Triangular norms, or t-norms for short, play an important role for the semantics of fuzzy logics. Although an enormous number of examples and a remarkable number of construction methods for this kind of operation has been established, a uniform approach is still outstanding. This paper is devoted to a specific algebraic-geometrical framework within which t-norms, up to isomorphism, can be descr...

Contour lines totally fix the structure of leftcontinuous t-norms. For each t-norm, these contour lines are determined by the corresponding residual implicator. Most properties involving residual implicators can now easily be translated into properties involving contour lines. As the portation law expresses associativity, we dispose of a powerful tool for constructing left-continuous t-norms. I...

Pictures are often used as stimuli in several fields, such psychology and neuroscience. However, co-occurring image-related properties might impact their processing, emphasizing the importance of validating materials to guarantee quality research professional practices. This is particularly relevant for pictures common items because wide applicability potential. Normative studies have already b...

Group beneficial norms are common in human societies. The persistence of such norms is consistent with evolutionary game theory, but existing models do not provide a plausible explanation for why they are common. We show that when a model of imitation used to derive replicator dynamics in isolated populations is generalized to allow for population structure, group beneficial norms can spread ra...

Each t-norm can be identified with its Cayley tomonoid, which consists of pairwise commuting order-preserving functions from the real unit interval to itself. Cayley tomonoids provide an easily manageable, yet versatile tool for the construction of t-norms. To give evidence to this claim, we review and reformulate several construction methods that are known in the literature. We adopt, on the o...

Societies are regulated by norms and, consequently, autonomous agents that want to be part of them must be able to reason about norms. However, no reasoning can be done if agents lack a model of norms that allows them to know how by complying with norms some of their goals might be affected. In this paper, a general model of norms is proposed. By contrast with current models of norms, our model...