A note on two-valued possibility (σ-maxitive) measures and Mesiar's hypothesis

摘要

This paper proposes to reformulate Mesiar's hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191-196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265-268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure under the additional condition that it is localizable.