Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making

Our purpose in this paper is to show the integration properties of the intuitionistic fuzzy-valued Choquet integrals, by which improper applications of this type of Choquet integral in the multicriteria decision making can be avoided. We first propose some important operational properties of intuitionistic fuzzy values (IFVs) and give a short review of the methods of comparing IFVs in the framework of the multicriteria decision making. Then we give a detailed discussion on the aggregation properties of the intuitionistic fuzzy-valued Choquet integral (IFCI) and the intuitionistic fuzzy-valued conjugate Choquet integral (IFCCI). The difference in aggregation characteristics between the IFCI and the IFCCI in multicriteria decision making are also be investigated. Finally, we present an application of the IFCI and IFCCI-based multicriteria decision making method to assess the software development risks.