Group decision making with incomplete intuitionistic preference relations based on quadratic programming models

• Quadratic programs are developed to complete an incomplete intuitionistic preference relation (IPR).
• A parameterized formula is devised to convert normalized interval fuzzy weights into additively consistent IPRs.
• Two quadratic programs are established to generate interval fuzzy weights from a complete IPR.
• A procedure is proposed to solve group decision problems with incomplete IPRs.

This paper presents a quadratic-program-based framework for group decision making with incomplete intuitionistic preference relations (IPRs). The framework starts with introducing a notion of additive consistency for incomplete IPRs, followed by a two-stage quadratic program model for estimating missing values in an incomplete IPR. The first stage aims to minimize inconsistency of the completed IPR and control hesitation margins of the estimated judgments within an acceptable threshold. The second stage is to find the most suitable estimates without changing the inconsistency level. Subsequently, a parameterized formula is proposed to transform normalized interval fuzzy weights into additively consistent IPRs. Two quadratic programs are developed to generate interval fuzzy weights from a complete IPR. The first model obtains interval fuzzy weight vectors by minimizing the squared deviation between the two sides of the transformation formula. By optimizing the parameter value, the second model finds the best weight vector based on the optimal solutions of the first model. A procedure is then developed to solve group decision problems with incomplete IPRs. A numerical example and a group selection problem for enterprise resource planning software products are provided to demonstrate the proposed models.