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Fuzzy Modeling with Population-based Optimization: Design and Analysis

  • Author / Creator
    Safari Mamaghani, Ali

  • Fuzzy Rule-based Systems (FRBS) form a commonly encountered category of fuzzy models and play an essential role by developing a human-centric modeling framework. Fuzzy rule-based modeling aims at identifying the structure and the parameters of “if-then” fuzzy rules so that a desired input/output mapping is achieved. One of the most widely-used architectures in fuzzy modeling come in the form of Takagi–Sugeno–Kang (TSK) rules (“if-then” rules), which use linear or, more generally, local polynomial functions in the conclusions (consequences) of the rules, rather than linguistic terms (fuzzy sets).
    This dissertation's primary aim is concerned with the structural identification and parametric optimization of data-driven fuzzy models using some population-based optimization methods. Three different architecture are introduced and studied.
    In the first architecture, the TSK model's structural optimization is achieved by the particle swarm optimization (PSO), with the intent of its complexity management. This is accomplished in two ways: (i) by structuralization of the antecedents and (ii) by structuralization of the consequences of the fuzzy rules. More specifically, this study contributes to the complexity management of fuzzy models by focusing on (i) the efficient arrangement (reduction) of the input spaces over which the antecedents of rules are formed and (ii) allocating the orders of local polynomial functions across the consequences of the rules. This architecture's originality comes with the flexibility of FRBS that is endowed by admitting variability of input spaces standing in the antecedents of different rules and the variability of orders of polynomials (local functions) forming the consequences of the rules. PSO as an optimization vehicle is guided by the root mean squared error (RMSE) accuracy criterion to realize the efficient arrangement of input spaces and an allocation of the orders of the individual polynomials. In this optimization process, the Fuzzy C-Means (FCM) algorithm is employed to create fuzzy sets in the rules' antecedents, while the standard Least Square Error (LSE) optimization criterion is minimized to determine the coefficients of the polynomials in the consequences. The proposed model's performance is quantified using numeric data, including both synthetic and machine learning datasets.
    The second architecture in this dissertation is realized with the aid of genetic programming (GP). The proposed architecture employs GP to form fuzzy logic expressions involving logic operators and information granules (fuzzy sets) located in the input space, and used to predict information granules in the output space. We propose an architecture realizing logic processing, with the structural optimization of the model accomplished by multi-tree genetic programming and the parametric optimization completed by gradient-based learning. The granulation of information used in this architecture is developed using the FCM clustering algorithm. The novelty of this study is two-fold: (i) it comes with the flexibility of the logic-oriented structure of fuzzy models, and (ii) our architecture is designed to handle high-dimensional data by alleviating the detrimental effect of distance concentration hampering the effectiveness of standard TSK FRBS. The study is illustrated through some experiments that give a detailed insight into the fuzzy models' performance. A comprehensive comparative analysis is also covered.
    The third architecture in this dissertation aimed at the generalization of the TSK FRBS. In the current literature, most of the TSK models with polynomial (linear) consequences have been studied; however, the TSK models' design with non-linear consequences has not been discussed to a great extent. The originality of the introduced architecture comes with the TSK model's generalization, which employs a family of non-linear and linear local models rather than only linear models forming the rules’ consequences. The proposed modification reduces the model’s complexity (number of rules) while preserving the desired accuracy. The introduced architecture benefits from PSO and LSE to extract the consequences, whereas fuzzy sets standing in the antecedents of rules are formed by the FCM clustering algorithm.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-a78g-2c69
  • License
    This thesis is made available by the University of Alberta Libraries 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.