Uncertain multi-attribute group decision making based on linguistic-valued intuitionistic fuzzy preference relations

The preference relations have shown some advantages in handling multi-attribute group decision making problems, which can assist decision makers to set priorities and make a reasonable decision. In real-life situations, decision makers sometimes express their preference with fuzzy and uncertain linguistic information including positive and negative sides at the same time. In order to deal with the decision-making problems with uncertain linguistic information, we propose an approach for uncertain multi-attribute group decision making based on linguistic-valued intuitionistic fuzzy preference relations (LIFPR). The presented LIFPR based on linguistic truth-valued intuitionistic fuzzy lattice can better express positive and negative evaluation information in the meanwhile. To aggregate linguistic information and reduce information loss of aggregation process, we propose linguistic-valued intuitionistic fuzzy 2-tuple representation model (LIF 2-tuple) and two kinds of linguistic-valued intuitionistic fuzzy aggregation operators. To deal with incomparable LIF 2-tuples, we present positive and negative LIF 2-tuple reference nearness degrees according to preferences. For the inconsistent LIFPR caused by subjective uncertainty, a consistency checking algorithm based on linguistic-valued intuitionistic fuzzy similarity is introduced to check and repair the consistency of a LIFPR. For the incomplete LIFPR caused by objective uncertainty, an improved LIFPR based on additive transitivity is presented to complement the LIFPR. We discuss the procedure of group decision making based on LIFPR with positive and negative evaluation information. An illustrate example shows the proposed approach for group decision making seems more effective for decision making under an uncertain linguistic environment. (C) 2019 Elsevier Inc. All rights reserved.