犹豫模糊信息集结算子的研究背景与现状及其研究意义;其次,总结了关于犹豫模糊集、双犹豫模糊集和区间直觉犹豫模糊集的定义、运算法则,归纳了模糊测度、Choquet积分和Quasi-Choquet算术平均。基于阿基米德t-模、阿基米德t-反模和Quasi-Choquet算术平均,提出了区间直觉犹豫模糊Quasi-Choquet几何算子,此算子可以集结区间直觉犹豫模糊数形式的参数,并且考虑了参数间属性相关联或相互独立的情况。之后,给出了区间直觉犹豫模糊Quasi-Choquet几何算子的优良性质;再次,展示了区间直觉犹豫模糊Quasi-Choquet几何算子族,它为决策者在区间直觉犹豫模糊环境下做决策提供了灵活有用的方法。之后利用此算子族中的算子,结合折中比值法、扩展的欧几里得距离和传统的TOPSIS方法来解决区间直觉犹豫模糊环境下的多准则群决策问题;最后,归纳全文,指出当前研究的优势和不足之处,并对未来工作方向和目标进行展望。
[Abstract]:The problem of multiple criteria decision making MCDMs exists in all aspects of modern society. The essence of the problem is that according to the given decision information, each group of alternatives is selected or sorted by some methods, and the optimal scheme is selected. In real life, due to the limitation of the decision-maker and the uncertainty of the target itself, it is very difficult for the decision-maker to give accurate evaluation and always linger between a number of values. In order to solve this problem, Torra put forward a hesitant fuzzy set. Up to now, many experts have studied the decision-making problem in uncertain environment, but the evaluation is always accurate. In real life, it is difficult to assign accurate value to the object of evaluation. In order to describe the preference of decision maker in detail, the interval information attracts people's strong attention. Although the theory and method of interval intuitionistic hesitation fuzzy sets have been systematically studied, the decision method of fuzzy multi-criteria group decision making problem based on interval intuitionistic hesitation information still needs to be improved. Firstly, the paper introduces the research background, status quo and significance of the multi-criteria group decision making problem, the hesitant fuzzy information and the aggregation operator based on the hesitant fuzzy information, and then summarizes the research on the hesitant fuzzy set. The definitions and algorithms of double hesitating fuzzy sets and interval intuitionistic hesitating fuzzy sets are discussed. The fuzzy measure Choquet integral and Quasi-Choquet arithmetic average are summarized. Based on Archimedean tmodules, Archimedean t- inverse modules and quasi-Choquet arithmetic averages, an interval intuitionistic hesitation fuzzy quasi-Choquet geometric operator is proposed, which can aggregate the parameters of interval intuitionistic hesitation fuzzy numbers. And consider the case that the parameters are related to each other or independent of each other. Then, the fine properties of interval intuitionistic hesitation fuzzy quasi-Choquet geometric operators are given, and the family of interval intuitionistic fuzzy quasi-Choquet geometric operators is shown, which provides a flexible and useful method for decision-makers to make decisions in interval intuitionistic hesitation fuzzy environment. Then, the extended Euclidean distance and the traditional TOPSIS method are used to solve the multi-criteria group decision making problem in the interval intuitionistic hesitation fuzzy environment by using the operators in the family of operators, combined with the compromise ratio method. The advantages and disadvantages of current research are pointed out, and the future work direction and goal are prospected.
【学位授予单位】：沈阳工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O225;O159

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