In previous studies, based on picture fuzzy sets, full implication algorithm and quintuple implication principle have been studied. The problem is, full implication algorithm did not consider the relationship between the input and antecedent of rule, while quintuple implication principle only considered the inclusion relationship between the rule’s antecedent and input. Both algorithms did not consider the similarity of rule’s antecedent and input. This leads to unreasonable calculation results in some cases. Therefore, we study fuzzy reasoning methods based on picture similarity measure for generalized modus ponens and generalized modus tollens in this paper. First of all, based on picture biresiduation, a new picture similarity measure between picture fuzzy sets is constructed. Then, representations of solutions of fuzzy reasoning methods based on picture similarity measure are given. Moreover, reducibility and robustness of fuzzy reasoning methods based on picture similarity measure are studied. Finally, two issues related to medical diagnosis are addressed by the proposed methods, demonstrate the rationality and effectiveness of our suggested methods.

中文翻译：

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基于图片相似度度量的模糊推理方法及其在医学诊断中的应用

以往的研究中，基于图像模糊集，研究了全蕴涵算法和五元蕴涵原理。问题在于，完全蕴涵算法没有考虑规则的输入与前件之间的关系，而五元蕴涵原理只考虑了规则的前件与输入之间的包含关系。两种算法都没有考虑规则的前件和输入的相似性。这在某些情况下会导致计算结果不合理。因此，本文研究了基于图片相似度测度的广义前取件和广义托伦斯模糊推理方法。首先，基于图片双残差，构造了一种新的图片模糊集之间的图片相似度度量。然后，给出了基于图片相似性度量的模糊推理方法的解的表示。此外，还研究了基于图片相似性度量的模糊推理方法的可归约性和鲁棒性。最后，所提出的方法解决了与医学诊断相关的两个问题，证明了我们所提出的方法的合理性和有效性。