Extension of Restricted Equivalence Functions and Similarity Measures for Type-2 Fuzzy Sets
Extension of Restricted Equivalence Functions and Similarity Measures for Type-2 Fuzzy Sets
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DOI：
10.1109/tfuzz.2021.3136349
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发表时间：
2022-09
影响因子：
11.9
通讯作者：
Laura De Miguel;R. Santiago;Christian Wagner;J. Garibaldi;Z. Takác̆;A.F. Roldan Lopez de Hierro;H. Bustince
中科院分区：
文献类型：
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作者：
Laura De Miguel;R. Santiago;Christian Wagner;J. Garibaldi;Z. Takác̆;A.F. Roldan Lopez de Hierro;H. Bustince
在这项工作中，我们推广的限制等价函数的概念，2型模糊集，导致扩展的限制等价函数的概念。我们还研究了如何在适当的条件下，这些新的功能恢复的标准公理限制等价功能的真实的设置。扩展的限制等价函数允许我们比较任何两个一般的2型模糊集，并生成2型模糊集的相似性度量。这种相似性的结果是同一参考集上的模糊集（即，域）作为所考虑的类型2模糊集。后者对于可解释的人工智能和决策等应用至关重要，因为它可以直观地解释模糊集的特定领域上下文中的相似性。我们展示了如何可以使用这种措施来比较2型模糊集与不同的隶属函数，以这样一种方式，连接到2型模糊集的不确定性不会丢失。这是通过生成模糊集而不是单个数值来实现的。此外，我们还展示了如何获得离散参考集的数值。
In this work, we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence functions allow us to compare any two general type-2 fuzzy sets and to generate a similarity measure for type-2 fuzzy sets. The result of this similarity is a fuzzy set on the same referential set (i.e., domain) as the considered type-2 fuzzy set. The latter is crucial for applications such as explainable AI and decision-making, as it enables an intuitive interpretation of the similarity within the domain-specific context of the fuzzy sets. We show how this measure can be used to compare type-2 fuzzy sets with different membership functions in such a way that the uncertainty linked to type-2 fuzzy sets is not lost. This is achieved by generating a fuzzy set rather than a single numerical value. Furthermore, we also show how to obtain a numerical value for discrete referential sets.