基于模糊软集的多准则群决策方法研究

发布时间：2018-04-06 07:08

本文选题：模糊软集　切入点：指标权重　出处：《湘潭大学》2017年硕士论文

【摘要】：在现实世界中,随着信息大爆炸时代到来,知识越来越表现出复杂性、模糊性、不确定性,因此,决策过程常常伴随着信息不对称、不完备、模糊等情况。为了解决不确定性和模糊性,1999年Molodtsov提出了软集概念。随着决策的复杂化,需要利用各方面参数对问题进行评估,这样就出现了模糊性参数和精确性参数的区分。对于决策过程中出现的模糊性参数(如英语水平高),不能纯粹用属于和不属于来区分,更不可能用精确的数字代表其具体含义。考虑以上情况,Maji提出了模糊软集概念。另一方面,当决策者由于自身知识不全面、问题复杂或同一决策组内出现意见分歧时,决策评价时都会出现犹豫状况,这时犹豫模糊软集是表示这一状况的有力工具。近来,模糊软集理论和方法逐渐被应用到各个领域,如预测、分类、医疗诊断、经济分析,特别是决策问题中。由于决策环境的改变和具体决策问题的不同,模糊软集理论与方法应该随之做出改进和调整。国内外学者都对模糊软集进行了研究,定义了模糊软集且、或、并、交等运算,在此基础上提出了各种集成算子,应用于各个领域,以进行综合评价。但是随着新情况的出现,已有方法尚不能更合理更有效地解决新问题,如,决策者地位、权重不一样在现实社会中普遍存在;决策者专业知识及领域不一致、利益偏好不同;评价指标权重、评价指标集也可能存在差异等。因此,怎样根据不同问题背景去综合各方信息,得到更符合群体偏好的评价结果具有非常重要的理论意义和适用价值。本文针对决策问题指标权重未知的情况,提出了根据历史相关信息确定指标权重的方法;针对决策者存在偏好和最低满足度要求的情形,提出了相应的模糊软集决策方法,使得决策结果最大程度满足决策群体意见;针对历史相关信息缺失的情况,提出了根据决策者总体偏好和局部偏好确定指标权重的方法,并把此方法应用到考虑可信度和存在犹豫的决策问题中。最后,考虑到决策者个体权责、地位对最终决策结果的影响作用,提出了权重可调节的模糊软集群决策方法。算例说明了以上决策方法的适用性和合理性。
[Abstract]:In the real world, with the advent of the era of information explosion, knowledge shows more and more complexity, fuzziness and uncertainty. Therefore, the decision-making process is often accompanied by information asymmetry, incomplete, fuzzy and so on.In order to solve the uncertainty and fuzziness, Molodtsov put forward the concept of soft set in 1999.With the complexity of decision making, it is necessary to use various parameters to evaluate the problem, so there is a distinction between fuzzy parameters and precision parameters.For the fuzzy parameters in the decision-making process (such as the high level of English), it is impossible to distinguish between belong and non-belong, and it is not possible to use exact numbers to represent its specific meaning.Considering the above situation, Maji put forward the concept of fuzzy soft set.On the other hand, when the decision makers have complex problems or different opinions in the same decision group because of their incomplete knowledge, there will be hesitancy in the evaluation of decision making. In this case, the fuzzy soft set of hesitations is a powerful tool to represent this situation.Recently, fuzzy soft set theory and methods have been gradually applied to various fields, such as prediction, classification, medical diagnosis, economic analysis, especially decision-making.Due to the change of decision environment and the difference of specific decision problems, fuzzy soft set theory and method should be improved and adjusted accordingly.Scholars at home and abroad have studied fuzzy soft sets and defined fuzzy soft sets and, or, and, intersection operations. On this basis, a variety of integration operators are proposed, which are applied to various fields for comprehensive evaluation.However, with the emergence of new situations, the existing methods can not solve the new problems more reasonably and effectively, such as, the status of decision makers, the weight of decision makers are not the same in the real society, the professional knowledge and domain of decision makers are not consistent, and the interests preference is different.Evaluation index weight, evaluation index set may also exist differences.Therefore, how to synthesize the information of all parties according to the background of different problems and get the evaluation results which are more in line with the group preference has very important theoretical significance and applicable value.In this paper, a method of determining index weight based on historical information is proposed, and a fuzzy soft set decision method is proposed for decision makers with preference and minimum satisfaction requirement.The decision result can satisfy the opinion of the decision group to the greatest extent. In view of the lack of historical information, the method of determining the index weight according to the overall preference and local preference of the decision maker is put forward.The method is applied to the decision problem considering credibility and hesitation.Finally a fuzzy soft cluster decision making method with adjustable weight is proposed considering the influence of the individual power and responsibility of the decision maker and the position on the final decision result.An example is given to illustrate the applicability and reasonableness of the above decision-making method.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：C934

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