Novel Transformation Methods Among Intuitionistic Fuzzy Models for Mixed Intuitionistic Fuzzy Decision Making Problems

As an extension of classical fuzzy set, intuitionistic fuzzy set (IFS) has been widely utilized in decision making. Based on IFS, intuitionistic fuzzy value (IFV) and linguistic intuitionistic fuzzy set (LIFS) have also been proposed to represent uncertain assessments of alternatives in different intuitionistic fuzzy decision environment. Theoretically, IFV, IFS or LIFS own themselves processing methods in decision making. However, they may be utilized to represent intuitionistic fuzzy assessments of alternatives in the same decision problem, i.e., multi-decision makers provide IFVs, IFSs or LIFSs to represent uncertain assessments of alternatives in the decision problem. In such case, the significant challenge is to unify IFVs, IFSs and LIFSs in the decision making matrices. In the paper, novel transformation methods are presented to unify IFVs, IFSs and LIFSs. To this end, mixed intuitionistic fuzzy decision matrix is presented to represent IFV, IFS or LIFS assessments of alternatives provided by decision makers, then transformation functions are developed to unify IFVs, IFSs and LIFSs in the decision making matrices, their properties are also analysed. The decision making method is presented to solve the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs, which is consisted of six main phases, accordingly the algorithm is designed to carry out the problems. Illustrative examples show that transformation functions are useful in intuitionistic fuzzy decision environment, the proposed decision making method is an effective and alternative tool for the intuitionistic fuzzy decision making problems with IFVs, IFSs or LIFSs.