Approach for group decision making based on linguistic truth-valued intuitionistic fuzzy lattice

The group decision-making is a process that multiple experts participate in analysis and decision-making for multiple attributes, which can assist decision makers to set priorities and make the best decision. The linguistic truth-valued intuitionistic fuzzy lattice can better express both comparable and incomparable linguistic information, which can also better to deal with positive and negative linguistic information at the same time. To deal with the decision-making problem with fuzzy linguistic information, we propose an approach for group decision making based on linguistic truth-valued intuitionistic fuzzy lattice. For the comparable fuzzy linguistic information, the linguistic truth-valued intuitionistic fuzzy weighted averaging operator and the linguistic truth-valued intuitionistic fuzzy ordered weighted averaging operator are presented to aggregate evaluation information of multiple experts. For the incomparable fuzzy linguistic information, positive reference nearness degree and negative reference nearness degree are introduced to deal with incomparable result with different preferences. We discuss an algorithm of group decision making, in which the decision results are alternative according to the decision makers' preferences. A practical example is provided to illustrate the validity and rationality of the developed approach.