Fuzzy Rule-Based Models of High-Dimensional Systems: Design and Analysis

• Author / Creator

  E, Hanyu

• Fuzzy models, especially fuzzy rule-based models, have received substantial attention as an important pursuit in the design and analysis of intelligent systems. In rule-based architectures, functional (Takagi-Sugeno) fuzzy rule-based models have been studied intensively resulting in a wealth of design strategies and applications. Due to the concentration effect, high dimensional data pose a genuine challenge to the efficient development process, quality of the models, and their ensuing interpretability. This research addresses these challenges in several fundamental and original ways.
  First, an original relational factorization based on fuzzy relational calculus and engaging triangular norms and conorms is developed. In terms of the enhancement of models, we propose two schemes. One is to construct a fuzzy rule-based model based on fuzzy relational factorization. The factorization facilitates an interpretable, logic-oriented encoding of conditions of the rules. Thus, the clustering algorithm commonly used in the design of TS models is replaced by the factorization so that the concentration effect is avoided. The other is to introduce and analyze the concept of distributed fuzzy rule-based models. The mechanisms of ensemble learning and gradient boosting are explored to construct the rules. In their realization, the data are sampled randomly and applied to each distributed rule-based model. Then the gradient boosting algorithm is involved to improve the quality of the models. Subsequently, some essential refinements of the fuzzy clustering method used in the formation of conditions of the rules are developed to further enhance the performance of the rule-based models. The augmentations of the clustering algorithm include: (i) an accommodation of extreme (minimal and maximal) values encountered in the output variable, (ii) a reduction of redundancy of the rules which is the result of overlap existing among fuzzy sets forming the condition parts of the rules. (iii) the development of the core (granular) structure of rules and analysis of their features. The proposed methods, novel identification of the major characteristics of data, and a novel construction of the model, constitute the originality of this thesis. The experimental results obtained for publicly available data are reported along with a solid comparative analysis.

• Subjects / Keywords

  • Fuzzy rule-based model
  • High dimensional systems
  • Matrix factorization
  • Information granular
  • Ensemble learning

• Graduation date

  Fall 2022

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/r3-37gb-c830

• License

  This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.