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  5. Method of comparison of the degree of excessity between the fuzzy sets of type 1 and interval fuzzy sets

Method of comparison of the degree of excessity between the fuzzy sets of type 1 and interval fuzzy sets

S. Olizarenko, A. Samokish, V. Kapranov
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Description: The method of comparing the degree of fuzzy between fuzzy sets of type 1 (HMT1) and interval fuzzy sets of type 2 (INMT2) is considered on the basis of analysis of the cardinal number of fuzzy sets. The application of HMT1 and INMT2 in the construction of fuzzy production models requires the use of new approaches in the design of decision support systems (DSS). It follows from the contradiction that, for complex dynamic systems of intelligence, in which the data formalization is used by INPM, and in which the high requirements for the adequacy of the source data, the use of INMT2 does not satisfy the time constraints, and the result is a set of requirements. To solve this problem, it is proposed to use mixed hierarchical fuzzy production models (ZINPM). This approach consists in the joint application when constructing INPM production models both on the basis of NMT1 and INMT2. This is due to the limitations of the mathematical apparatus of fuzzy inference. So НМТ1 allows to build algorithms of fuzzy inference, the execution time of which does not exceed the specified limitations. In comparison with НМТ1, the algorithm of fuzzy inference based on INMT2 requires more execution time, but the adequacy of the results is higher than that of NMT1. In the paper, the use of hierarchical fuzzy production models (INPM) with the combined use of fuzzy sets of different types, namely both on the basis of HMT1 and INMT2, was proposed. In this case, fuzzy sets can have different degrees of fuzziness. In connection with this, when constructing an INMT, it is advisable to analyze the degree of fuzziness of linguistic variables from the composition of fuzzy production rules. Definitions of the degree of fuzziness are defined. The main methods for determining the degree of fuzziness based on the analysis of the cardinal numbers of fuzzy sets are analyzed. The results of comparison of the developed method with existing methods are given.


Keywords: fuzzy sets, interval fuzzy sets, hierarchical fuzzy production model, degree of fuzziness, cardinal number

Reference:
 Olizarenko, S.A., Samokish, A.V. and Kapranov, V.O. (2018), “Metod porivniannia stupeniu nechitkosti mizh nechitkymy mnozhynamy typu 1 ta intervalnymy nechitkymy mnozhynamy” [Method of comparison of the degree of excessity between the fuzzy sets of type 1 and interval fuzzy sets], Systems of Arms and Military Equipment, No. 2(54), pp. 136-141. https://doi.org/10.30748/soivt.2018.54.19.