A methodology for building interval type‐3 fuzzy systems based on the principle of justifiable granularity

International Journal of Intelligent SystemsEarly View RESEARCH ARTICLE A methodology for building interval type-3 fuzzy systems based on the principle of justifiable granularity Oscar Castillo, Corresponding Author Oscar Castillo ocastillo@tectijuana.mx orcid.org/0000-0002-7385-5689 Division of Graduate Studies, Tijuana Institute of Technology, University in Tijuana, Tijuana, Mexico Correspondence Oscar Castillo, Tijuana Institute of Technology, Calzada Tecnologico s/n, Fracc. Tomas Aquino, Tijuana 22379, Mexico. Email: ocastillo@tectijuana.mxSearch for more papers by this authorJuan R. Castro, Juan R. Castro Faculty of Engineering, UABC University, Campus Tijuana, Tijuana, MexicoSearch for more papers by this authorPatricia Melin, Patricia Melin Division of Graduate Studies, Tijuana Institute of Technology, University in Tijuana, Tijuana, MexicoSearch for more papers by this author Oscar Castillo, Corresponding Author Oscar Castillo ocastillo@tectijuana.mx orcid.org/0000-0002-7385-5689 Division of Graduate Studies, Tijuana Institute of Technology, University in Tijuana, Tijuana, Mexico Correspondence Oscar Castillo, Tijuana Institute of Technology, Calzada Tecnologico s/n, Fracc. Tomas Aquino, Tijuana 22379, Mexico. Email: ocastillo@tectijuana.mxSearch for more papers by this authorJuan R. Castro, Juan R. Castro Faculty of Engineering, UABC University, Campus Tijuana, Tijuana, MexicoSearch for more papers by this authorPatricia Melin, Patricia Melin Division of Graduate Studies, Tijuana Institute of Technology, University in Tijuana, Tijuana, MexicoSearch for more papers by this author First published: 19 May 2022 https://doi.org/10.1002/int.22910Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract In this article a design methodology for Mamdani interval type-3 fuzzy systems with center-of-sets type reduction is outlined. The methodology utilizes statistical measures, fuzzy c-means clustering and granular computing, to establish the justifiable footprint of uncertainty (JFOU) of the fuzzy granules, as explainable semantic abstractions that form the fuzzy model. The design methodology is presented in three general steps, first we use the principle of justifiable granularity to build a diagram of the justifiable information granule that contains a data structure with the descriptive measures of the experimental evidence of the data set. These measures are obtained from the partition matrix of the utilized clustering process, and these measures are used to evaluate the parameters of membership functions and characterize their JFOU. Second, we use the data structure of the justifiable information granule to characterize and parameterize the asymmetric interval type-3 membership functions. Lastly, the main procedure to obtain all the justifiable information fuzzy granules that define the knowledge base and the inference process of the fuzzy model is presented. Experiments were made with synthetic and real benchmark data from automated learning repositories, computing R adj 2 ${R}_{\mathrm{adj}}^{2}$ and root-mean-squared error to measure the reliability of the methodology, while keeping the justifiable uncertainty of the model. Early ViewOnline Version of Record before inclusion in an issue RelatedInformation