Combinatorics

Fuzzy set operations

Defuzzification

Mathematics

Mathematical optimization

Evolutionary algorithm

Artificial intelligence

Fuzzy control system

Fuzzy number

Interval (graph theory)

Interpretability

Fuzzy rule

Computer science

Fuzzy set

Membership function

Fuzzy logic

IEEE Transactions on Fuzzy Systems

This article proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets (FSs) can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 FSs, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 FSs, there are both type-1 FSs and interval type-2 FSs in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty of the interval type-2 (IT2) FS is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of FSs is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and FS updating algorithm is employed to initialize the reference rule base and the type of FS, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

Multiobjective Optimization Design of Interpretable Evolutionary Fuzzy Systems With Type Self-Organizing Learning of Fuzzy Sets