The purpose of this article is to explore the group of the operators, which can be used for aggregation of the fuzzy sets. There were scrutinized operators to be used for the intersection and union such as the triangular norm and triangular co-norm in the article. All of those operators are defined as the binary operations, where there was indicated that the norms and co-norms are two-valued functions of [0, 1]. Furthermore, there were discussed properties of norm and co-norm functions such as symmetry, associativity, neutral entry and null entry properties, monotonicity properties. Moreover, the consideration of the properties of norm and co-norm functions have routed investigation of the norm and co-norm operators to go further to prove theorem, which converts the union into intersection and vice versa in terms to all possible norm and co-norm functions based on the fuzzy logic sets.

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Основы формирования у учащихся исследовательских умений и ИКТ-компетенций . . . 443 Ключевые слова: информатика, математика, компетенция, ИКТ-компетенции, ориентировочные основы действия, исследовательская деятельность, задачи динамического характера, решение задачи.Библиография: 36 названий.

Under the influence of the general informatization of education, the creation of the information educational environment (IEE) and the issues of preparing teachers for professional and pedagogical activity are taking place and how its functionality changes in IEE remain at the center of attention of research. One of the objectives of this article is the attempt of the authors to reveal the content, features, meaning, role of the concept, the influence of various factors on the functional of the teacher in the conditions of informatization of education.A modern teacher in his work faces a whole layer of problems: from the introduction of the Federal State Educational Standards to the implementation of the main educational programs, the creation of teaching materials like teaching staff of the Federal State Educational Standards, the choice of appropriate methods and means of organizing education, etc. A modern educational institution is required to introduce new approaches to learning, which, along with fundamental training and compliance with the requirements of the Federal State Educational Standard, provide an information-educational environment. Therefore, the readiness of the teacher for professional activity is considered by us as professionally and personally significant qualities of a university graduate, as knowledge and skills in a particular field, and ICT competence as a readiness for innovation activity.The work emphasizes that the role and importance of the content of the course informatics in the formation of everything necessary for a full-fledged professional activity of a modern teacher of informatics in accordance with its information culture and computer literacy, as information and communication technology (ICT) become key elements in improving educational system. However, the impact of ICT on the result of a teacher’s activity will be qualitative only when ICT have a specific impact on the content of the components of his professional and pedagogical activity.The study noted a number of objective and subjective factors that have a significant impact on the ways the teacher works and the organization of training in the information educational environment, on the content of the components of professional and pedagogical activity. Thus, the need to purposely train future teachers to work in such an environment is beyond doubt.