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首页> 外文期刊>IEEE Transactions on Fuzzy Systems >From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures
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From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

机译：从模糊集到区间值和Atanassov直觉模糊集：不同公理测度的统一视图

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摘要

This paper examines a broad collection of axiomatic definitions from various and diverse contexts within the domain of fuzzy sets (FS) to evaluate their respective extensions to the case of interval-valued fuzzy (IVF) sets and intuitionistic fuzzy (IF) sets from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures. This fact allows us to formulate a general procedure that encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of IVF or IF sets from a specific real-valued measure in the context of FSs. These three processes agglutinate a multitude of particular constructions found in the literature.
机译：本文研究了模糊集（FS）范围内来自各种不同上下文的公理定义的广泛集合，以评估它们对于纯纯区间值模糊（IVF）集和直觉模糊（IF）集的情况的扩展正式的观点。我们得出结论，大量此类扩展遵循类似的正式程序。这一事实使我们能够制定一个通用程序，将所有已审查的扩展作为特定情况包含在内。新的通用公式使我们能够确定三种不同的程序，以便从FS的特定实值度量中得出IVF或IF集领域的相应扩展。这三个过程凝集了文献中发现的许多特殊结构。

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