Grid Partitioning And Rough Set Method Approach For Fuzzy Rule Generation

Abstract

The generation of accurate and interpretable fuzzy rules plays a crucial role in various data analysis and decision-making systems. In this research, we propose a mathematical model based on grid partitioning and the rough set method for fuzzy rule generation. The model combines the advantages of grid partitioning, which enables localized analysis, and the rough set method, which captures the uncertainty in the dataset. By partitioning the input space into grids and determining the lower and upper approximations within each grid, the model generates accurate and representative fuzzy rules. These rules provide meaningful insights into the relationships between input variables and output variables, enhancing interpretability. The model is applied in a case example of temperature control to demonstrate its effectiveness. Additionally, a numerical example showcases the predictive performance and applicability of the model. The limitations of the research, such as dependency on data quality and scalability issues, are also discussed. Despite these limitations, the mathematical model contributes to the field of data analysis and decision-making systems by offering an approach that integrates grid partitioning and rough set method for fuzzy rule generation. It holds promise for applications in various domains, providing accurate and interpretable fuzzy rules for decision support systems and intelligent automation.