General OG-functions and their application to optimized pooling in convolutional neural networks

Aggregation functions and fuzzy logic operators have wide applications in information fusion and uncertainty in artificial intelligence. On the basis of in-depth research on various fuzzy logic operators and information aggregation operators, this paper proposes a new concept called general OG-function (abbreviated as GOG-function), which makes many existing concepts become its special cases. After systematically studying the basic properties of GOG-functions and their relationships with various fuzzy logic operators, this paper provides several constructive theorems of GOG-functions and proves that any GOG-function is generated by a general quasi-overlap function (or a general quasi-grouping function) and a MC-function (monotonic commutative function) in a special way, thus incorporating a series of related structural theorems into a unified framework. Furthermore, the concept of binary GOG-function is extended to n-dimensional GOG-function, and the general construction method and some examples of GOG-functions are given. Moreover, by using n-dimensional GOG-functions, the pooling operation in traditional Convolutional Neural Networks (CNNs) has been modified, and the new CNNs are applied to image classification tasks. Experiments on multiple publicly available datasets have shown that the classification accuracy of image classification is significantly improved compared to traditional CNNs.