Design of fuzzy rule-based models with fuzzy relational factorization

Abstract

This study opens an original avenue of designing interpretable fuzzy rule-based models realized in the presence of data characterized by a large number of attributes (input variables). In the presence of such high-dimensional data, the development of rule-based models faces serious challenges both at the design and interpretability level. To address these two problems, we develop a new architecture of the rules and establish a two-step design process. First, the dimensionality reduction is realized with the aid of a fuzzy relational matrix factorization which transforms original fuzzy set-based encoded variables and yields a logic-oriented level of activation of individual rules. The results of relational factorization are logic expressions built over the encoded input variables forming condition parts of the rules. Second, the conclusions of the rules are built by optimizing local functions (both constant and linear functions are considered). A number of experiments are reported along with comparative studies involving a standard Takagi-Sugeno (TS) model.