State transformation and reconstruction of systems with bipolar uncertainty relatedness

For uncertain state transition systems, fuzzy switch graph and fuzzy activity graph were introduced to characterize the system reconstruction by state transitions. However, traditional univariate membership functions do not have symmetric features and they only depict the uncertainty of things from one angle, rather than the negative uncertainty prospect. In order to simultaneously characterize the positive and negative uncertainties in the change of system states, it is imperative to elaborate a bipolar membership function to facilitate the characterization of the opposite side. In this article, we introduce several bipolar graphs to characterize intricate relatedness in a structure system with bipolar uncertainty information. Some illustrative examples are manifested and several theoretical conclusions are yielded in light of algebra tricks. Finally, we demonstrate its applications in economic field.