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In this paper, the concept of intuitionistic fuzzy sets is applied to residuated lattices. The notion of intuitionistic fuzzy¯lters of a residuated lattice is introduced and some related properties are investigated. The characterizations of intuitionistic fuzzy¯lters are obtained. We show that the set of all the intuitionistic fuzzy¯lters of a residuated lattice forms a complete lattice and we¯nd the distributive sublattices of it. Finally, the correspondence theorem for intuitionistic fuzzȳ lters is established.

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In this paper, we introduce and study a corresponding logic toequality-algebras and obtain some basic properties of this logic. We provethe soundness and completeness of this logic based on equality-algebrasand local deduction theorem. Then we introduce the concept of (prelinear)equality-algebras and investigate some related properties. Also, westudy -deductive systems of equality-algebras. In particular, we provethat every prelinear equality-algebra is a subdirect product of linearly orderedequality-algebras. Finally, we construct prelinear equality logicand prove the soundness and strong completeness of this logic respect toprelinear equality-algebras.

In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms.