The fuzzy theory based on AFS algebras and AFS structure
Let \(X,M\) be sets. The triple \((M,\tau,X)\) is called an AFS structure, where \(\tau= X\times X\to 2^M\) satisfying some conditions. After adding a \(\sigma\)-algebra \(\sigma\) and a positive measure over \(\sigma\), the author establishes the notions of semi-cognitive fields and cognitive fields. Based on these structures, the author defines a membership function and gives the definition of a fuzzy variable. The author believes that people can use mathematical analysis to study such a fuzzy theory and to process fuzzy information.
scientific article; zbMATH DE number 1115480