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articles

Search for the maximum-size independent set in a fuzzy graph

Published in № 2(56) 30 april 2015 year
Rubric: Mathematical methods
Authors: German Y., German O.
Аn original approach to find a maximum-size independent set in a fuzzy graph is presented together with the necessary formalization technique. The approach is oriented at practical usage in applied artificial intelligent systems using fuzzy logic and modal logic concepts. The problem may be encountered in face recognition with some possible distortions. The vertices stand for the points in the face image with approximately similar color and brightness. Obviously, in the case of image distortion the arcs in the graph may be assigned with the values in 0,1‑diapason. A fuzzy graph contains some nodes (arcs) with indefinite measure of their belonging to the graph. The situation may appear when no constrict classifying rules exist as explained in the paper. One can use a measure of 0.5 to interpret indefiniteness. This an interpretation enables one to apply modal logic for problem formalization and solving. The modality of the type «possible» is interpreted by the 3‑valued formula with truth value not less than 0.5; the modality of the type «necessary» is interpreted by the 3‑valued formula with the truth value equal to 1. The approach represented in the paper may be interesting for the researchers engaged in the recognition and classifying problems.

The author:

German Y.

Degree:

PhD in Technique, Associate Professor, Belarussian State University of Informatics and Radioelectronics

Location:

Minsk

The author:

German O.

Degree:

PhD in Technique, Associate Professor, Belarussian State University of Informatics and Radioelectronics

Location:

Minsk