Abstract
This article proposes a goal programming framework for deriving intuitionistic fuzzy weights from intuitionistic preference relations (IPRs). A new multiplicative transitivity is put forward to define consistent IPRs. By analyzing the relationship between intuitionistic fuzzy weights and multiplicative consistency, a transformation formula is introduced to convert normalized intuitionistic fuzzy weights into multiplicative consistent IPRs. By minimizing the absolute deviation between the original judgment and the converted multiplicative consistent IPR, two linear goal programming models are developed to obtain intuitionistic fuzzy weights from IPRs for both individual and group decisions. In the context of multicriteria decision making with a hierarchical structure, a linear program is established to obtain a unified criterion weight vector, which is then used to aggregate local intuitionistic fuzzy weights into global priority weights for final alternative ranking. Two numerical examples are furnished to show the validity and applicability of the proposed models.
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Acknowledgments
This work is partially supported by the Ministry of Education, Humanities and Social Sciences Project (Grant No. 11YJA630202), the Innovation Program of Shanghai First-class Business Management Discipline, the National Natural Science Foundation of China under Grant Nos. 71572040 and 71271188, the Natural Sciences and Engineering Research Council of Canada Discovery Grant, and the Natural Science Foundation of Zhejiang Province under Grant No. LY15G010004.
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Zhang, Y., Li, K.W. & Wang, ZJ. Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights. Group Decis Negot 26, 409–436 (2017). https://doi.org/10.1007/s10726-016-9503-9
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DOI: https://doi.org/10.1007/s10726-016-9503-9