An extended VIKOR method for decision making problem with linguistic intuitionistic fuzzy numbers based on some new operational laws and entropy

Since linguistic intuitionistic fuzzy numbers (LIFNs) can more easily express the fuzzy information in a qualitative setting, it is necessary to extend their operational rules and develop the decision making method based on the LIFNs. In this paper, we propose some new operational laws such as the subtraction and division, score function and accuracy function for (LIFNs), and we develop the linguistic intuitionistic fuzzy entropy, which can measure not only the fuzziness but also the intuitionism. Then we propose a method for determining the objective weight of attributes by the proposed entropy. In addition, because the VIKOR(from Serbian: VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximizing group utility and minimizing individual regret, we extended the VIKOR method to process the linguistic intuitionistic fuzzy information (LIFI) based on the new operational laws, and proposed an extended VIKOR method for the multiple attribute decision making (MADM) problems with LIFI. An illustrative example shows the effectiveness and advantages of the proposed approach.