An order induced by implications on bounded lattices

In this study, a relation denoted by ≼_I has been introduced by means of an implication I and the conditions making it an order have been investigated. Also, some relationships between the order ≼_I and the natural order on L have been studied. The greatest and the least elements of the partially ordered set (L,≼_I ) have been discussed. Even if L is a lattice, by some examples, it has been shown that L need not be a lattice with respect to ≼_I. Some conditions making L being a lattice have been determined. The independece of the orders induced by a continuous t-norm T and its residual implication I_T has been presented by means of some examples. It has been shown that the order induced by the implication I(x,y)=N(x)∨y defined on a bounded lattice L coincides with the natural order on L.