The categorical approach is proposed to the formalization of fuzzy graph grammars obtained as a result of generalization of sequential graph grammars. This approach takes into consideration the basic types of fuzziness that arise in constructing categories of fuzzy objects and describing transformations of fuzzy graphs generated by fuzzy sets. All the problems of undecidability that are well known for Chomsky grammars are proved to hold true for fuzzy graph grammars.
The categorical approach is proposed to formalize transformations of FD-graphs that consist of networks of distributed components whose nodes are specified by fuzzy graphs. Necessary and sufficient conditions are formally defined for FD-graph transformations that do not violate structure integrity and can be constructed componentwise. FD-grammars that generalize fuzzy graph grammars are proposed to describe the admissible transformations of FD-graphs.
An approach to solving a linear interpolation problem in a fuzzy information space is proposed. Two different schemes of interpolation are outlined: a heuristic one, based on the geometrical interpretation of operations, and an optimization one, based on the expansion principle. The results obtained allow performing fuzzy linear prediction.
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