【作者】 王霞；

【导师】 陈京荣；

【作者基本信息】 兰州交通大学 ， 应用数学， 2021， 硕士

【摘要】 决策问题在人们的生活中处处可见,大到国家社会小到公司个人,国家利益和公司及个人命运都离不开正确的决策.伴随着决策理论的发展与完善,出现了多属性决策,多属性决策的相关知识在工程、经济以及军事等多个领域发挥了不可或缺的作用.随着社会的不断发展、经济的逐步繁荣,问题的复杂性也逐渐增加,不确定因素的数量日益增多,决策难的问题日益突出,模糊学恰好能解决此类问题.对于模糊多属性决策问题,用什么形式的模糊数能更加合理地体现决策信息的不确定性,是本论文主要研究的问题.论文通过给出直觉梯形模糊数、勾股梯形模糊数、区间勾股梯形模糊数,并结合不同的排序方法,提出了基于梯形模糊数的多属性决策方法,同时将其运用到了建厂选址、绿色供应商选择、市场投资等实例中,通过验证这些例子,阐明了所提出方法的有效性.主要研究内容如下:(1)对梯形模糊集理论及梯形模糊多属性方法和应用进行了现状分析,阐述了本文的研究内容、研究目的及意义.并对多属性决策的基础知识进行了整理.(2)对于属性权重未知的直觉梯形模糊多属性决策问题,给出了直觉梯形模糊数的Hamming距离,根据离差最大化的思想构建最优化模型,求得了属性权重,然后结合TOPSIS方法,计算出各方案与正、负理想方案的距离及贴近度,根据贴近度的大小对方案进行了排序,给出了基于属性权重未知的直觉梯形模糊多属性决策的方法步骤.最后,结合实例验证了该方法的有效性,对于权重未知的直觉梯形模糊多属性决策问题提出了一种新的解决方法.(3)对于勾股梯形模糊多属性决策问题,首先计算出勾股梯形模糊数的集结算子,然后根据直觉梯形模糊数的期望值假设了勾股梯形模糊数的期望值,改进了勾股梯形模糊数的得分函数和精确函数.由集结算子得出新得分函数和原得分函数的大小,并对方案进行了排序,给出了根据得分大小来排名的勾股梯形模糊多属性决策方法.最后,通过实例验证了用原得分函数和新得分函数得到的排名是一样的,说明了该方法的有效性.(4)对于区间勾股梯形模糊多属性决策问题,由于目前还没有学者定义区间勾股梯形模糊数间的距离,所以很多学者都是通过得分函数的大小对其方案进行排名.本文定义了区间勾股梯形模糊数的Hamming距离,并对其进行了证明.将TOPSIS方法与之结合,提出区间勾股梯形模糊多属性决策方法,给出了决策步骤.最后,将其方法运用到实例中,此方法和用得分函数大小排序的结果是相同的,证明了此种方法的有效性.更多还原

【Abstract】 Decision making problems can be seen everywhere in people’s life.From countries and societies to companies and individuals,the interests of a country and the fate of a company and an individual are inseparable from correct decisions.With the development and improvement of decision theory,multiple attribute decision making has appeared.And the knowledge related to multiple attribute decision making has played an indispensable role in many fields such as engineering,economy and military.With the continuous development of the society and the gradual prosperity of the economy,the complexity of the problem is gradually increasing,the number of uncertain factors is increasing,and the problem of difficult decision making is becoming more and more prominent.Fuzzy theory can just solve such problems.For the fuzzy multiple attribute decision making problem,which form of fuzzy number can more reasonably reflect the uncertainty of the decision information that is the main research problem of this paper.By giving intuitionistic,Pythagorean and interval-valued Pythagorean trapezoidal fuzzy numbers,and different ranking methods are combined,this paper give multiple attribute decision making methods based on the trapezoidal fuzzy numbers.At the same time,the proposed method is applied to some examples,such as plant site selection,green supplier selection,market investment,etc.And the validity of the proposed method is illustrated by verifying these examples.The main research contents are as follows:(1)The present situation of trapezoidal fuzzy set theory and trapezoidal fuzzy multi-attribute method and its application are analyzed.The research content,purpose and significance of this paper are expounded.The basic knowledge of multiple attribute decision making is summarized.(2)For the problem of intuitionistic trapezoidal fuzzy multiple attribute decision making with unknown attribute weights.The Hamming distance of intuitionistic trapezoidal fuzzy numbers is given.An optimization model is built according to the idea of maximizing deviation.And we use the method of TOPSIS to calculate for each plan and degree and distance of positive and negative ideal scheme.By comparison the size of the degree scheme for the sorting.Based on the attribute weights are unknown intuitionistic trapezoidal fuzzy multiple attribute decision making method of steps is presented.Finally,an example is given to show the effectiveness of this method.And a new method for intuitionistic trapezoidal fuzzy multiple attribute decision making with unknown weight is proposed.(3)For Pythagorean trapezoidal fuzzy multiple attribute decision making problem,its aggregation operator is calculated.Then the expected value of Pythagorean trapezoidal fuzzy number is assumed according to the expected value of intuitionistic trapezoidal fuzzy number.The scoring function and the exact function of fuzzy number of Pythagorean trapezoid are improved.The sizes of the new score function and the original score function are obtained by the aggregation operator,and the schemes are sorted.The fuzzy multiple attribute decision method of the Pythagorean trapezoidal fuzzy numbers’ ranking according to the score is given.Finally,an example is given to verify that the original score function is the same as the new score function,which shows the effectiveness of the proposed method.(4)For the interval-valued Pythagorean trapezoidal fuzzy multiple attribute decision making problem.Since no scholars have defined the distance between the interval-valued Pythagorean trapezoidal fuzzy numbers,many scholars rank their schemes by the size of the score function.In this paper,we define and prove its Hamming distance.The TOPSIS method is combined with it,and its fuzzy multiple attribute decision method is proposed,and the decision steps are given.Finally,the method is applied to an example,and the result of this method is the same as that of sorting by the size of score function,which proves the effectiveness of this method.更多还原