On distance distribution functions-valued submeasures related to aggregation functions

TL;DR

This paper introduces probabilistic submeasures that generalize classical submeasures, focusing on their algebraic properties and connections with aggregation functions, especially those based on triangular norms and semi-copulas.

Contribution

It presents a new class of probabilistic submeasures linked to aggregation functions, expanding the theoretical framework and analyzing their algebraic properties.

Findings

Probabilistic submeasures generalize classical submeasures.

Algebraic properties of these submeasures are characterized.

Connections with triangular norms and semi-copulas are established.

Abstract

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied.