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arXiv · 1301.4609

Two-valued sigma-maxitive measures and Mesiar's hypothesis

Paul Poncet
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Abstract

We 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 $σ$-principal.

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Paul Poncet. 2013-01-19. Two-valued sigma-maxitive measures and Mesiar's hypothesis. https://doi.org/10.1016/j.fss.2007.04.019

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