Fuzzy Logic and the Generalized Mudus Ponens (Journal Article)

摘要

The paper deals with generalized modus ponens in fuzzy logic. The generalized modus ponens deduces from the two premises (1) 'if S(1) is P(2)' and (2) 'S(1) is Q(1)', the conclusion 'S(2) is Q(2)'. The authors assume that P(1) and P(2) are both increasing linguistic notions, and the if ... then-relation represents a positive association between the antecedent and the consequent. The predicate P(1) in the antecedent of the if-then rule is fuzzy, hence the condition 'S(1) is P(1)' to derive 'S(2) is P(2)' is not strict. The objective therefore is to find the strongest or most informative fuzzy set Q(2), given P(1), P(2) and Q(1). To perform this, the authors set up a series of criteria which Q(2) should satisfy, given certain values of P(1), P(2) and Q(1). These criteria are based upon possibility theory, where shifted hedges are used. It turns out that two extra criteria are based upon possibility theory, where shifted hedges are used. It turns out that two extra criteria are needed to construct a procedure with input fuzzy sets P(1), P(2) and Q(1), and output a fuzzy set Q(2).