Possibility theory is not fully compositional! A comment on a short note by H.J. Greenberg

Abstract A recent short note [H.J. Greenberg, Fuzzy Sets and Systems 86 (1997) 249–250] has assumed that a possibility measure is fully compositional with respect to negation, conjunction and disjunction. Up to a trivial exception, such a possibility measure does not exist. This short note recalls that the calculus of possibility measures on Boolean propositions is not compositional (except for the disjunction) and has little to do with the fully compositional max-min calculus of degrees of truth for fuzzy propositions.

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