二型直觉模糊集

二型模糊集和直觉模糊集都具有很强的实际应用背景.二型模糊集增强了系统处理不确定性的能力,直觉模糊集为解决人们判断问题所出现的犹豫信息提供了理论依据.本文在二型模糊集和直觉模糊集的基础上,给出了二型直觉模糊集的概念,证明了二型直觉模糊集是一型模糊集、直觉模糊集、区间值模糊集、区间值直觉模糊集的广义形式,讨论了二型直觉模糊集的基本运算和二型直觉模糊关系.最后,研究了基于二型直觉模糊理论的近似推理,并实例说明了二型直觉模糊集的实际应用背景.

Type-2 intuitionistic fuzzy sets

Type-2 fuzzy sets and intuitionistic fuzzy sets have a wide range of practical applications. Type-2 fuzzy sets enhance the ability of the system for dealing with uncertainties. Intuitionistic fuzzy sets provide a theoretical basis to manage the hesitation information appearing to people in judging questions. In this paper, we introduce the concept of type-2 intuitionistic fuzzy sets under type-2 fuzzy sets and intuitionistic fuzzy sets. Furthermore, we prove that type-2 intuitionistic fuzzy sets are the generalized forms of type-1 fuzzy sets, intuitionistic fuzzy sets, interval-valued fuzzy sets and interval-valued intuitionistic fuzzy sets. The basic operations of type-2 intuitionistic fuzzy sets and type-2 intuitionistic fuzzy relations are discussed. Finally, the approximation reasoning based on the type-2 intuitionistic fuzzy theory is studied. A practical example illustrates the practical application background of type-2 intuitionistic fuzzy sets.