Ruiz, GonzaloHagras, HaniPomares, HéctorRojas, IgnacioBustince Sola, Humberto2019-04-032019-04-032016G. Ruiz, H. Hagras, H. Pomares, I. Rojas and H. Bustince, "Join and Meet Operations for Type-2 Fuzzy Sets With Nonconvex Secondary Memberships," in IEEE Transactions on Fuzzy Systems, vol. 24, no. 4, pp. 1000-1008, 1 Aug. 2016. doi: 10.1109/TFUZZ.2015.24892421063-6706 (Print)1941-0034 (Electronic)10.1109/TFUZZ.2015.2489242https://academica-e.unavarra.es/handle/2454/32796In this paper we will present two theorems for the join and meet operations for general type-2 fuzzy sets with arbitrary secondary memberships, which can be non-convex and/or non-normal type-1 fuzzy sets. These results will be used to derive the join and meet operations of the more general descriptions of interval type-2 fuzzy sets presented in [1], where the secondary grades can be non-convex. Hence, this work will help to explore the potential of type-2 fuzzy logic systems which use the general forms of interval type-2 fuzzy sets which are not equivalent to interval valued fuzzy sets. Several examples for both general type-2 and the more general forms of interval type-2 fuzzy sets are presented.9 p.application/pdfeng© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other workGeneral type-2 fuzzy logicNonconvex fuzzy setsType-2 fuzzy logicinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess