Authors
German O.
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Degree
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PhD in Technique, Associate Professor, Belarussian State University of Informatics and Radioelectronics |
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E-mail
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ovgerman@tut.by |
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Location
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Minsk |
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Articles
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Search for the maximum-size independent set in a fuzzy graphАn 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.
Read more...
About one cluster analysis model on incomplete dataThe clusterization problem on incomplete data is considered with its application to classification of the partly defined objects. The problem may arise in different practical areas including diagnosis making, forecasting, face recognition and so on. An original approach is outlined which involves a solution technique based on maximum independent set (maximum clique) definition in fuzzy graph (with evident interpretation of a cluster as some maximum clique in a fuzzy graph). An input partly defined object then gets to one of the cliques (clusters) with a decision undertaken specific to that clique. The entire approach subsequently uses a modal logical system, providing necessary formalization to find the maximum independent set (maximum clique) in fuzzy graph. This formalization is based on the transition from modal logic to Lukasewich multi-valued logics accordingly to Tarski theoretical results. The next step consists in transformation of the Lukasewich multi-valued logic to a classical boolean-valued system accordingly to suggested scheme. It is then shown how to formulate a pseudo-boolean optimization (pbo) problem and solve it by means of the suggested simple heuristic method which delivers a solution to a multipple kanpsack problem which we use instead of pbo. It is also noticed that there is a possibility to use different multi-valued Lukasewich logics to interpret a modal system in order to increase an accuracy of the solution. We give also a Python code realizing a standard imputation of the missing data by means of using average values and show that this technique gives incorrect results while the suggested method provides a right solution. Together with acceptable computational complexity of the suggested approach this gives good reasons to recommend the entire rechnique to practical usage. Read more... |
