二型模糊集（T2 FS）由于其对高阶模糊不确定性简洁而深刻的刻画能力，在近年受到研究者们的广泛关注。其中，区间二型模糊集（IT2 FS）因可视性强、较一般二型模糊集简化而成为研究的主要对象。但区间二型模糊系统（IT2 FLS）极高的计算复杂度和对高阶不确定性机理分析的缺失使得相关研究困难重重。复杂度随着不确定性阶的提升呈指数增长，相关成果很难推广到高阶模糊系统。总结以往IT2 FLS的研究工作发现，造成研究难以深入的根本原因在于IT2 FLS采取的“一般分解”方法及降型过程采取的“折衷策略”。在经典IT2 FLS模型中，IT2 FS被分解为若干内嵌一型模糊集（eT1 FS）分别参与计算，得到的所有运算结果按照某种“折衷策略”进行加权组合作为系统输出，由此带来的大量计算在所难免。针对此问题，本课题组提出的自适应循优区间二型模糊系统（AotIT2 FLS）用“含参分解+自适应循优”模型代替“一般分解+折衷策略”模型。该模型将IT2 FS等价表示为含参量化区间二型模糊集（pqIT2 FS）。然后，系统根据当前状态自适应地确定pqIT2 FS中的参数取值，从而唯一确定参与计算的eT1 FS，计算复杂度大大降低。实验表明，AotIT2 FLS在保持经典IT2 FLS逼近能力和鲁棒性的同时在运行速度上得到了显著提升。基于AotIT2 FLS设计的模糊控制器（FLC）在控制性能上较基于经典IT2 FLS构造的FLC有显著提升。生成pqIT2 FS的“生成方式”及根据当前状态自适应确定pqIT2 FS中参数取值的“选择策略”是构造AotIT2 FLS的重点。“生成方式”和“选择策略”多种多样，如何对他们进行构造及组合目前还缺乏研究。一般性理论的缺乏导致设计的AotIT2 FLS性能无法得到保证，在实际应用前也只能依靠对待处理模型的先验知识或反复的实验验证。作为对解决该问题的尝试，本文重点探讨了AotIT2 FLS模型中选择策略的构造及其与pqIT2 FS生成方式的组合问题。本文主要工作如下：1) 综述T2 FS和IT2 FLS的基础理论，详细介绍AotIT2 FLS的相关理论及其中的“生成方式”和“选择策略”。2) 在以正弦函数作为选择策略的AotIT2 FLS中引入正弦函数的频率因子作为自由参数参与训练，构造名为AotIT2-PERT-SIN FLS的系统，对比其与经典IT2 FLS在函数逼近和模糊控制方面的性能，说明AotIT2 FLS理论的优势。3) 提出使用BP神经网络作为选择策略的AotIT2 FLS，命名为AotIT2-PERT-NNET FLS。该工作极大地增加了“选择策略”的自由度，BP神经网络对函数强大的逼近能力使得用它作为选择策略的近似时，系统的性能在理论上能够得到保证。在时间序列预测和模糊控制实验中，系统均表现出了很好的性能。在本文提出的所有模糊系统中，AotIT2-PERT-NNET FLS的函数逼近能力最好。4) 提出使用一型模糊系统作为选择策略的AotIT2 FLS，命名为AotIT2-HOMO-FS FLS。模糊系统良好的函数逼近能力和抗噪能力使得用它作为选择策略的近似时，系统的性能在理论上能够得到保证。在时间序列预测和模糊控制实验中，系统均表现出了很好的性能。在本文提出的所有模糊系统中，AotIT2-HOMO-FS FLS用作模糊控制器时控制过程上升时间最短，超调量最小。5) 论文最后对全文进行了总结和展望。本文提出了具有高自由度选择策略的AotIT2 FLS的设计方法，构造出具有很高实用价值的区间二型模糊系统。本文的研究对AotIT2 FLS的相关理论起到了肯定和完善的作用。

Recently, Type-2 Fuzzy Set (T2 FS) has aroused wide attention from researchers because of its powerful ability of descripting high order fuzzy uncertainties. In order to simplify visualization and computation process, a special T2 FS named Interval Type-2 Fuzzy Set (IT2 FS) and its correlation theory became the focus of attention. High computational complexity in Interval Type-2 Fuzzy Logic System (IT2 FLS) and few studies on mechanisms of high order uncertainty make researches on type-2 fuzzy theory suffer from all kinds of difficulties. As computational complexity grows exponentially with the order of uncertainties, research findings of IT2 FS cannot be easily extended to high order fuzzy systems.Through summarizing previous research findings, we found that root causes of high computational complexity in IT2 FLS are normal decomposition of IT2 FS and aggregation strategy used in output processing. In traditional IT2 FLS, a large numbers of embedded Type-1 Fuzzy Sets (eT1 FSs) are decomposed from IT2 FS and participate in computing separately, the output of system are the weighted combination of all intermediate results using aggregation strategy. That’s why the high computation complexity is inevitable. Our research group proposed a new model of IT2 FLS named Adaptive-Optimal-trajectory-IT2 FLS (AotIT2 FLS) by replacing “general decomposition + aggregation strategy” model with “parametric decomposition + adaptive optimal trajectory” model. In AotIT2 FLS, IT2 FSs are equivalently represented as parametric qualitative Interval Type-2 Fuzzy Sets (pqIT2 FSs). Only one eT1 FS will participate in