Generalized measures and integrals

Abstract

From the many generalizations of the concept of a classical (σ-additive) measure which can be found in the literature we shall present two concepts where t-norms and t-conorms are used explicitly.

Now, additivity is the most important property of ordinary measures. It is, however, doubtful that an individual uses a “measure” with additivity when he subjectively measures fuzziness. Though a reasonable man is imagined in the theory of subjective probabilities, it would be more realistic to assume that an actual man has no additive measure, because his behaviors are often contradictory to the assumption that he uses an additive measure in evaluating things.

Michio Sugeno