As an important kind of aggregation functions, overlap functions are widely used in information fusion, data intelligence, image processing, decision science, etc. It is also used to construct new fuzzy rough set models. Moreover, fuzzy rough sets have been deeply studied and made great progress in data analysis and mining, feature selection and other fields. However, after studying a large amount of literature, we find that the current research includes the following issues: (1) Existing fuzzy rough set models based on overlap functions (O-FRSs) need to be optimized (for example, the definition of fuzzy rough lower approximation in (IO, O)-fuzzy rough sets is not flexible, which restricts the application of (IO, O)-fuzzy rough sets). (2) The application research of O-FRSs is rarely involved, and the advantages of O-FRSs in feature selection and image processing are not presented. In this paper, combining the above aspects, we extend (IO, O)-fuzzy rough sets to (I, O)-fuzzy rough sets (IOFRS), which are applied to feature selection and image edge extraction systematically. First, (I, O)-fuzzy rough set model and fuzzy mathematical morphological operators based on IOFRS (IO-FMM operators) are proposed, and their relations and properties are sufficiently analyzed. Second, we propose and implement the IOFRS-based feature selection algorithm (IO-FS algorithm), and the results of 750 experiments show that the classification accuracy of IO-FS algorithm's results is better than others. Finally, combining the IO-FMM operators and fuzzy C-meaning (FCM) algorithm, an image edge detection algorithm (IO-FCM algorithm) is proposed and implemented, the result of 35 experiments show that the IO-FCM algorithm not only introduces the least noise, but also extracts the complete image edge. The excellent performance of IOFRS in feature selection and image edge extraction fully demonstrates the advantages of O-FRSs.

Fuzzy rough sets are important mathematical tool for processing data using existing knowledge. Fuzzy rough sets have been widely studied and used into various fields, such as data reduction and image processing, etc. In extensive literature we have studied, general quasi overlap functions and fuzzy neighborhood systems are broader than other all fuzzy operators and knowledge used in existing fuzzy rough sets, respectively. In this article, a novel fuzzy rough sets model (shortly (I,Q,NS)-fuzzy rough sets) is proposed using fuzzy implications, general quasi overlap functions and fuzzy neighborhood systems, which contains almost all existing fuzzy rough sets. Then, a novel feature selection algorithm (called IQNS-FS algorithm) is proposed and implemented using (I,Q,NS)-fuzzy rough sets, dependency and specificity measure. The results of 12 datasets indicate that IQNS-FS algorithm performs better than others. Finally, we input the results of IQNS-FS algorithm into single hidden layer neural networks and other classification algorithms, the results illustrate that the IQNS-FS algorithm can be better connected with neural networks than other classification algorithms. The high classification accuracy of single hidden layer neural networks (a very simple structure) further shows that the attributes selected by the IQNS-FS algorithm are important which can express the features of the datasets.