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A Note on “Generalized Fuzzy Filters of MTL-Algebras”
Xueling Ma and Jianming Zhan

In [X. Ma, J. Zhan and Y. Xu, Generalized fuzzy filters of MTL-algebras, J. Mult-Valued Logic and Soft Computing, 14 (2008), 119–128.], we obtained the following results:

Let F be a fuzzy set of a MTL-algebra L and J ={ t | t ∈ (0, 1] and U (F ; t ) is an empty set or a filter of L }. In particular, if J = (0, 1], then F is an ordinary fuzzy filter of L (Theorem 2.5 in [1]); if J = (0, 0.5 ], F is an ( ∈, ∈ v q)-fuzzy filter of L (Theorem 3.8 in [1]).

Naturally, we can ask if J = (0.5, 1], which kind of fuzzy filter of L is F ?

In this paper, we completely resolve this question.

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