Let us consider the following situation: An oracle provides us with a finite set of examples considered as words belonging to a regular language. This oracle is not available again. In this paper we study a new and general inference algorithm of fuzzy regular grammars based on this set of words. This algorithm is created by adapting a process discovery method. The main issues in the adaptation are the development of a fuzzy version, the assignation of membership degrees to each production in the grammar, and the treatment of consecutive repeated symbols. In addition to this inference algorithm we present a practical use for automatically generating artistic designs. Specifically, we have collected a set of paintings by Piet Mondrian (1872-1944) and obtained new Mondrian-style paintings. To achieve this, we designed a code to transform the paintings into strings and also to carry out the reverse conversion. We view these strings, which represent the paintings, as words belonging to a regular language and from this finite set of examples infer a fuzzy regular grammar. The entire process has been implemented and some new paintings from the inference algorithm have been obtained. An art expert has judged that these computer-generated paintings are fully in the spirit of those painted by Mondrian.
@article{urn:eudml:doc:39168,
title = {Inference of fuzzy regular grammars from examples.},
journal = {Mathware and Soft Computing},
volume = {6},
year = {1999},
pages = {277-291},
zbl = {0954.68510},
mrnumber = {MR1774572},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39168}
}
Fortes, Inmaculada; Morales, Rafael; Pérez de la Cruz, José Luis; Triguero, Francisco; Comino, M. A. Inference of fuzzy regular grammars from examples.. Mathware and Soft Computing, Tome 6 (1999) pp. 277-291. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39168/