Multi-Fuzzy Sets as Aggregation Subjective and Objective Fuzziness

The non-factor fuzziness is considered as one of the forms of uncertainty modeling by detecting hidden knowledge contained in the original data array (cloud of data) and fuzzy set. It is shown that the objective component of the fuzziness consists of 2 parts: 1-subset of ordered pairs, calculated on the basis of tensor decomposition structured as a 2D or 3D tensor of the initial data array; 2 - the immersion of the interval of possible values of the fuzzy set into a special matrix (Toeplitz), followed by a tensor decomposition. The results obtained: it is shown that in the general case analysis of uncertainty must be performed using a multi-fuzzy set; with restrictions on the formation of the membership function it is suggested to use a subset of ordered pairs on the basis of objective fuzziness; the developed algorithm for reducing the multi-fuzzy set to FS-1 type. The following examples illustrate the effectiveness of the proposed methodology.