The concept of a ambda-lattice generalizes a lattice by substituting associativity by the so-called skew associativity. When a bounded ambda-lattice is equipped with a monotonous unary involution which is a complementation, it is called a ambda-ortholattice. For ambda-ortholattices a Sheffer operation is constructed and, moreover, a derived algebra analogous to an MV-algebra is assigned whenever the ambda-lattice has antitone involutions on sections.
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The concept of fuzzy implication algebra is weakened replacing the exchange axiom by an essentially weaker version. To each such algebra a groupoid is assigned. We get conditions under which this groupoid is commutative and show when a fuzzy implication algebra becomes a lattice with antitone involutions on all sections.
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