| Abstrakt: |
Fuzzy implications, as a generalization of the classical implication, are not only required in fuzzy logic systems and fuzzy control but also have an important effect on solving fuzzy relational equations, fuzzy mathematical morphology, image processing and etc. Therefore, it is necessary for us to investigate multiple types of fuzzy implications on different truth values sets. In this paper, we devote to propose the Q L -(operators) implications derived from quasi-overlap (quasi-grouping) functions and negations on bounded lattices. Firstly, we exactly investigate some desirable properties of Q L -operators. Afterwards, we provide a necessary and sufficient condition along with a sufficient condition for the Q L -operator to be a Q L -implication and study various prime properties of Q L -implications. Moreover, we show the relationship between Q L -implications and L-automorphisms on bounded lattices. Finally, we consider the Q L -implications to analyze their intersection with I G , N -implications derived from quasi-grouping functions and negations on bounded lattices. [ABSTRACT FROM AUTHOR] |
