几种度量下Lukasiewicz型直觉模糊推理三Ⅰ算法的性质分析

发布时间：2018-12-14 06:20

【摘要】：直觉模糊集作为模糊集概念的推广,由于它借助隶属度和非隶属度来刻画事物的模糊性,可同时表示模糊现象中的“支持”、“中立”和“反对”三种状态,因此在模式识别、机器学习及图像处理等领域得到广泛的应用.作为模糊推理的推广,直觉模糊推理的核心问题是求解直觉Fuzzy Modus Ponens(IFMP)和直觉Fuzzy Modus Tollens(IFMT)问题,而某种推理算法能否在实际中得到应用取决于该推理算法性质的优劣,本文主要研究了直觉模糊推理三Ⅰ算法的相关性质,主要内容如下:(1)在有限论域的情形下,利用模糊集间的Hamming距离定义了直觉模糊集之间的Hamming距离,从而建立了有限论域上的直觉模糊度量空间.针对无穷论域,利用模糊集间的自然距离定义了两种直觉模糊集之间的自然距离,从而建立了无穷论域上的直觉模糊度量空间.(2)在直觉模糊度量空间中研究了Lukasiewicz型直觉模糊推理三Ⅰ算法的连续性和逼近性.(3)在直觉模糊度量空间中研究了Lukasiewicz型直觉模糊推理三Ⅰ算法的鲁棒性.
[Abstract]:As an extension of the concept of fuzzy sets, intuitionistic fuzzy sets can represent the "support", "neutrality" and "opposition" of fuzzy phenomena by virtue of membership degree and non-membership degree to describe the fuzziness of things, so they are used in pattern recognition. Machine learning and image processing are widely used. As a generalization of fuzzy reasoning, the core problem of intuitionistic fuzzy reasoning is to solve intuitionistic Fuzzy Modus Ponens (IFMP) and intuitionistic Fuzzy Modus Tollens (IFMT) problems. Whether a certain reasoning algorithm can be applied in practice depends on the properties of the reasoning algorithm. In this paper, we mainly study the related properties of the three 鈪，

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