Some remarks on axiomatic definition of entropy measure

The entropy measure is predefined as a mapping, increasing with an increase in the fuzziness of evaluated set. The relation "is less fuzzy than" is strictly modeled by an inequality fulfilled by membership functions. This inequality is systematically repeated across the literature. In this paper we show that it is incorrect. We prove that the relation "is less fuzzy than" should be modeled by an inclusion. Obtained conclusions are applied in a more precise definition of entropy measure.