ELECTRE methods in prioritized MCDM environment

In most cases, ELECTRE methods just apply to traditional multicriteria decision making (MCDM) problems with independent criteria. However, there exist more or less interdependences among criteria in actual situations. A special case is MCDM with prioritizations among criteria, called prioritized MCDM. In recent years, how to deal with MCDM problems in the environment of prioritized criteria becomes hot topic increasingly. Lots of existing methods, including PROMETHEE, are modified for the prioritized MCDM, but the advantages of ELECTRE have not been exploited to the prioritized MCDM. In my opinion, design specific ELECTRE methods for prioritized MCDM problems will benefit the developments of both ELECTRE and prioritized MCDM. In this paper, we firstly reformulate the expressions of concordance and discordance indices for use in the MCDM problems with dependent criteria, especially prioritized criteria, based on the concepts of fuzzy measures and digraphs respectively. After replacing the fuzzy measure by a prioritized measure, we successfully validate the concordance of an assertion under prioritized criteria. Furthermore, we design an approach to validate the discordance of the assertion based on a digraph constructed by the criteria and their prioritizations. Finally, we design three procedures to construct outranking relations in the prioritized MCDM environment according to the ideas of ELECTRE-I, ELECTRE-Iv, and ELECTRE-IS respectively. It is meaningful of this paper to provide a new idea to solve the prioritized MCDM problems and widen the application scope of ELECTRE methods by means of the reformulations of concordance and discordance.