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In this paper we propose a general approach to the theory of fuzzy algebras, while the early existing papers deal with a particular type of fuzzy structures as fuzzy groups, fuzzy ideals, fuzzy vector spaces and so on.
We investigate some local versions of congruence permutability, regularity, uniformity and modularity. The results are applied to several examples including implication algebras, orthomodular lattices and relative pseudocomplemented lattices.
We get an interrelation between an algebraic closure system and its conjugated interior system. We introduce the concept of algebraic interior system and we get its representation.
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