Open Access
On completeness and direction in fuzzy relational systems
(Universitat Politècnica de Catalunya, 1998) Burillo López, Pedro; Fuentes González, Ramón; González, L.; Automática y Computación; Automatika eta Konputazioa
The concepts of bounded subset, complete subset and directed subset, which are well known in the context of partially ordered sets (X, ≤), are extended in order to become applicable, with coherence, in fuzzy relational systems (X, R). The properties of these generalized structures are analyzed and operative examples of them are presented.
Open Access
On fuzzy orderings of crisp and fuzzy intervals
(EUSFLAT, 2001) Fuentes González, Ramón; Burillo López, Pedro; Mayor, Gaspar; Automática y Computación; Automatika eta Konputazioa
First, fuzzy membership functions for the assertion '[x,y] is a positive interval' are proposed and characterized via non-decreasing real maps. Last, using those functions together with the intervaldifference and the notion of average index, comparison indexes between intervals and the ones between fuzzy intervals are proposed.
Open Access
Fuzzy morphological operators in image processing
(Universitat Politècnica de Catalunya, 2003) Burillo López, Pedro; Frago Paños, Noé Natalio; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa
First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz´s one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout´s manner) that satisfies the axioms of Divyendu and Dogherty. Second, we propose a method to define fuzzy morphological operators (erosions and dilations). A family of fuzzy implication operators and the inclusion grade are the basis for this method.
Open Access
Overtaker binary relations on complete completely distributive lattices related to the level sets of the L-fuzzy sets
(Universitat Politècnica de Catalunya, 1994) Núñez, A.; Burillo López, Pedro; Fuentes González, Ramón; González, L.; Automática y Computación; Automatika eta Konputazioa
The class of overtaker binary relations associated with the order in a lattice is defined and used to generalize the representations of L-fuzzy sets by means of level sets or fuzzy points.
Open Access
Generation of fuzzy mathematical morphologies
(Universitat Politècnica de Catalunya, 2001) Burillo López, Pedro; Frago Paños, Noé Natalio; Fuentes González, Ramón; Automática y Computación; Automatika eta Konputazioa
Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications), the paper includes a study on their practical effects on digital image processing. We also present some graphic examples of erosion and dilation with three different structuring elements B(i,j)=1, B(i,j)=0.7, B(i,j)=0.4, i,j∈{1,2,3} and various fuzzy implications.
Open Access
On contrast intensification operators and fuzzy equality relations
(Universitat Politècnica de Catalunya, 2000) Burillo López, Pedro; Fuentes González, Ramón; González, L.; Marín Martínez, Ángel; Automática y Computación; Automatika eta Konputazioa
The class of contrast intensification operators is formally defined and its lattice structure studied. The effect of these operators in the referential classification derived from special kinds of fuzzy relations is also determined. Results and examples are presented providing contrast intensification operators which keep quasi-uniformity structures generated by fuzzy relations while diminishing the fuzziness or the entropy of the relations.