直觉模糊推理SIS算法的统一形式及其性质研究
发布时间：2019-01-05 18:28
【摘要】：直觉模糊集作为模糊集的推广,它引入了真隶属度和假隶属度的概念,可以更广泛的解释事物或现象的不确定性.并且与模糊推理研究方法类似,直觉模糊推理的核心问题是求解直觉模糊取式(简称IFMP)和直觉模糊拒取式(简称IFMT).目前,模糊推理的CRI算法和三I算法已经被成功地推广到直觉模糊推理的框架之下,而与CRI算法和三I算法相比,模糊推理的SIS算法具有无条件还原性的优点,本文拟将模糊推理的SIS算法推广到直觉模糊推理的框架下并研究该算法的相应性质.本文主要研究三部分内容,首先,我们在剩余型直觉模糊蕴涵算子的统一框架下,提出了求解直觉模糊推理IFMP问题及IFMT问题的SIS算法并给出了解的统一表达式,证明了剩余型直觉模糊推理的SIS算法是不需要附加任何条件的还原算法,并且讨论了剩余型直觉模糊推理SIS算法的-水平解.其次,研究了求解Lukasiewicz型直觉模糊推理IFMP及IFMT问题的SIS算法的连续性,并证明了该算法关于两种直觉模糊自然距离都是连续的.最后,研究了求解Lukasiewicz型直觉模糊推理IFMP及IFMT问题的SIS算法关于两种直觉模糊自然距离的鲁棒性.
[Abstract]:As a generalization of fuzzy sets, intuitionistic fuzzy sets introduce the concepts of true membership and false membership, which can explain the uncertainty of things or phenomena more widely. And similar to the research method of fuzzy reasoning, the core problems of intuitionistic fuzzy reasoning are solving intuitionistic fuzzy selection (IFMP) and intuitionistic fuzzy rejection (IFMT). At present, the CRI algorithm and the triple I algorithm of fuzzy reasoning have been successfully extended to the framework of intuitionistic fuzzy reasoning. Compared with the CRI algorithm and the triple I algorithm, the SIS algorithm of fuzzy reasoning has the advantage of unconditional reducibility. In this paper, the SIS algorithm of fuzzy reasoning is extended to the framework of intuitionistic fuzzy reasoning and the corresponding properties of the algorithm are studied. In this paper, we mainly study three parts. Firstly, under the unified framework of residual intuitionistic fuzzy implication operator, we propose a SIS algorithm for solving intuitionistic fuzzy reasoning IFMP problem and IFMT problem, and give the unified expression of the solution. It is proved that the SIS algorithm of residual intuitionistic fuzzy reasoning is a reduction algorithm without any conditions, and the horizontal solution of the residual intuitionistic fuzzy reasoning SIS algorithm is discussed. Secondly, the continuity of the SIS algorithm for solving the IFMP and IFMT problems of Lukasiewicz type intuitionistic fuzzy reasoning is studied, and it is proved that the algorithm is continuous for both intuitionistic fuzzy natural distances. Finally, the robustness of the SIS algorithm for solving the IFMP and IFMT problems of Lukasiewicz type intuitionistic fuzzy reasoning is studied on the two kinds of intuitionistic fuzzy natural distances.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
本文编号：2402141
[Abstract]:As a generalization of fuzzy sets, intuitionistic fuzzy sets introduce the concepts of true membership and false membership, which can explain the uncertainty of things or phenomena more widely. And similar to the research method of fuzzy reasoning, the core problems of intuitionistic fuzzy reasoning are solving intuitionistic fuzzy selection (IFMP) and intuitionistic fuzzy rejection (IFMT). At present, the CRI algorithm and the triple I algorithm of fuzzy reasoning have been successfully extended to the framework of intuitionistic fuzzy reasoning. Compared with the CRI algorithm and the triple I algorithm, the SIS algorithm of fuzzy reasoning has the advantage of unconditional reducibility. In this paper, the SIS algorithm of fuzzy reasoning is extended to the framework of intuitionistic fuzzy reasoning and the corresponding properties of the algorithm are studied. In this paper, we mainly study three parts. Firstly, under the unified framework of residual intuitionistic fuzzy implication operator, we propose a SIS algorithm for solving intuitionistic fuzzy reasoning IFMP problem and IFMT problem, and give the unified expression of the solution. It is proved that the SIS algorithm of residual intuitionistic fuzzy reasoning is a reduction algorithm without any conditions, and the horizontal solution of the residual intuitionistic fuzzy reasoning SIS algorithm is discussed. Secondly, the continuity of the SIS algorithm for solving the IFMP and IFMT problems of Lukasiewicz type intuitionistic fuzzy reasoning is studied, and it is proved that the algorithm is continuous for both intuitionistic fuzzy natural distances. Finally, the robustness of the SIS algorithm for solving the IFMP and IFMT problems of Lukasiewicz type intuitionistic fuzzy reasoning is studied on the two kinds of intuitionistic fuzzy natural distances.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159
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