Type-(2,k) Overlap Indices

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. {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.

Automated summary

Automatic image detection is crucial in various real-world scenarios, and overlap indices provide an important tool for comparing fuzzy objects. These indices have been successfully applied in fields such as image processing and decision making. This article introduces the concept of type-(2, k) overlap index in the context of type-2 fuzzy sets and explores its relationships with algebraic structures. The usage of type-(2, k) overlap indices in fuzzy rule-based systems involving type-2 fuzzy sets is also illustrated.