Abstract
Hierarchical fuzzy systems (HFSs) have been regarded as a useful solution for overcoming the major issues in fuzzy logic systems (FLSs), i.e., rule explosion due to the increase in the number of input variables. In HFS, the standard FLS are reformed into a low-dimensional FLS subsystem network. Moreover, the rules in HFS usually have antecedents with fewer variables than the rules in standard FLS with equivalent functions, because the number of input variables in each subsystem is less. Consequently, HFSs manage to decrease rule explosion, which minimises complexity and improves model interpretability. Nevertheless, the issues related to the question of “Does the complexity reduction of HFSs that have multiple subsystems, layers and different topologies really improve their interpretability?” are not clear and persist. In this paper, a comparison focusing on interpretability and complexity is made between two HFS’ topologies: parallel and serial. A detailed measurement of the interpretability and complexity with different configurations for both topologies is provided. This comparative study aims to examine the correlation between interpretability and complexity in HFS.
Highlights
The In a range of applications, interpretability is recognised as one of the most desirable features of fuzzy systems [1], especially in those with considerable human involvement, where it is a must [2]
The experiment aims to investigate the relationship between the interpretability and complexity of different hierarchical fuzzy systems (HFSs), i.e., parallel and serial, using the proposed method
In conclusion, we have proposed a method for systematically comparing the HFS topologies
Summary
The In a range of applications, interpretability is recognised as one of the most desirable features of fuzzy systems [1], especially in those with considerable human involvement, where it is a must [2]. The curse of dimensionality, on the other hand, is a fundamental drawback of traditional fuzzy systems: the number of needed rules rises exponentially with the number of input variables [8]. This problem, known as rule explosion, has the potential to reduce the openness and interpretability of FLSs [9]. The most extreme rule reduction is if the HFS structure has two input variables for each low-dimensional FLS and has (n − 1) layers [10]. The total of rules (R) is a linear function [16] of the total of the input variables n and can be represented as:
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