ALTERNATIVE SUBSETS OF ORDERED PAIRS AND THEIR APPLICATION IN DECISION-MAKING PROBLEMS UNDER CONDITIONS OF UNCERTAINTY

In economic science, a new scientific direction has appeared, associated with the so-called prospects theory, which has been among the leading for decision-making under conditions of uncertainty, not only for economic science. The fuzzy set theory, in which the fuzzy set (FS) is one of the types of numerous Non-factors, needs a qualitative modernization since we have a limited possibility to solve many classes of problems. The usage of fuzzy sets is almost universal for solving problems in different fields if there is uncertainty, inaccuracy. At the same time, the difficulty in choosing the membership function should be considered. The process of choosing an MF by a person (expert) is based on common sense, experience, and is not always rational. For solving tasks in conditions of uncertainty, the authors proposed the use of the tensor methodology. The authors showed the possibility to form a subset of ordered pairs based on the tensorization of the interval of a universal set with subsequent decomposition. It was suggested to use Toeplitz matrix, most effectively modeling fuzziness, as one of the ways of tensorization and taking into account the phenomenon of fuzziness. The universal set (US) on which the FS is formed contains, in the tensor format, hidden information that can be used to make a decision no less effectively than the heuristically assigned membership function, in addition, the existence of a formally calculated subset of ordered pairs (SsOP) can serve as a convincing comparative example: Having this SsOP, you can objectively refuse to assign a heuristic MF; SsOP has significantly less interval uncertainty. Alternative SsOP are formed in a uniform manner. Basic characteristics for FS and SsOP comparison are quite close or practically coincide. Examples that illustrate the higher efficiency of SsOP usage in comparison with standardly spaced FS are given.
Показана возможность формирования подмножество упорядоченных пар на основании тензоризации интервала универсального множества с последующей декомпозицией. В качестве одного из способов тензоризации и учета феномена нечеткости предложено использовать теплицеву матрицу, наиболее эффективно моделирующую нечеткость. Универсальное множество (УМ), на котором сформировано НМ, в тензорном формате содержит скрытую информацию, которая может быть использована при принятии решения не менее эффективно, чем эвристически назначенная ФП. Кроме того, наличие формально вычисленного ПмУП может служить убедительным сравнительным примером: располагая данным ПмУП, можно объективно отказаться от назначения эвристической ФП. Установлено, что ПмУП обладают существенно меньшей интервальной неопределенностью; приведены примеры, показывающие более высокую эффективность использования ПмУП по сравнению со стандартно сформированными НМ.