Abstract A novel model termed a bipolar complex fuzzy N‐soft set (BCFN‐SS) is initiated for tackling information that involves positive and negative aspects, the second dimension, and parameterised grading simultaneously. The theory of BCFN‐SS is the generalisation of two various theories, that is, bipolar complex fuzzy (BCF) and N‐SS. The invented model of BCFN‐SS helps decision‐makers to cope with the genuine‐life dilemmas containing BCF information along with parameterised grading at the same time. Further, various algebraic operations, including the usual type of union, intersection, complements, and a few others types, are invented. Certain primary operational laws for BCFN‐SS are also invented. Moreover, a technique for order preference by similarity to the ideal solution (TOPSIS) approach is devised in the setting of BCFN‐SS for managing strategic decision‐making (DM) dilemmas containing BCFN‐SS information. Keeping in mind the usefulness and benefits of the TOPSIS approach, two various types of TOPSIS approaches in the environment of BCFN‐SS are devised and then a numerical example for exposing the usefulness of the devised TOPSIS approach is interpreted. To disclose the prominence and benefits of the devised work, the devised approaches with numerous prevailing work are compared.