Generalized cross-entropy based group decision making with unknown expert and attribute weights under interval-valued intuitionistic fuzzy environment

This paper focuses on the multiple attribute decision making problems widespread in industry engineering, typically the supplier selection problems, and investigates effective methods utilizing preference information objectively for multiple attribute group decision making (MAGDM) with unknown attribute weights and expert weights under interval-valued intuitionistic fuzzy environments (IVIFEs). Firstly, a novel generalized cross-entropy measure for interval-valued intuitionistic fuzzy sets (IVIESs) is proposed to enable decision makers to express attitudinal characteristic information of hesitation degree rather than arbitrary equal assignment by other cross-entropy methods. Further, based on the generalized cross-entropy measure, simultaneously considering the divergence of attribute assessments from the most fuzzy number in IVIESs and the deviation between attribute assessments, a maximizing optimization model is proposed for objectively obtaining unknown attribute weights, which is then extended to accommodate decision situations with incomplete attribute weighting information. And also based on the generalized cross-entropy measure, an integrated algorithm is developed for ensurement of unknown expert weights by fusing two optimization models: one is to maximize divergence of decision matrices from positive or negative ideal decision matrix, and the other is to minimize similarity degree between individual decision matrices. Then based on the aforeproposed models, an approach is constructed for MAGDM problems with unknown attribute and expert weights under IVIFEs. Finally, case study on a simplified but representative supplier selection problem is carried out, and comparative experiments indicate the practicality and effectiveness of proposed methods. (C) 2014 Elsevier Ltd. All rights reserved.