A New Class of Interval-Valued Discrete Sugeno-like Integrals - Jacobino, Nicolas; Zumelzu, Nicolás; Callejas, Claudio; Palmeira, Eduardo; Bedregal, Benjamin (My University, 2025)
Discrete Sugeno integrals form a significant family of aggregation functions. Several variants of these integrals have been proposed, most of which replace the minimum operation with alternative operations, such as product, overlap functions, and t-norms. Notably, the associativity of t-norms in discrete Sugeno integrals has no significant consequences, leading us to relinquish this property and introduce the concept of partial t-norms. Although interval-valued versions of the discrete Sugeno integral or its variants have been limited, this paper presents a novel approach based on interval-valued partial t-norms, admissible orders, and interval-valued fuzzy measures. We provide rigorous proofs of the properties of this operator class.
Keywords: admissible orders; partial t-norms; fuzzy measures; sugeno-like integrals