Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

195218

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

Amadeo Monreal

pp. 497-515

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 SC1 and SC2. 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 SC1 and SC2. 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.

Publication details

Published in:

Seising Rudolf, Sanz González Veronica (2012) Soft computing in humanities and social sciences. Dordrecht, Springer.

Pages: 497-515

DOI: 10.1007/978-3-642-24672-2_25

Full citation:

Monreal Amadeo (2012) „T-norms, t-conorms, aggregation operators and Gaudí's columns“, In: R. Seising & V. Sanz González (eds.), Soft computing in humanities and social sciences, Dordrecht, Springer, 497–515.