T-norms, T-conorms, aggregation operators and Gaudí's columns

Abstract

A Gaudí's column GC, also known as 'double twist' or 'double rotation' column, can be conceived as split into different pieces or spans and each of them is defined as the intersection of two salomonic columns SC 1 and SC 2. Thus, the distance of a point in the boundary of a section of GC to the axis of the column GC is the Minimum of the distances of the corresponding points of SC 1 and SC 2. The conjunction 'and' is then modeled by the Minimum t-norm. Replacing the Minimum by other t-norms, new Gaudí's-like columns can be obtained. In the same way, replacing the t-norm by a t-conorm, and thus considering that our column is the disjunction of both salomonic ones, a new kind of Gaudí's-like columns can be generated. The Minimum is also an aggregation operator. Replacing this aggregation by other ones, new families of Gaudí's-like columns are obtained. This paper provides a mathematical model of the double twist columns and investigates the effect of the use of different t-norms, t-conorms and aggregation operators in the generation of columns and other longitudinal objects such as capitals, towers, domes or chimneys. © 2012 Springer-Verlag Berlin Heidelberg.