W4: Smooth Fuzzy Models for Dimension Reduction in Data Driven Systems (109)

Description

Presenters: Ebrahim Navid Sadjadi, University of Carlos III in Madrid, Mohammad Bagher Menhaj, Amirkabir University of Technology, Iran

The objective of this half-day workshop is to cover the state-of-the-art in modeling and analysis of the fuzzy models for dimension reduction of the systems represented by their input-output data. During the last years, we have witnessed major successes of fuzzy logic systems in the academia and industries; from the analysis of data of the customers in online marketing, to fast detection of diseases like cancer, classification of the complex images, and generation of captions for the images in the personalized media of the incomplete and noisy information. In many applications, fuzzy models could outperform all the existing machine learning and model-based control methods. Hence, they are one of the few areas that receive on-going interest of the researchers and engineers. Although fuzzy models have been employed for a long time so far, however, the recent research in the fuzzy systems demonstrate that some kinds of fuzzy compositions can enlarge the design space into the higher dimensions through the Fourier expansion of the membership functions and thereby, facilitate the frequency analysis and modeling of the nonlinear system with the fuzzy models. Frequency analysis of the fuzzy models could facilitate the modeling and analysis of the nonlinear systems in the different aspects. First is the dedication of the sufficient number of rules for the fuzzy models, which avoids making the fuzzy structure complicated beyond what is really required. The contribution in this area could facilitate the understanding, utilization and tuning of the fuzzy models, plus improvement in the performance of the consequent algorithms. The second is the ability to handle the systems disturbances and noises soft and smoothly. The increase of the system robustness will facilitate the operation of the industrial processes inside their margins and respect to the operational limits. The third aspect is the ability to perform on-line and fast processing and decision making tasks in the compressed space, considering the computational complexities of the data driven processes. Hence, the purpose of providing this workshop is to give a detailed introduction to the recent developments in the fuzzy systems for the researchers, graduate students and practitioners. The main focus of the course is on comprehensive study of the new achievements on the structural properties of fuzzy models with the smooth compositions for the dimension reduction. Therefore, the novelty in this half-day workshop is the comprehensive coverage of the state-of-the-art in the application of the smooth fuzzy models for dimension reduction of the data driven process with the special attention to the frequency analysis of the control systems, identification processes and the signal processing applications. We also will present some examples of the employment of the smooth fuzzy models in image processing and biomedical engineering.

Schedule

1. Introduction of the fuzzy theories, algorithms, and implementation of fuzzy systems

• Fuzzy compositions
• Fuzzy relational equations
• Smooth TS fuzzy models

2. Structural properties of the smooth fuzzy systems

• Approximation properties of the smooth fuzzy models
• Monotonicity of the smooth fuzzy models
• Stability of the smooth fuzzy systems
• Optimization based control of the smooth fuzzy systems

3. Applications of the smooth fuzzy models and their properties

• Smooth fuzzy model identification
• Smooth fuzzy models for self-learning
• Some structural comparisons to the classical fuzzy approaches
• Application to the nonlinear systems (e.g. chemical processes, biomedical engineering, automotive industry, etc.)

4. Analysis of the smooth fuzzy models in the frequency domain

• New architectures for the fuzzy model representation
• Two useful techniques for estimation of the sufficient number of fuzzy rules
• Applications to the image processing

5. Some challenging problems and concluding remarks