Teleconsultation is conducive to the rational use of health resources and plays a key role in the realization of hierarchical diagnosis and treatment. Previous research on telemedicine multicriteria decision making methods rarely consider the difference in responsibilities between remote experts and attending physicians. To show the difference precisely, this article first defines the intuitionistic hesitant fuzzy linguistic term set (IHFLTS) as an extended mathematical expression of the fuzzy set. We propose two kinds of correlation measuring methods and related hesitancy degrees based on information energy and statistics with different application scenarios. Based on information entropy and distance measurement, two criterion weight determination methods are studied. To formally implement the joint decision-making process of remote experts and attending physicians, a telemedicine decision-making model is established for designing the teleconsultation decision support system. We apply the proposed methods to a sinusitis teleconsultation case to demonstrate their effectiveness. The weight determination methods are applied, and the influence of parameter variation in the distance-based method is analyzed. Finally, the rationality and applicability of the proposed methods are verified by comparisons. The results show that by considering the importance and differences between the two roles of teleconsultation, IHFLTS can obtain a more realistic result for the referral problems.