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Использование Z-чисел для описания набора данных
The concept of Z-number was proposed by Prof. Lotfi Zadeh to describe partial reliability of information, and it is a kind of fusion of fuzziness and probabilistic uncertainty. Z-number can be presented as a pair of fuzzy numbers Z(A,B) used to describe a value of a random variable X. The first component (A) is a fuzzy restriction on values of X, while B is treated as a fuzzy reliability of A, and it is described as a value of probability measure of A. Imprecision of B stems from imprecise information about actual probability distribution related to X. In other words, fuzziness of B implies existence of a fuzzy set G of probability distributions of X. The essence of Z-number concept lies in the fact that, due to uncertainty, in practical problems it is necessary to consider not one probability distribution, but a set of those, some sort of family of distributions. The reason may be related to the fact that the actual distribution p is not exactly known, or it is variative. A family of distributions forms the basis of the Z-number structure. Since the first article related to Z-numbers, a large number of papers have been published on theoretical and practical issues of their use. However, there are relatively few papers devoted to the actual process of Z-numbers construction. This article considers the issue of constructing Z-numbers as a means of generalized linguistic description of complex data sets characterized by the presence of distribution families. Methods for extracting these families using clustering, classification, sampling and other means are the cornerstone of the proposed methodology. Fuzzy estimates of A and B constructed for the obtained families is the primary result of the study. For these estimates the corresponding
informative (intuitively clear) linguistic description can be found. The importance and relevance of the idea is that it will allow to obtain an intuitively clear interpretation of complex data. Furthermore, the proposed methodology is characterized by relatively low computational complexity. A limitation of the proposed approach is the use of a 'hard' (purely formal) computational framework. To the opinions of the authors, an important aspect of the further development of the idea addressed in the study is the need to consider participation of humans at the appropriate stages of the process of constructing Z-numbers to clarify (viz. fine-tune) certain details of the calculations, identify nuances and make the results more clear. The proposed approach can be used for interpreting complex data in various databases and information systems.