A novel approach to fuzzy modeling based on the tuning of parametric conjunction operations is proposed. First, some novel methods for the construction of parametric generalized conjunction operations simpler than the known parametric classes of conjunctions are considered and discussed. Second, several examples of function approximation by fuzzy models, based on the tuning of the parameters of the new conjunction operations, are given and their approximation performances are compared with the approaches based on a tuning of membership functions and other approaches proposed in the literature. It is seen that the tuning of the conjunction operations can be used for obtaining fuzzy models with a sufficiently good performance when the tuning of membership functions is not possible or not desirable.

Determination of markers of systemic inflammation is one of the important directions in the study of pathogenesis and improvement of diagnosis of chronic obstructive pulmonary disease (COPD), asthma-COPD overlap (ACO), and bronchial asthma (BA). The aim of our work was a comparative study of the features of changes in serum levels of IL-17, IL-18, and TNF-α in patients with COPD, ACO, and BA with various severity of the disease, as well as evaluation of the relationship between the level of these cytokines and lung ventilation function. A total of 147 patients with COPD (n=58), ACO (n=57), and BA (n=32) during a stable period have been examined in this study. The control group included 21 healthy nonsmokers with similar sex-age indicators. Serum levels of IL-17, IL-18, and TNF-α were determined by ELISA. The concentrations of these cytokines in the circulation in the studied patients with COPD, ACO, and BA were higher than those in healthy nonsmokers (p≤0.001). IL-17 and IL-18 levels in the blood serum were comparable in all examined patients. The mean TNF-α concentrations in the circulation in COPD and ACO were significantly higher than those in BA (p<0.001). In patients with COPD, the levels of IL-17 and TNF-α increased progressively against the background of a decrease in numerous spirometric indicators, which allows us to consider these cytokines as systemic biomarkers of disease severity. In BA, the inverse correlations between the level of IL-17 and FEV1/FVC (%) and FEV1 have been found. In patients with ACO, the increase in IL-18 levels was associated with a decrease in FEV1 and TNF-α with FEV1/FVC (%). These findings indicate that IL-17, IL-18, and TNF-α can participate in the mechanisms of systemic inflammation and the genesis of disorders of airway obstruction in COPD, AСO, and BA. An increase in the levels of IL-17 and TNF-α may be associated with impaired bronchial patency in COPD and BA. The established associations of the IL-18 concentration in the blood serum and FEV1 only in patients with ACO allow using the level of IL-18 as a potential marker of the degree of impaired airway obstruction in this disease.

It is surprising that last two decades many works in time series data mining and clustering were concerned with measures of similarity of time series but not with measures of association that can be used for measuring possible direct and inverse relationships between time series. Inverse relationships can exist between dynamics of prices and sell volumes, between growth patterns of competitive companies, between well production data in oilfields, between wind velocity and air pollution concentration etc. The paper develops a theoretical basis for analysis and construction of time series shape association measures. Starting from the axioms of time series shape association measures it studies the methods of construction of measures satisfying these axioms. Several general methods of construction of such measures suitable for measuring time series shape similarity and shape association are proposed. Time series shape association measures based on Minkowski distance and data standardization methods are considered. The cosine similarity and the Pearson's correlation coefficient are obtained as particular cases of the proposed general methods that can be used also for construction of new association measures in data analysis.

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Recently it was introduced a negation of a probability distribution. The need for such negation arises when a knowledge-based system can use the terms like NOT HIGH, where HIGH is represented by a probability distribution (pd). For example, HIGH PROFIT or HIGH PRICE can be considered. The application of this negation in Dempster-Shafer theory was considered in many works. Although several negations of probability distributions have been proposed, it was not clear how to construct other negation. In this paper, we consider negations of probability distributions as point-by-point transformations of pd using decreasing functions defined on [0,1] called negators. We propose the general method of generation of negators and corresponding negations of pd, and study their properties. We give a characterization of linear negators as a convex combination of Yager's and uniform negators.

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Abstract. The definition and the general methods of construction of non-statistical association measures on different domains are discussed. An association measure is a function of two variables defined on a set X with involutive operation and satisfying the properties similar to the properties of the Pearson's correlation coefficient. Such measure can be used for analysis of the possible positive and negative relationships between variables. The methods of construction of association measures using similarity measures and pseudo-difference operations associated to t-conorms are discussed. The examples of association measures on different domains are considered.

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