Preference relations based on hesitant-intuitionistic fuzzy information and their application in group decision making

• Hesitant-IFN has been proposed which is a synthesized intuitionistic fuzzy number.
• Some aggregation operators and their good properties have been studied.
• Hesitant-IFPR and its complementary form (Hesitant-IFCPR) have been produced.
• The approximate consistency tests and decision-making steps have been constructed.
• Two case studies are presented to illustrate the proposed methods and tests.

Preference relations are a powerful quantitative decision approach that assists decision makers in expressing their preferences over alternatives. In real-life applications, decision makers may not be able to provide exact preference information with crisp numbers. To solve this problem, a hesitant-intuitionistic fuzzy number (Hesitant-IFN) is proposed in this paper, and a proposal for the hesitant-intuitionistic fuzzy preference relation (Hesitant-IFPR) and its complementary form (Hesitant-IFCPR) for uncertain preference information are presented. Compared with other preference relations, the proposed relations use hesitant fuzzy elements (HFEs) to express the priority intensities of decision makers and produce the corresponding non-priority intensities by a conversion formula. In addition, we have deduced the operational laws and comparative methods of Hesitant-IFNs and used such information to investigate the corresponding aggregation operators and the approximate consistency tests. Next, we have constructed a group decision-making approach under a hesitant-intuitionistic fuzzy environment. Finally, two case studies are presented to illustrate the preference relations, the approximate consistency tests and the group decision method.