Generalisation of A-equitable preference in multiobjective optimisation problems

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, ${⪯}_{e\left(A\right)}$, 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 ${⪯}_{e\left(A\right)}$. The other contribution of this paper is the use of the preference relation ${⪯}_{e\left(\mathrm{\Delta }A\right)}$ to solve the multio objective optimisation problems instead of ${⪯}_{e\left(A\right)}$. This has the advantage that the decision-maker has more freedom to choose the preferences matrix A. The relation ${⪯}_{e\left(\mathrm{\Delta }A\right)}$ has become an equitable rational preference relation by imposing the weaker conditions on entries of A, in comparison to the relation ${⪯}_{e\left(A\right)}$.

Keywords:

• Preference
• Pareto
• efficiency
• equitability
• multiobjective programming

Mathematics Subject Classifications:

• 90C29
• 91B08
• 90B50

Disclosure statement

No potential conflict of interest was reported by the authors.