computing for every single input, which is adaptively chosen by system. In this way, computational complexity is greatly reduced. Experiments shows that AotIT2 FLS has a significantly improvement in running speed while keeping high approximation ability and robustness of classic IT2 FLS. Fuzzy Logic Controller (FLC) based on AotIT2 FLS has a significant controlling performance boost compared with FLC based on classic IT2 FLS.The “generation method” that generates pqIT2 FS and the “choice mechanism” that chooses values of parameter based on current situation are core of constructing AotIT2 FLS. There are many kinds of “generation method” and “choice mechanism”, but how to choose and combine them are not been studied until now. Without general theory, the performance of AotIT2 FLS cannot be guaranteed and large amounts of expert experience about the model to be processed or repeated experiments are required before the designed AotIT2 FLS is used in actual application. As an attempt to solve the problem, this article focuses on how to construct “choice mechanism” and combine it with “generation method” of pqIT2 FS.Main works of this article are listed below:1) Reviewed basic theories of T2 FS, IT2 FLS and AotIT2 FLS. Descripted the “generation method” and “choice mechanism” of AotIT2 FLS in detail. 2) Added frequency factor of SIN function as a free parameter to AotIT2 FLS which uses SIN function as its “choice mechanism” and learned this parameter in training process, the constructed system was named as AotIT2-PERT-SIN FLS. Compared the approximation ability and controlling performance of AotIT2-PERT-SIN FLS and classic IT2 FLS, gave out the advantages of AotIT2 FLS.3) Proposed an AotIT2 FLS named AotIT2-PERT-NNET FLS that using BP neural network as its choice mechanism. This work greatly increased the degree of freedom of "strategy choice". The great function approximation ability of BP neural network guarantees the performance of AotIT2 FLS when using it as the approximation of “choice mechanism”. In time series predicting and fuzzy control experiment, this system got a good performance. AotIT2-PERT-NNET FLS has the best function approximation ability among all the T2 FLSs mentioned in this article.4) Proposed an AotIT2 FLS named AotIT2-HOMO-FS FLS that using fuzzy system as its choice mechanism. The great function approximation ability and good ability to resist noise of fuzzy system guarantees the performance of AotIT2 FLS when using it as the approximation of “choice mechanism”. In time series predicting and fuzzy control experiment, this system got a good performance. When using as fuzzy logic controller, AotIT2-HOMO-FS has the best performance on response time, prediction accuracy and robustness among all the T2 FLS mentioned in this article.5) We summarized the works of this article and give out some prospects in future research.In this article, we proposed several design approaches of AotIT2 FLS which uses “choice mechanism” of high degree of freedom and constructed IT2 FLSs of great application value. Researches in this article also validated and consummated theories of AotIT2 FLS.