Abstract-Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve interpretability of fuzzy logic systems (FLSs). In recent years, a variety of indices have been proposed to measure the interpretability of FLSs such as the Nauck index and Fuzzy index. However, interpretability indices associated with HFSs have not so far been discussed. The structure of HFSs, with multiple layers, subsystems, and varied topologies, is the main challenge in constructing interpretability indices for HFSs. Thus, the comparison of interpretability between FLSs and HFSs-even at the index level-is still subject to open discussion. This paper begins to address these challenges by introducing extensions to the FLS Nauck and Fuzzy interpretability indices for HFSs. Using the proposed indices, we explore the concept of interpretability in relation to the different structures in FLSs and HFSs. Initial experiments on benchmark datasets show that based on the proposed indices, HFSs with equivalent function to FLSs produce higher indices, i.e. are more interpretable than their corresponding FLSs.

No abstract

In recent years, researchers have become increasingly more interested in designing an interpretable Fuzzy Logic System (FLS). Many studies have claimed that reducing the complexity of FLSs can lead to improved model interpretability. That is, reducing the number of rules tends to reduce the complexity of FLSs, thus improving their interpretability. However, none of these studies have considered interpretability and complexity from human perspectives. Since interpretability is of a subjective nature, it is essential to see how people perceive interpretability and complexity particularly in relation to creating FLSs. Therefore, in this paper we have investigated this issue using an initial user study. This is the first time that a user study has been used to assess the interpretability and complexity of designs in relation to creating FLSs. The user study involved a range of expert practitioners in FLSs and received a diverse set of answers. We are interested to see whether, from the perspectives of people, FLSs are necessarily more interpretable when they are less complex in terms of their design. Although the initial user study is based on small samples (i.e., 25 participants), nevertheless this research provides initial insight into this issue that motivates our future research.

No abstract

Hierarchical fuzzy systems (HFSs) have been shown to have the potential to improve the interpretability of fuzzy logic systems (FLSs). However, challenges remain, such as: "How can we measure their interpretability?", "How can we make an informed assessment of how HFSs should be designed to enhance interpretability?". The challenges of measuring the interpretability of HFSs include issues such as their topological structure, the number of layers, the meaning of intermediate variables, and so on. In this paper, an initial framework to measure the interpretability of HFSs is proposed, combined with a participatory user design process to create a specific instance of the framework for an application context. This approach enables the subjective views of a range of practitioners, experts in the design and creation of FLSs, to be taken into account in shaping the design of a generic framework for measuring interpretability in HFSs. This design process and framework are demonstrated through two classification application examples, showing the ability of the resulting index to appropriately capture interpretability as perceived by system design experts.