An extended C-TODIM method with linguistic intuitionistic fuzzy numbers

As the extension of intuitionistic fuzzy numbers (IFNs), linguistic intuitionistic fuzzy numbers (LIFNs) are proposed. LIFNs are expressed by linguistic variables and take the membership degree (MD) and non-membership degree (NMD) into consideration. The MD and NMD of LIFNs can easier describe complex and fuzzy information in multiple attribute decision-making (MADM) problems. The TODIM method based on prospect theory can reflect the psychological factors of the decision makers (DMs). However, existing TODIM methods neither handle the decision-making problems under linguistic intuitionistic environment nor consider interrelations among multiple attributes. Based on these problems, in this paper, combining the fuzzy measure with the TODIM method, an extended Choquet-TODIM method is proposed to process the MADM problems. The extended Choquet-TODIM method considers the interrelationship of multiple attributes and the bounded rationality of DMs. Firstly, the relative theories of LIFNs, the classical TODIM method and lambda-fuzzy measures are briefly reviewed. Secondly, the TODIM method is extended to linguistic intuitionistic fuzzy environment and C-TODIM method of LIFNs is proposed. Then lambda-fuzzy measure is extended to the classical TODIM method and a model of determining fuzzy measures is proposed. The proposed method gives the new solution to calculate the fuzzy measures and address the MADMproblems with interrelationship among different attributes. Lastly, two numerical examples are used to compare with two existing methods and explain the effectiveness and superiority of this method.