Abstract
Lattice structures of fuzzy flip-flops are described. A binary flip-flop (e.g. D, T, set-type SR, or reset-type SR flip-flop) can be extended to a fuzzy flip-flop in various ways. Under max-min fuzzy logic, there are 4 types of D fuzzy flip-flops extended from a binary D flip-flop, 136 types of SR fuzzy flip-flops extended from a binary SR flip-flop, and only one T fuzzy flip-flop. There is a lattice structure among different types of fuzzy flip-flops extended from a same binary flip-flop in terms of the order of ambiguity and the order of fuzzy logical value. These results show that fuzzy flip-flops under max-min fuzzy logic construct distributive lattice structures. Moreover D and T fuzzy flip-flops constructs Boolean lattice. And there exists a order monotone between two lattices of same fuzzy flip-flop under the order of ambiguity and the order of fuzzy logical value. Proposed analysis and results have potential to establish a fuzzy sequential system design method.
| Original language | English |
|---|---|
| Pages (from-to) | 661-668 |
| Number of pages | 8 |
| Journal | Journal of Advanced Computational Intelligence and Intelligent Informatics |
| Volume | 9 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Nov 2005 |
| Externally published | Yes |
Keywords
- B-ternary logic
- fuzzy flip-flop
- lattice
- max-min logic
- order of ambiguity