Hierarchical multi-criteria decision making with group voting information: New Tanino’s additive consistency intuitionistic fuzzy translation and utility vector acquisition

Abstract

The frame of intuitionistic fuzzy preference relations (IFPRs) is an effective tool of representing pairwise preference order based group voting information. However, existing intuitionistic fuzzy translations of Tanino’s additive consistency and previous methods of acquiring utility vectors from IFPRs are often unable to achieve a satisfactory solution for hierarchical multi-criteria decision making (HMCDM) with IFPRs. This study analyzes existing notions of additively consistent IFPRs (ACIFPRs) and shows their shortages. A novel intuitionistic fuzzy translation of Tanino’s additive consistency is developed and an index computational formula is provided to measure additive inconsistency of IFPRs. A new approach is offered to generate ACIFPRs from vectors with intuitionistic fuzzy elements and a frame is put forward to normalize intuitionistic fuzzy vectors. Subsequently, a closed-form solution based method is presented to secure normalized intuitionistic fuzzy utility vectors from ACIFPRs and a linear program is built to acquire an optimal and normalized intuitionistic fuzzy utility vector from any IFPR. An approach is proposed to tackle HMCDM problems with pairwise preference order based group voting information. The reasonability and performance of the models developed are validated by an illustrative example and a case study about outstanding teacher recommendation based on large-scale group votes on teaching satisfaction.

Keywords:

• Hierarchical multi-criteria decision making
• intuitionistic fuzzy preference relation
• additive consistency
• hesitancy
• linear program

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is partially supported by the National Natural Science Foundation of China under Grant 72171209 and the Natural Science Foundation of Zhejiang Province of China under Grant LY22G010006.