Aggregating information and ranking alternatives in decision making with intuitionistic multiplicative preference relations

• A transformation mechanism including three transformation functions between intuitionistic fuzzy preference relations and intuitionistic multiplicative preference relations are established.
• Some “ordered” weighted operators for aggregating intuitionistic multiplicative information are developed, including the IMOWA, IMOWG, GIMOWA and GIMOWG operators.
• This paper has made some comparisons of the proposed methods and the previous work and analyzed their differences in details through a numerical example.

The intuitionistic multiplicative preference relation (IMPR), whose all elements are measured by an unsymmetrical scale (Saaty's 1–9 scale) instead of the symmetrical scale in the intuitionistic fuzzy preference relation (IFPR), is suitable for describing the asymmetric preference information. In decision making process, one of the most crucial issues is how to rank alternatives from the given preference relation constructed by the decision maker. In this paper, two approaches are proposed for deriving the ranking orders of the alternatives from two different angles. To do it, a transformation mechanism is developed to transform an IMPR to a corresponding IFPR, and then all alternatives depicted by the given IMPR can be ranked via solving a familiar IFPR. In addition, the generalized intuitionistic multiplicative ordered weighted averaging (GIMOWA) and the geometric (GIMOWG) operators are given by taking fully account of the different weights associated with the particular ordered positions and their desirable properties are also discussed. After that, through a practical example, the proposed approaches are compared with the previous work and a numerical analysis of the results is also given.

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