Generalization of adaptive neuro-fuzzy inference systems

Area of Science:

• Computational Intelligence
• Machine Learning
• Fuzzy Systems

Background:

• Adaptive network-based fuzzy inference systems (ANFIS) are powerful tools for system modeling.
• Existing ANFIS models primarily rely on Takagi-Sugeno (TS) or compositional rule of inference (CRI) models.
• There is a need for more generalized fuzzy inference systems to handle diverse system complexities.

Purpose of the Study:

• To extend the adaptive network-based fuzzy inference systems (ANFIS) to a generalized ANFIS (GANFIS).
• To propose a generalized fuzzy model (GFM) and a generalized radial basis function (GRBF) network.
• To demonstrate the application of GANFIS for modeling complex multivariable systems, such as the stock market.

Main Methods:

• Development of a generalized fuzzy model (GFM) incorporating properties of both TS and CRI models.
• Introduction of a generalized radial basis function (GRBF) network with a generalized Gaussian function.
• Establishing the functional equivalence between GRBF networks and GFM, enabling GRBF to learn GFM parameters.

Main Results:

• The proposed GFM can be converted to either the TS-model or the CRI-model under specific conditions.
• The GRBF network architecture is designed to effectively learn GFM parameters.
• The study investigates normalized versus non-normalized GRBF networks and an error surface symmetry property.

Conclusions:

• The generalized ANFIS (GANFIS) provides a more flexible and comprehensive framework for fuzzy inference.
• The GRBF network serves as an effective learning mechanism for the proposed GFM.
• GANFIS demonstrates potential for modeling complex, multivariable systems like financial markets.