Affiliations: [a] School of Information Science and Engineering, Linyi University, Linyi, China
| [b] School of Mathematics and Statistics, Linyi University, Linyi, China
Correspondence:
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Corresponding authors. Zhi Qiang Liu, School of Information Science and Engineering, Linyi University, Linyi 276005, China. E-mail: [email protected] and Zhen Ming Ma, School of Mathematics and Statistics, Linyi University, Linyi 276005, China. E-mail: [email protected].
Abstract: The present paper investigates the hesitant fuzzy filters on residuated lattices. A one-to-one correspondence between the set of all hesitant fuzzy filters and the set of all hesitant fuzzy congruences is established and a quotient residuated lattice with respect to a hesitant fuzzy filter is induced. Furthermore, several special types of hesitant fuzzy filters such as hesitant fuzzy implicative, regular and Boolean filters are introduced, and some alternative definitions of them are obtained, then some typical logical algebras are characterized by these identity forms.
