Ranking using PROMETHEE when weights and thresholds are imprecise: a data envelopment analysis approach

Abstract

Multicriteria decision making (MCDM) provides tools for the decision makers (DM) to solve complex problems with multiple conflicting criteria. Scalarization of criteria values requires using weights for criteria. Determining weights creates controversy as they are influential on the final ranking and challenges the DM as they are hard to elicit. PROMETHEE method is widely used in MCDM for ranking the alternatives and appropriate in situations when there is limited information on the preference structure of the DM. The DM should provide exact values for parameters such as criteria weights and thresholds of preference functions. Data Envelopment Analysis (DEA) is used for measuring the relative efficiency of alternatives in a non-parametric way without requiring any weight input. In this study, we propose two novel PROMETHEE based ranking approaches that address the determination of weight and threshold values by using an approach inspired by DEA. The first approach can deal with imprecise specification of criteria weights, and the second approach can utilize both imprecise weights and thresholds. The proposed approaches provide the DM substantial flexibility on the required level of information on those parameters. An illustrative example and a real-life case study are presented to show the utility of the proposed approaches.

Keywords:

• Multicriteria
• data envelopment analysis
• PROMETHEE
• decision support systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The equivalence may be a result of negative differences.

${\Delta }^j{}_{ki}=S_k^j-S_i^j=-{\Delta }_{ik}^j\hspace{1em}\forall k,i.$ Thus, $\left|{\Delta }^j{}_{ki}\right|=|-{\Delta }^j{}_{ik}|\hspace{1em}\forall k,i$ resulting $n(n+1)/2$ distinct $\left|{\Delta }^j{}_{ki}\right|$ values at most. Diagonals are equal to zero resulting $n(n-1)/2+1$ values at most (${\Delta }^j{}_{kk}=0\hspace{1em}\forall k$). Except these, two alternatives may have the same scores resulting 0 difference as in the diagonals case. Two alternatives may have same scores resulting in equalities. If alternative k and l have the same scores than for every other alternative ($\left|{\Delta }^j{}_{ik}\right|=|S_{ij}-S_{kj}|=|S_{ij}-S_{lj}|=\left|{\Delta }^j{}_{il}\right|\hspace{1em}\forall i$ except k, l). Even the alternative scores may result in different scores. There may be alternatives i, k, l, m such that no two of them have the same scores, but resulting differences would be the same, $\left|{\Delta }_{ik}\right|=|S_i-S_k|=|S_l-S_m|=\left|{\Delta }_{lm}\right|.$