The article presents an application of fuzzy sets with triangular norms and balanced fuzzy sets with balanced norms to decision making modelling. We elaborate on a vector-based method for decision problem representation, where each element of a vector corresponds to an argument analysed by a decision maker. Vectors gather information that influence given decision making task. Decision is an outcome of aggregation of information gathered in such vectors. We have capitalized on an inherent ability of balanced norms to aggregate positive and negative premises of different intensity. We have contrasted properties of a bipolar model with a unipolar model based on triangular norms and fuzzy sets. Secondly, we have proposed several aggregation schemes that illustrate different real-life decision making situations. We have shown suitability of the proposed model to represent complex and biased decision making cases.