2,375 research outputs found

    Interpretability indices for hierarchical fuzzy systems

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    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

    A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

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    In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

    Towards a framework for capturing interpretability of hierarchical fuzzy systems - a participatory design approach

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    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

    A new fuzzy set merging technique using inclusion-based fuzzy clustering

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    This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets

    Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

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    Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf

    Hierarchical Fuzzy Systems: Interpretability and Complexity

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    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
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