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Humans use multiple sources of sensory information to estimate environmental properties and has innate ability to integrate information from heterogeneous data sources. How the multi-sensory and multimodal information are integrated in human brain? There is consensus that it depends on the prefrontal cortex (PFC). The PFC has top-down control (favor weak) and rule-based mechanisms, and we propose to incorporate the favor weak mechanism into rule-based fuzzy logic systems (FLS) via using upper and lower membership functions. The inference engine of favor weak fuzzy logic system is proposed under three different categories based on fuzzifiers. We observe that the favor weak FLS is a special type-1 FLS which is embeded in an interval type-2 FLS, so it's much simpler in computing than an interval type-2 FLS. We apply the favor weak FLS to situation understanding based on heterogeneous sensor network, and it shows that our favor weak fuzzy logic system has clear advantage comparing to the type-1 FLS. The favor weak FLS can increase the probability of threat detection, and provides timely indication & warning (I&W).