Properties and Relations Between Implication Operators
Fourteen properties and their interdependencies contributed to the analysis of six classes implication operators–S-implications, R-implications, QL-implications, Force implication, f- generated implication operator and g- generated implication operator– are explored in this paper. It is found that all the properties can be inferred from three mutually independent properties. Then, the proven concerning which properties are true, false or satisfied for each of the six classes of implication operators is given. Based on which, the author get the property I(x(n(x)) = n (x) for all x ∈[0,1] that does not hold for force implication, f-generated implication operator and g-generated implication operator.
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