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fuzzy inference; fuzzy entropy; compositional rule of inference; continuity
The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes.
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