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摘要翻译：
Novotny和Pawlak([8,9,10])提出了三种近似（粗糙）等式，以使用户的知识参与确定在数学意义上可能不相等的集合的相等性。这些概念是由Tripathy、Mitra和Ojha([13])推广的，他们引入了集合的近似（粗糙）等价的概念。粗糙等价在比粗糙等价更高的层次上捕获集合的相等性。在[14]中建立了这些概念的更多性质。结合这两类近似等式的条件，Tripathy[12]又引入了两个近似等式，并对它们的相对效率进行了比较分析。文[15]通过考虑粗糙模糊集而不是只考虑粗糙集，推广了这四类近似等式。事实上，引入了水平近似等式的概念，并研究了它的性质。在本文中，我们引入并研究了基于粗糙直觉模糊集而不是粗糙模糊集的近似等式。即我们引入了直觉模糊集的近似（粗糙）等式的概念，并研究了它们的性质。我们给出了一些实际的例子来说明模糊集的粗糙等式和直觉模糊集的粗糙等式的应用。
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英文标题：
《Approximate Equalities on Rough Intuitionistic Fuzzy Sets and an
Analysis of Approximate Equalities》
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作者：
B. K. Tripathy, G. K. Panda
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最新提交年份：
2012
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equalities were introduced by Tripathy [12] and a comparative analysis of their relative efficiency was provided. In [15], the four types of approximate equalities were extended by considering rough fuzzy sets instead of only rough sets. In fact the concepts of leveled approximate equalities were introduced and properties were studied. In this paper we proceed further by introducing and studying the approximate equalities based on rough intuitionistic fuzzy sets instead of rough fuzzy sets. That is we introduce the concepts of approximate (rough)equalities of intuitionistic fuzzy sets and study their properties. We provide some real life examples to show the applications of rough equalities of fuzzy sets and rough equalities of intuitionistic fuzzy sets.
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PDF链接：
https://arxiv.org/pdf/1205.5866
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