Abstract
The concept of A-equitable efficiency in solving the multiobjective optimisation problems have recently been introduced by Mut and Wiecek [Generalised equitable preference in multiobjective programming. Euro J Oper Res. 2011;212:535–551], where A is an arbitrary matrix with non-negative entries. The preference relation of this concept solution, , does not satisfy the strict monotonicity and strict principle of transfers axioms in general, therefore the set of A-equitably efficient solutions is not contained within the set of equitably efficient solutions and the set of Pareto-optimal solutions for the same problem. In this paper, we extend the work done by Mut and Wiecek and state the new conditions on the matrix A that guarantee to satisfy these axioms by the preference relation . The other contribution of this paper is the use of the preference relation to solve the multio objective optimisation problems instead of . This has the advantage that the decision-maker has more freedom to choose the preferences matrix A. The relation has become an equitable rational preference relation by imposing the weaker conditions on entries of A, in comparison to the relation .
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