An extended TODIM approach with intuitionistic linguistic numbers

Abstract

In many practical problems, multiple alternatives are ranked with respect to related criteria, and the criteria's weights are usually unknown. In order to solve this kind of multicriteria decision making (MCDM) problem, this paper proposes an interactive MCDM approach based on an acronym in Portuguese of interactive and multicriteria decision-making (TODIM) method and nonlinear programming (NLP) with intuitionistic linguistic numbers (ILNs). First, by comparing the existing operations and comparison methods for ILNs, new operations and a new comparison method are defined based on linguistic scale functions to obtain rational results. Second, considering their linguistic terms, membership degrees, and nonmembership degrees as a whole, the generalized distance between ILNs is defined with an adjustable parameter. Third, the total ranking of alternatives is obtained using the proposed NLP-based TODIM approach based on the generalized ILN distance. Finally, an example of selecting hotels from a tourism website is presented to verify the validity and feasibility of the proposed approach. A comparison with existing methods is also conducted and analyzed.