## Volume 10, No. 1, 2015

- Lotfi A. Zadeh

**«Fuzzy sets»**

A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.Resources: title page of the article.

- Batyrshin I.Z.

**«Measures of association of plausible events»**

The paper considers the general methods of construction of non-statistical association measures on a set with given involutive operation. The measure of association is defined as a function satisfying the properties of the Pearson’s correlation coefficient. The methods of construction of association measures on [0,1] with generators of involutive negations are proposed. The examples of association measures on [0,1] obtained by means of generators of Yager negation and pseudo-difference operations associated to basic t-conorms are considered.Keywords: association measure, correlation coefficient, fuzzy negation, involution, similarity measure, t-conorm.

Resources: title page of the article.

Bibliographic citationBatyrshin I.Z. Measures of association of plausible events.*Nechetkie Sistemy i Myagkie Vychisleniya*[Fuzzy Systems and Soft Computing], 2015, vol. 10, no. 1, pp. 23-34. (in Russian) - Rzayev R., Jamalov Z., Mehdiyev T., Hasanov V.

**«Time series modeling based on fuzzy analysis of position-binary components of historical data»**

It is offered new predictive models of volatile time series based on fuzzy analysis of position-binary components of historical data. One of the distinctive features of the proposed models are rules fuzzification of historical data and defuzzification of fuzzy forecasts. In the context of this study, we propose a new criterion for assessing the adequacy of a model based on the use of the Hamming metric, which is on par with classical statistical evaluation criteria was used to evaluate the results.Keywords: time series, fuzzy set, fuzzy prediction, fuzzy relation, point estimation, Hamming distance.

Resources: title page of the article.

Bibliographic citationRzayev R., Jamalov Z., Mehdiyev T., Hasanov V. Time series modeling based on fuzzy analysis of position-binary components of historical data.*Nechetkie Sistemy i Myagkie Vychisleniya*[Fuzzy Systems and Soft Computing], 2015, vol. 10, no. 1, pp. 35-73. (in Russian) - Zotov M.A., Tulupyev A.L., Sirotkin A.V.

**«Complexity statistical estimates of straightforward and greedy algorithms for algebraic Baesian networks syntesis»**

The paper considers straightforward and greedy minimal joint graph synthesis algorithms. Comparative statistical analysis of runtime was done based on experiments run on specially generated datasets. A new algorithm for generating the loads with certain characteristics was developed. Statistical analysis pointed out three subintervals of joint graph vertex set cardinality (number of elements): that of 5--35 where the greedy algorithm had sufficiently higher speed than the straightforward algorithm did, that of 60--105 the straightforward algorithm had sufficiently higher speed than the greedy algorithm did, and that of 35--60 where the algorithms advantage in their speed depended on each specific initial dataset. According to rank statistics, there may be detected a few outbursts in the subinterval of 5--60.Keywords: uncertainty representation, algebraic Bayesian networks, probabilistic graphical models, knowledge pattern, knowledge with uncertainty, probabilistic-logic inference, statistical indicators for algorithm's complexity.

Resources: title page of the article.

Bibliographic citationZotov M.A., Tulupyev A.L., Sirotkin A.V. Complexity statistical estimates of straightforward and greedy algorithms for algebraic Baesian networks syntesis.*Nechetkie Sistemy i Myagkie Vychisleniya*[Fuzzy Systems and Soft Computing], 2015, vol. 10, no. 1, pp. 75-91. (in Russian) - Toropova A.V., Suvorova A.V., Tulupyev A.L.

**«Model for socially significant behavior rate estimate: consistency diagnostics»**

We considered a problem of consistency diagnostics for socially significant behavior model based on the data about behavior episodes. We described the extention of the model and provided the examples of consistency estimates. We suggested possible improvements for this model.Keywords: diagnostics, consistency evaluation, socially significant behavior, last episodes, Bayesian belief networks.

Resources: title page of the article.

Bibliographic citationToropova A.V., Suvorova A.V., Tulupyev A.L. Model for socially significant behavior rate estimate: consistency diagnostics.*Nechetkie Sistemy i Myagkie Vychisleniya*[Fuzzy Systems and Soft Computing], 2015, vol. 10, no. 1, pp. 93-107. (in Russian)