In this paper the set F of all IF sets is embedded to an lscr-group. By using the previous researches on the calculus of IF sets the theory of derivative is construct and the properties of derivative on the lscr-group are studied.

Ganoderma is a cosmopolitan genus of wood-decaying basidiomycetous macrofungi that can rot the roots and/or lower trunk. Among the standing trees, their presence often indicates that a hazard assessment may be necessary. These bracket fungi are commonly known for the crust-like upper surfaces of their basidiocarps and formation of white rot. Six species occur in central European urban habitats. Several of them, such as Ganoderma adspersum, G. applanatum, G. resinaceum and G. pfeifferi, are most hazardous fungi causing extensive horizontal stem decay in urban trees. Therefore, their early identification is crucial for correct management of trees. In this paper, a fast technique is tested for the determination of phytopathologically important urban macrofungi using fuzzy interference system of Sugeno type based on 13 selected traits of 72 basidiocarps of six Ganoderma species and compared to the ITS sequence based determination. Basidiocarps features were processed for the following situations: At first, the FIS of Sugeno 2 type (without basidiospore sizes) was used and 57 Ganoderma basidiocarps (79.17%) were correctly determined. Determination success increased to 96.61% after selecting basidiocarps with critical values (15 basidiocarps). These undeterminable basidiocarps must be analyzed by molecular methods. In a case, that basidiospore sizes of some basidiocarps were known, a combination of Sugeno 1 (31 basidiocarps with known basidiospore size) and Sugeno 2 (41 basidiocarps with unknown basidiospore size) was used. 84.72% of Ganoderma basidiocarps were correctly identified. Determination success increased to 96.83% after selecting basidiocarps with critical values (11 basidiocarps).

Reliable database of image samples is crucial for image recognition system development. One of rich sources of such data is the Internet. In this paper we describe a system, which collects specific image data from certain web pages. This image data will serve as samples for automatic recognition system. Collecting of image data is performed automatically according to user defined templates, which are defined in web browser environment.

Among statistical methods used in data analysis processes, correlation analysis holds one of the most significant places. Using correlation, analysts measure prediction potential between values of a pair of attributes of a dataset which can be summarized into a correlation matrix for any multidimensional dataset. Such matrices are usually sizable, and hard to read. Pruning of the correlation matrix for the precise selection of attribute pairs of a considered dataset which bear strong prediction potential is conventionally conducted via correlation matrix masks. Since these masks are commonly designed as crisp borders for the acceptability of values in the matrix, there is a strong lack of nuance in this approach. The work presented in the scope of this study focuses on the design and implementation of fuzzy masks for correlation matrices. This objective is divided into three main tasks - firstly, the visualization of correlation coefficient value frequency and its relationship to fuzzy membership function is designed and implemented, then visualisation of basic regression analysis and correlation context of attribute pairs in the fuzzy area of a studied dataset is designed and implemented, and lastly, the proposed approach is evaluated via case studies on three benchmarking datasets. The results obtained with the fuzzy approach to correlation matrix masks show a qualitative improvement in the matrix pruning task and a more appropriate identification of the relevant parts of the dataset compared to the conventional, crips approach.