Localizable composable measures of fuzziness - II

Summary.

We consider measures of intrinsic uncertainty, or fuzziness. Two earlier papers introduced the axiom of localization and the direct product composition law and determined explicit forms for measures of fuzziness with these properties. In addition, justification was provided for choosing “Prod” over “Min” for the fuzzy direct product. In the present paper we continue to pursue the issue of the most appropriate fuzzy direct product. Indeed, supposing only that the fuzzy direct product is a t-norm, we find all possible localizable composable measures of fuzziness and their corresponding fuzzy direct products.