Picture fuzzy tensor and its application in multi-attribute decision making

Abstract

In this paper, picture fuzzy tensor is proposed, and some related properties are studied. In the meantime, the decomposition theorem of picture fuzzy tensors is established by using picture fuzzy cutting tensors and picture fuzzy t-norm. Moreover, we propose the generalized picture fuzzy weighted interaction aggregation (GPFWIA) operator and the generalized picture fuzzy weighted interaction geometric (GPFWIG) operator. Finally, an application of picture fuzzy tensor in multi-attribute decision making (MADM) problems is presented, that is, a method is suggested to solve picture fuzzy MADM problems with multi-dimensional data characteristics. It is found that our proposed method is feasible and effective by a typical application example.