Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions

Overlap functions are a class of aggregation that measure the overlapping degree between two values. They have been successfully applied as fuzzy conjunction operation in several problems which associativity is not required, such image processing and classification. Interval-valued overlap were defined an extension to express interval-valued data, they usually when there uncertainty regarding assignment membership degrees, rule-based classification systems. In this context, choice total order for intervals can be significant, motivated recent developments on increasing given admissible order, is, refines usual partial intervals. Also, width preservation has considered these works, intent avoid increase guarantee information quality, but no deeper study was made relation widths input output interval, applying functions, or how one control propagation based relation. Thus, paper we: (i) introduce develop concepts width-limited limiting presenting theoretical approach analyze bivariate with special attention functions; (ii) concept ( , b ) -ultramodular less restrictive one-dimension convexity important predictable behaviour respect extended context; (iii) define taking into account function controls interval new notion increasingness pair orders ? 1 2 ; (iv) present compare three construction methods considering may not, showcasing adaptability our developments.