关于模糊蕴涵及其应用的研究

发布时间：2018-08-09 11:16

【摘要】：模糊蕴涵作为重要的连接词,是通过其单调性和边界条件来定义的,在模糊决策,模糊控制等很多领域都有重要作用.对于模糊蕴涵的性质及其应用已经有许多研究成果.在模糊控制领域,对任意输入值,基于模糊规则库,运用模糊推理机制输出控制结论.模糊推理机制的核心技术之一是使用适当的模糊蕴涵.本文主要研究模糊蕴涵的生成方法,提出几种将多个蕴涵组合在一起生成新蕴涵的方法,并考虑模糊蕴涵算子在模糊推理方面的应用问题.本文的主要研究内容与结论如下:提出一些生成模糊蕴涵的新方法,即通过对一个或多个选定的模糊蕴涵的第一变元和第二变元进行多重迭代,生成一些新的函数形式.经分析得到,当生成这些函数的原蕴涵具有某些性质时,此函数为模糊蕴涵,本文称其为多重模糊蕴涵.进一步,分析选定的模糊蕴涵具有某些好的性质时,生成的多重模糊蕴涵仍保持这些性质,例如:幂等性,单位元,左边界性等.接下来,又研究了一些多重模糊蕴涵满足相互交换律,及与分配律相关的逻辑等式的问题,给出这些逻辑等式成立的充分必要条件.进一步,将以上生成的多重模糊蕴涵应用于全蕴涵推理算法,得到了当全蕴涵算法里面的蕴涵为多重模糊蕴涵时其解的形式.最后,受全蕴涵算法求解原理的启发,利用模糊相似度的概念,提出基于全蕴涵算法的模糊相似度推理算法,给出解的通式,并分析当其中的蕴涵为一些重要蕴涵时其解的形式.这些结果将为模糊蕴涵在模糊推理,模糊控制及模糊决策等领域的应用提供支持.
[Abstract]:As an important conjunction, fuzzy implication is defined by its monotonicity and boundary conditions. It plays an important role in many fields such as fuzzy decision making, fuzzy control and so on. There have been many research results on the properties and applications of fuzzy implication. In the field of fuzzy control, the fuzzy inference mechanism is used to output the control conclusion for any input value based on fuzzy rule base. One of the core technologies of fuzzy reasoning is the use of appropriate fuzzy implication. In this paper, the method of generating fuzzy implication is studied, and several methods of combining multiple implication to generate new implication are put forward, and the application of fuzzy implication operator in fuzzy reasoning is considered. The main contents and conclusions of this paper are as follows: some new methods for generating fuzzy implication are proposed, that is, by iterating the first variable and the second variable of one or more selected fuzzy implication, some new function forms are generated. It is obtained by analysis that when the original implication of generating these functions has some properties, the function is fuzzy implication, which is called multiple fuzzy implication in this paper. Furthermore, when the selected fuzzy implication has some good properties, the generated multiple fuzzy implication still retains these properties, such as idempotent, unit element, left boundary, etc. Then, we study some problems of multiple fuzzy implication satisfying the law of mutual exchange and the logical equality related to the distribution law, and give the necessary and sufficient conditions for these logical equalities to hold. Furthermore, the multiple fuzzy implication generated above is applied to the full implication reasoning algorithm, and the form of the solution is obtained when the implication in the full implication algorithm is multiple fuzzy implication. Finally, inspired by the principle of full implication algorithm, a fuzzy similarity reasoning algorithm based on full implication algorithm is proposed by using the concept of fuzzy similarity, and the general formula of the solution is given. The form of solution is analyzed when the implication is some important implication. These results will support the application of fuzzy implication in fuzzy reasoning, fuzzy control and fuzzy decision making.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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