二型模糊系统降型算法综述

二型模糊系统降型过程的计算精度、计算时间和系统信息的损失会对整个二型模糊系统的性能产生很大地影响. 本文首先介绍了二型模糊集合的基本概念及二型模糊系统的计算过程，然后分别对区间二型模糊系统和广义二型模糊系统的降型算法的研究现状进行了详细综述，并对不同降型算法计算的复杂性进行了全面的分析和比较. 最后，总结了各类降型算法存在的问题，并给出了未来研究的展望. 指出，降型算法的计算成本仍是提升二型模糊系统性能的瓶颈，从理论上完善各种降型算法，通过数学方法解决其计算的复杂性问题，并将其应用于实时系统会是未来研究的重点. 

Overview of Type-Reduction Algorithms for Type-2 Fuzzy Logic Systems

The computation precision, computation time, and the loss of system information of the type-reduction process have a great influence on the performance of type-2 fuzzy logic systems. In this paper, the basic concept of type-2 fuzzy sets and the computation process of type-2 fuzzy logic systems are briefly introduced. Then, a detailed review of the research on type-reduction algorithms is given for both interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems. The computational complexity of different type-reduction algorithms is analyzed and compared. Finally, the problems faced with each type-reduction algorithm are summarized, and potential future research directions are presented. The computation cost of type-reduction algorithms remains as the bottleneck in type-2 fuzzy logic system improvement. The key direction of future research should be the improvement of the theory behind type-reduction algorithms, the solving of the computational complexity through mathematical methods, and applying this to real-time systems.