Type-(2,k) overlap indices Roldán López de Hierro, Antonio Francisco Roldán, Concepción Tíscar, Miguel Ángel Takac, Zdenko Santiago, Regivan H.N. Dimuro, Graçaliz P. Fernández, Javier Bustince, Humberto Overlap function Overlap index Type-2 fuzzy set Función de solapamiento Índice de solapamiento Conjunto difuso Conjunto difuso de tipo 2 Puede consultarse en abierto la versión aceptada del artículo en: https://academica-e.unavarra.es/server/api/core/bitstreams/5e75f204-6753-4291-95fe-d3c707eb22c1/content Automatic image detection is one of the most important areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices. They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully applied in the following fields: image processing, fuzzy rule-based systems, decision making, and computational brain interfaces. This notion of overlap indices is also necessary for applications in which type-2 fuzzy sets are required. In this article, we introduce the notion of type-(2,k) overlap index (k in {0, 1, 2}) in the setting of type-2 fuzzy sets. We describe both the reasons that have led to this notion and the relationships that naturally arise among the algebraic underlying structures. Finally, we illustrate how type-(2,k) overlap indices can be employed in the setting of fuzzy rule-based systems when the involved objects are type-2 fuzzy sets. 2026-01-13T09:51:50Z 2026-01-13T09:51:50Z 2023-03 journal article A. F. Roldán López de Hierro, C. Roldán, M. Á. Tíscar, Z. Takac, R. H. N. Santiago, G. P. Dimuro, J. Fernández, H. Bustince (2023). Type-(2,k) overlap indices, IEEE Trans. Fuzzy Syst., vol. 31, no. 3, pp. 860-874 https://hdl.handle.net/10481/109601 10.1109/TFUZZ.2022.3188918 eng embargoed access IEEE-Inst Electrical Electronics Engineers Inc.