The development of effective methods of data processing belongs to important challenges of modern applied mathematics and theoretical information science. If the natural uncertainty of the data means their vagueness, then the theory of fuzzy quantities offers relatively strong tools for their treatment. These tools differ from the statistical methods and this difference is not only justifiable but also admissible. This relatively brief paper aims to summarize the main fuzzy approaches to vague data processing, to discuss their main advantages and also their essential limitations, and to specify their place in the wide scale of information and knowledge processing methods effective for vague data.
The cluster analysis and the fonnal concept analysis are both used to identity significiant groups of similar objects. Rice & Siff’s algorithm for the clustering joins these two methods in the case where the values of an object-attribute model are 1 or 0 and often reduce an amount of concepts. We use a certain type of fuzzification of a concept lattice for generalization of this clustering algorithm in the fuzzy case. For the purpose of finding dependencies between the objects in the clusters we use our method of the induction of generalized annotated programs based on multiple using of the crisp inductive logic programming. Since our model contains fuzzy data, it should have work with a fuzzy background knowledge and a fuzzy set of examples - which are not divided clearly into positive and negative classes, but there is a monotone hierarchy (degree, preference) of more or less positive / negative examples. We have made experiments on data describing business competitiveness of Slovak companies.