FOCUS Toward a development of general type-2 fuzzy classifiers applied in diagnosis problems through embedded type-1 fuzzy classifiers Emanuel Ontiveros-Robles 1 • Patricia Melin 1 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract Nowadays, with the emergence of computer-aided systems, diagnosis problems are one of the most important application areas of artificial intelligence. The present paper is focused on a specific kind of computer-aided diagnosis system based on General Type-2 Fuzzy Logic. The main goal is the generation of General Type-2 Fuzzy Classifiers that can handle the data uncertainty. The concept of embedded Type-1 Fuzzy membership functions has been proposed to be used in the design of General Type-2 Fuzzy Classifiers. A methodology for generating the embedded Type-1 fuzzy membership functions is introduced, and the subsequent approach for developing the Footprint of Uncertainty of the General Type-2 Fuzzy Classifier is presented. On the other hand, the proposed approach performance is evaluated by the experimentation with different diagnosis benchmark problems. In addition, a statistical comparison with respect to another existing approach of General Type-2 Fuzzy classifiers is presented. Keywords General type-2 fuzzy logic  Fuzzy classifier  Footprint of uncertainty 1 Introduction The emergence of computer-aided diagnosis systems has demonstrated the reliability of artificial intelligence in real- world problems. For example, in Liao et al. (2018) the authors show the efficiency of deep convolutional neural networks for the diagnosis of multiple types of cancer, in Erkaymaz and Ozer (2016) the authors introduce an approach based on feedforward neural networks for the diagnosis of diabetes with interesting results, in Babapour Mofrad et al. (2019) the authors propose to use a decision tree for the interpretation of CSF biomarkers in the diag- nosis of Alzheimer’s disease, and more cases can be found in the literature, for example Saritas (2012), Subasi (2013), Elyan and Gaber (2016), Davari Dolatabadi et al. (2017), Asl and Zarandi (2017), Rakhmetulayeva et al. (2018), Vogado et al. (2018), Wang et al. (2018), Acharya et al. (2018), Qi et al. (2019), Afifi et al. (2019). The present paper aims at designing a computer-aided diagnosis system based on General Type-2 Fuzzy Logic and called General Type-2 Fuzzy Classifier (GT2 FC). The methodology for obtaining the parameters of the system and a new approach to estimate the uncertainty of the system is presented. The main contribution of the present paper is applying the concept of embedded Type-1 Fuzzy memberships for the parameterization of the Footprint of Uncertainty (FOU) of GT2 membership functions in a GT2 Fuzzy Classifier. Remembering that the FOU is modeling the uncertainty in the Type-2 Fuzzy Systems, it is proposed that is possible to find the parameters for modeling the uncertainty based on n subsets resulting from applying a uniform sampling with replacement, and based on multiple Type-1 Fuzzy mem- bership functions (one per each subset) it is possible to generate a single GT2 Fuzzy Classifier. The proposed approach is in focused on Diagnosis problems; however, the methodology for uncertainty modeling can be extended to other kind of problems for example time series. The concept of embedded Type-1 fuzzy membership functions is not new, it was presented for example in Hagras (2008), but the methodology to be applied in classification prob- lems and especially in diagnosis problems is interesting and obtains interesting results. Communicated by O. Castillo, D. K. Jana. & Patricia Melin pmelin@tectijuana.mx 1 Tijuana Institute of Technology, Calzada Tecnologico s/n, Fracc. Tomas Aquino, 22379 Tijuana, Mexico 123 Soft Computing https://doi.org/10.1007/s00500-019-04157-2