Distributed Decision Making with S-approximation Spaces

The combination of identical S-approximation spaces, except with different decider mappings, is studied in this paper by considering the construction of more complex S-approximation spaces from simpler ones that use different decision criteria, e.g., due to levels of expertise. It can be used to model group decision making problems where each decider makes an independent decision based on a shared knowledge map, e.g., several doctors with the same knowledge and different, independent decision criteria decide on a possible disease(s) for a patient, based on the same set of observations. These results can formalize the management of distributed uncertainty and can be used to invent novel distributed uncertain data processing algorithms. Also, we introduce the decider significance concept to minimize the number of combinations to obtain the same effect as the original combination. We show that finding a minimum set of significant deciders is NP-hard. and give an illustrative example in a medical expert system.