An analysis of the asymptotic behavior of the cardinality of some classes of logical connectives and aggregation functions defined on finite chains

Abstract

[eng] The enumeration of certain classes of logical connectives and aggregation functions defined on a finite chain has garnered significant attention in recent years, particularly due to its usefulness in various applied domains such as image processing and decision-making. However, in some instances, the sheer magnitude of this enumeration makes its exact value less critical. Instead, the focus often shifts to understanding its asymptotic growth order. This perspective is valuable for anticipating and planning computational costs, and more importantly, for assessing the restrictiveness of properties imposed on a class of logical operators. Consequently, this paper delves into the asymptotic behavior of several expressions already proposed in the literature, mainly in the enumeration of discrete negations, discrete implications and discrete aggregation functions and some subclasses. Additionally, in this paper a measure is proposed to quantify the degree of restrictiveness associated with an additional property within a class of logical operators.