<i>N</i>-Dimensional Admissibly Ordered Interval-Valued Overlap Functions and Its Influence in Interval-Valued Fuzzy-Rule-Based Classification Systems

Overlap functions are a type of aggregation that not required to be associative, generally used indicate the overlapping degree between two values. They have been successfully as conjunction operator in several practical problems, such fuzzy-rule-based classification systems (FRBCSs) and image processing. Some extensions overlap were recently proposed, general and, interval-valued context, n -dimensional functions. The latter allow them applied problems with inputs, where one can apply FRBCSs (IV-FRBCSs). In this case, choice an appropriate total order for intervals, admissible order, play important role. However, neither relationship interval function (which may or increasing order) nor impact process studied literature. Moreover, there is clear preferred IV-FRBCS. Hence, article, we: first, present some new results on orders, which us introduce concept admissibly ordered functions, is, respect order; second, develop width-preserving construction method kind function, derived from discussing its features; finally, analyze behavior combinations orders (admissibly ordered) when IV-FRBCSs. All all, contribution article resides pointing out effect both theoretical points view, considering problems.