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JACIII Vol.9 No.6 pp. 661-668
doi: 10.20965/jaciii.2005.p0661
(2005)

Paper:

Lattice Structure of D, T, and SR Fuzzy Flip-Flops Under Max-Min Logic

Shinichi Yoshida*, and Kaoru Hirota**

*Information Science Research Center, Aoyama Gakuin University, N603, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan

**Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G3-49, 4259 Nagatsuta, Midori-ku, Yokohama-city 226-8502, Japan

Received:
March 10, 2005
Accepted:
June 7, 2005
Published:
November 20, 2005
Keywords:
fuzzy flip-flop, lattice, max-min logic, B-ternary logic, order of ambiguity
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.

Cite this article as:
Shinichi Yoshida and Kaoru Hirota, “Lattice Structure of D, T, and SR Fuzzy Flip-Flops Under Max-Min Logic,” J. Adv. Comput. Intell. Intell. Inform., Vol.9, No.6, pp. 661-668, 2005.
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