Fuzzy owa operator

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I am reading about the allocation of OWA weigts from the article here

In it one way of finding weights is through

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Here with varying values for a,b they have shown this. Three situations are where (a,b)= (0.3,0.8),(0,0.5),(0.5,1)
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But what does this mean? Say if the fuzzy rule is

IF a and b and c then d

Then does "at least half" means when at least half of the a,b,c conditions are satisfied then d happens.
Is it something like that. Can someone please explain the effect from a,b?