### Abstract

J-K flip-flops are elementary digital units providing sequential features/memory functions. Their definitive equation is used both in the minimal disjunctive and conjunctive forms. Fuzzy connectives do not satisfy all Boolean axioms, thus the fuzzy equivalents of these equations result in two non-equivalent definitions, "reset and set type" fuzzy flip-flops (F^{3}) by Hirota & al. when introducing the concept of F^{3}. There are many alternatives for "fuzzifying" digital flip-flops, using standard, algebraic or other connectives. The paper gives an overview of some of the most famous F^{3}-s by presenting their definitions and presenting graphs of the inner state for a typical state value situation. Then a pair of non-associative operators is introduced, and the properties of the respective F^{3} are discussed. The investigation of possible fuzzy flip-flops is continued by examining Türksen's IVFS, its midpoint values, and by introducing "minimized IVFS" (MIVFS), along with the MIVFS midpoints.

Original language | English |
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Title of host publication | Advances in Soft Computing |

Pages | 643-652 |

Number of pages | 10 |

Volume | 42 |

DOIs | |

Publication status | Published - 2007 |

### Publication series

Name | Advances in Soft Computing |
---|---|

Volume | 42 |

ISSN (Print) | 16153871 |

ISSN (Electronic) | 18600794 |

### Fingerprint

### Keywords

- Fuzzy logic
- IVFS
- J-K flip-flop
- Logical normal forms

### ASJC Scopus subject areas

- Computational Mechanics
- Computer Science Applications
- Computer Science (miscellaneous)

### Cite this

*Advances in Soft Computing*(Vol. 42, pp. 643-652). (Advances in Soft Computing; Vol. 42). https://doi.org/10.1007/978-3-540-72434-6_65

**Fuzzy flip-flops revisited.** / Kóczy, L.; Lovassy, Rita.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Soft Computing.*vol. 42, Advances in Soft Computing, vol. 42, pp. 643-652. https://doi.org/10.1007/978-3-540-72434-6_65

}

TY - CHAP

T1 - Fuzzy flip-flops revisited

AU - Kóczy, L.

AU - Lovassy, Rita

PY - 2007

Y1 - 2007

N2 - J-K flip-flops are elementary digital units providing sequential features/memory functions. Their definitive equation is used both in the minimal disjunctive and conjunctive forms. Fuzzy connectives do not satisfy all Boolean axioms, thus the fuzzy equivalents of these equations result in two non-equivalent definitions, "reset and set type" fuzzy flip-flops (F3) by Hirota & al. when introducing the concept of F3. There are many alternatives for "fuzzifying" digital flip-flops, using standard, algebraic or other connectives. The paper gives an overview of some of the most famous F3-s by presenting their definitions and presenting graphs of the inner state for a typical state value situation. Then a pair of non-associative operators is introduced, and the properties of the respective F3 are discussed. The investigation of possible fuzzy flip-flops is continued by examining Türksen's IVFS, its midpoint values, and by introducing "minimized IVFS" (MIVFS), along with the MIVFS midpoints.

AB - J-K flip-flops are elementary digital units providing sequential features/memory functions. Their definitive equation is used both in the minimal disjunctive and conjunctive forms. Fuzzy connectives do not satisfy all Boolean axioms, thus the fuzzy equivalents of these equations result in two non-equivalent definitions, "reset and set type" fuzzy flip-flops (F3) by Hirota & al. when introducing the concept of F3. There are many alternatives for "fuzzifying" digital flip-flops, using standard, algebraic or other connectives. The paper gives an overview of some of the most famous F3-s by presenting their definitions and presenting graphs of the inner state for a typical state value situation. Then a pair of non-associative operators is introduced, and the properties of the respective F3 are discussed. The investigation of possible fuzzy flip-flops is continued by examining Türksen's IVFS, its midpoint values, and by introducing "minimized IVFS" (MIVFS), along with the MIVFS midpoints.

KW - Fuzzy logic

KW - IVFS

KW - J-K flip-flop

KW - Logical normal forms

UR - http://www.scopus.com/inward/record.url?scp=52249107148&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52249107148&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-72434-6_65

DO - 10.1007/978-3-540-72434-6_65

M3 - Chapter

AN - SCOPUS:52249107148

SN - 9783540724339

VL - 42

T3 - Advances in Soft Computing

SP - 643

EP - 652

BT - Advances in Soft Computing

ER -