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**Fuzzy filters of MTL-algebras.**
*(English)*
Zbl 1077.03044

Summary: Characterizations of fuzzy filters in MTL-algebras are given. The fuzzy filter generated by a fuzzy set is considered. The notion of Boolean fuzzy filters and MV-fuzzy filters are introduced and related properties are investigated. A condition for a fuzzy filter to be Boolean is provided. A characterization of a Boolean fuzzy filter is given. A congruence relation on an MTL-algebra induced by a fuzzy filter is established, and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice.

### MSC:

03G25 | Other algebras related to logic |

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\textit{Y. B. Jun} et al., Inf. Sci. 175, No. 1--2, 120--138 (2005; Zbl 1077.03044)

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### References:

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[3] | Kim, K.H.; Zhang, Q.; Jun, Y.B., On fuzzy filters of MTL-algebras, Journal of fuzzy mathematics, 10, 4, 981-989, (2002) · Zbl 1022.06500 |

[4] | Turunen, E., BL-algebras of basic fuzzy logic, Mathware and soft computing, 6, 49-61, (1999) · Zbl 0962.03020 |

[5] | X.H. Zhang, On filters in MTL-algebras, submitted for publication. |

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