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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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References:

[1] Esteva, F.; Godo, L., Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy sets and systems, 124, 271-288, (2001) · Zbl 0994.03017
[2] Hájek, P., Metamathematics of fuzzy logic, (1998), Kluwer Academic Press Dordrecht · Zbl 0937.03030
[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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