【作者】 王宁；

【导师】 朱萍；

【作者基本信息】 北京邮电大学 ， 数学， 2022， 硕士

【摘要】 作为一种更符合人类思维的决策工具,三支决策通过引入接受、拒绝和延迟决策,减少了决策过程中造成的损失。由于实际问题的复杂性和信息的模糊性,决策者很难直接给出定量的评价,而是使用语言给出定性的评价。为了更好地处理语言信息,语言术语集被拓展为犹豫模糊语言术语集、双层犹豫语言术语集和概率语言术语集等。基于这些语言术语集的三支决策也不断被研究。然而直接给出符合这些语言术语集形式的语言评价并不容易,决策者可能直接用他们觉得合适的词进行评价。词可以表示为一个基本集上的模糊集,其语义可以由隶属函数表示。词的使用意味着要用它进行计算,当决策者直接用词进行评价时,基于语言术语集的三支决策模型无法处理这些语言信息,所以我们提出了一个基于词计算的三支决策方法。本文研究的主要内容如下:(1)首先,基于词计算的思想,我们提出了一个将词转化为一个给定语言术语集上语言分布评估的算法。我们将语言术语集视为一些特殊词所组成的集合,并提出了一个基于词计算的转换算法,该算法将词转化为一个给定语言术语集上的语言分布评估,即用一些已有的语言术语的分布来描述词。通过一个转换,我们有望处理更多的语言信息。(2)其次,结合决策理论粗糙模糊集的优点,我们提出了一个基于决策理论粗糙模糊集的词环境下的三支决策。考虑各个属性的权重可能不同,以及决策者对各个属性的重要度也可能用词进行评价,所以我们提出了一个基于层次分析法的属性权重获取方法。然后,我们将属性的值和损失函数的值推广到词的环境下,并利用提出的转换算法对语言信息进行处理,同时给出了条件概率和阈值的计算方法。相比于传统的基于语言术语集的三支决策模型,我们的模型处理语言信息的范围更广,且决策者在表达语言信息上更加的灵活。另外,区间二型模糊集作为一型模糊集的拓展,在表达不确定信息上优于一型模糊集,但计算会更加复杂。为了提高模型处理不确定信息的能力,在一型模糊集的基础上,我们还研究了基于区间二型模糊集的多属性三支决策。更多还原

【Abstract】 As a decision-making tool that is more in line with human thinking,threeway decision reduces the loss caused in the decision-making process by introducing accept,reject,and delay decision.Due to the complexity of practical problems and the ambiguity of information,it is difficult for decision makers to give quantitative evaluations directly,but to use language to give qualitative evaluations.In order to better express linguistic information,linguistic term sets are extended to hesitant fuzzy linguistic term sets,double hierarchy linguistic term sets,probabilistic linguistic term sets and so on.Three-way decisions based on these linguistic term sets are also being studied.However,it is not easy to directly give linguistic evaluations in the form of these linguistic term sets,and decision makers may directly use the words that are suitable for evaluation.Words can be represented as fuzzy sets over a basic set whose semantics can be represented by membership functions.The use of words means that they are used for computation.When decision makers use words to evaluate directly,the three-way decision model based on linguistic term sets cannot process these linguistic information.So we propose a three-way decision method based on computing with words.The main contents of this paper are given as follows:(1)First,based on the idea of computing with words,we propose an algorithm that converts words into the linguistic distribution assessments over a given linguistic term sets.We use treat the linguistic term set as a collection of special words,and propose a transformation algorithm based on computing with words.The algorithm converts words into linguistic distribution assessments over a given linguistic term set,that is,words are described by the distribution of some existing linguistic terms.With one transformation,we can process more linguistic information.(2)Secondly,combined with the advantages of decision-theoretic rough fuzzy sets,we propose a three-way decision based on decision-theoretic rough fuzzy sets in the environment of words.Considering that the weights of each attribute may be different,and the evaluation of each attribute by decision makers may also be evaluated by words,so we propose an attribute weight acquisition method based on analytic hierarchy process.Then,we generalize the values of attributes and the values of loss functions to the context of words,and use the proposed transformation algorithm to process the linguistic information,and also give the calculation methods of conditional probability and thresholds.Compared with the traditional three-way decision model based on linguistic term sets,our model processes a wider range of linguistic information,and the decision maker is more flexible in expressing linguistic information.In addition,interval type-2 fuzzy sets,as an extension of type-1 fuzzy sets,are superior to type-1 fuzzy sets in expressing uncertain information,but the calculation will be more complicated.In order to improve the ability of the model to deal with uncertain information,on the basis of type-1 fuzzy sets,we also study the multi-attribute three-way decision based on interval type-2 fuzzy sets.更多还原