Type-2 Fuzzy Broad Learning System
Abstract : The broad learning system (BLS) has been identified as an important research topic in machine learning. However, the typical BLS suffers from poor robustness for uncertainties because of its characteristic of the deterministic representation. To overcome this problem, a type-2 fuzzy BLS (FBLS) is designed and analyzed in this article. First, a group of interval type-2 fuzzy neurons was used to replace the feature neurons of BLS. Then, the representation of BLS can be improved to obtain good robustness. Second, a fuzzy pseudoinverse learning algorithm was designed to adjust the parameter of type-2 FBLS. Then, the proposed type-2 FBLS was able to maintain the fast computational nature of BLS. Third, a theoretical analysis on the convergence of type-2 FBLS was given to show the computational efficiency. Finally, some benchmark and practical problems were used to test the merits of type-2 FBLS. The experimental results indicated that the proposed type-2 FBLS can achieve outstanding performance.
? One of the motivations for using simulated annealing with fuzzy systems is that it does not require the existence of mathematical properties such as differentiability in the problem, which allows the possibility of using all fuzzy structure components including non-differentiable t-norms and non-differentiable membership functions.
? However, the existence of uncertainties and lack of information in many real-world problems makes it difficult to model such problems using expert knowledge only.
? These uncertainties exist in a large number of real-world applications.
? Therefore, the existence of uncertainties in the majority of real-world applications makes the use of type-1 fuzzy logic inappropriate in many cases especially with problems related to inefficiency of performance in fuzzy logic control.
? We also wish to mention that Tu¨rksen and his students, beginning with, have written on the important problem of how to elicit information from a subject and how that information can then be mapped into the MF of a T1 FS.
? Once it was clear what could be done with T1 FSs, it was only natural for people to then look at more challenging problems.
? It is possible to formulate and solve forward problems, i.e. to go from parametric IT2 FS models to data with associated uncertainty bounds.
? There still may be a problem to use an IT2 FLS for real-time applications, because of the computational bottleneck of TR.
• Many approaches have been proposed to learn and tune type-1 and type-2 fuzzy logic systems including search algorithms such as genetic algorithms and particle swarm algorithms, as well as local search algorithms and classical learning methods.
• There are some representations for type-2 fuzzy sets that have been proposed in the literature such as vertical-slice representation, wavy-slice representation, geometric representation, alpha-planes, alpha cuts and Z-slices.
• Our proposed practical design methodology aims to reduce the computations needed to get the best footprint of uncertainty (FOU).
• The collapsing method proposed in has been used to calculate the centroids of the interval type-2 sets needed to compute the center-of-area.
? It is one of the most useful results in T2 FS theory because it can be used to derive many things that are associated with that theory, both old and new, in a simple and straightforward manner.
? Arbitrary traditional t-norms (or s-norms) can be used to calculate these functions.
? A tremendously useful feature of this approach is that the resultant MF preserves triangular shapes of the two arguments, and this way the approximate t-norms can be expanded to multi-argument form.
? We begin by specializing the Representation Theorem to IT2 FSs, because it has been and continues to be widely used for such FSs.
? So, a by-product of T2 works, the KM algorithms, can now be used to compute the solution to a non-T2 problem, the FWA.
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