Implication operators generating pairs of weak negations and their algebraic structure

Negations operators have been developed and applied in many fields such as image processing, decision making, mathematical morphology, fuzzy logic, etc. One of the most effective non-monotonic operators are weak negations. This paper studies the algebraic structure and the characterization of the adjoint triples and Galois implication pairs which provides a fixed pair of weak negations. The obtained results allow the user to select the best conjunctor and implications associated with the most suitable negation to be used in the computations of the problem to be solved.Partially supported by the State Research Agency (AEI) and the European Regional Development Fund (ERDF) project TIN2016-76653-P, European Cooperation in Science & Technology (COST) Action CA17124

Разработка алгоритмов поиска формальных понятий в нечётких контекстах

Текст работы публикуется с изъятиями.В результате исследований проведён обзор существующих подходов обобщения анализа формальных понятий на нечёткие контексты, разобраны подробные примеры для каждого подхода, разработаны алгоритмы FuzzyCbO и DirectCbO. Создан комплекс программ, реализующий алгоритмы Янга, Белоглавека, FuzzyCbO и DirectCbO, проведены вычислительные эксперименты для сравнения реализованных алгоритмов

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft