DETERMINATION THE INDEX OF CLEARNESS FOR THE DISTRIBUTION OF FUZZY MEASURES - Bocharnikov, Victor (Proceedings of National Aviation University (archive), 2018)
Objective: To justify the need and propose a new clarity index for the distribution of a fuzzy measure with an arbitrary modality. Conduct a study of the new index and show its effectiveness, sensitivity and ease of use for analyzing fuzzy data. Methods: for solving the problem using methods of set theory, fuzzy measures theory and functional analysis, and formal logic. Results: A new index is justified and proposed, which provides an estimate of the clarity for the distribution of a fuzzy measure with an arbitrary modality. Formulas are proposed for calculating the clarity index for a fuzzy measure on a discrete and continuous space. It is proved that the proposed index satisfies the properties that are advanced to the clarity indices. Additional dependencies are obtained to calculate the clarity index based on the use of level sets for the fuzzy measure density function. Discussion: the results of the calculation of the clarity index for a family of fuzzy measures with various modalities are presented. It is shown that the proposed index completely satisfies the advanced requirements to the logic of the performance of the clarity index and takes into account the modality of the fuzzy measure.