- Tytuł:
- Aggregation and related functions in fuzzy set theory: dualities and monotonicity-based generalizations
- Autorzy:
-
Mesiar, R.
Kolesarova, A. - Powiązania:
- https://bibliotekanauki.pl/articles/384570.pdf
- Data publikacji:
- 2017
- Wydawca:
- Sieć Badawcza Łukasiewicz - Przemysłowy Instytut Automatyki i Pomiarów
- Tematy:
-
aggregation function
conjuctor
directional monotonicity
disjunctor
duality
implication function
pre-aggregation function
pre-implication function - Opis:
- We discuss several extensions of binary Boolean functions acting on the domain [0, 1]. Formally, there are 16 disjoint classes of such functions, covering a majority of binary functions considered in fuzzy set theory. We introduce and discuss dualities in this framework, stressing the links between different subclasses of considered functions, e.g., the link between conjunctive and implication functions. Special classes of considered functions are characterized, among others, by particular kinds of monotonicity. Relaxing these constraints by considering monotonicity in one direction only, we generalize standard classes of aggregation functions, implications, semicopulas, etc., into larger classes called pre-aggregations, pre-implications, pre-semicopulas, etc. Note that the dualities discussed for the standard classes also relate the new extended classes of pre-functions.
- Źródło:
-
Journal of Automation Mobile Robotics and Intelligent Systems; 2017, 11, 3; 58-61
1897-8649
2080-2145 - Pojawia się w:
- Journal of Automation Mobile Robotics and Intelligent Systems
- Dostawca treści:
- Biblioteka Nauki
Artykuł