  Bilattice-based triangle provides an elegant algebraic structure for
reasoning with vague and uncertain information. But the truth and knowledge
ordering of intervals in bilattice-based triangle can not handle repetitive
belief revisions which is an essential characteristic of nonmonotonic
reasoning. Moreover the ordering induced over the intervals by the
bilattice-based triangle is not sometimes intuitive. In this work, we construct
an alternative algebraic structure, namely preorder-based triangle and we
formulate proper logical connectives for this. It is also demonstrated that
Preorder-based triangle serves to be a better alternative to the
bilattice-based triangle for reasoning in application areas, that involve
nonmonotonic fuzzy reasoning with uncertain information.
