© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.Fuzzy Cognitive Maps (FCMs), first introduced by Kosko, are graph-based knowledge representation tools. In order to improve the efficiency, robustness and accuracy of FCMs, different learning approaches and algorithms have been introduced in the literature. The algorithms aim to revise the initial knowledge of experts and/or extract useful knowledge from historical records in order to yield learned weights. One considerable drawback of FCM is that, in its original form, it often yields the same output under different initial conditions. Since the results of the learning algorithms are highly dependent on the reasoning mechanism (i.e. updating function) of FCMs, this drawback also affects the performance and accuracy of these algorithms. Therefore, problems including (conflicting) multiple initial vectors, multiple weight matrices and multiple desired final state vectors have received only limited attention. In order to address this issue and provide a better modeling framework for this type of problems, a compromise-based new fuzzy cognitive mapping approach based on particle swarm optimization is suggested. To justify the effectiveness and applicability of the proposed approach, an illustrative example is provided.