二值σ-极大测度与Mesiar假设
Two-valued sigma-maxitive measures and Mesiar's hypothesis
摘要：
我们重新制定Mesiar的假设[可能性措施，集成和模糊的可能性措施，模糊集和系统92（1997）191-196]，这是不真实的Murofushi [二值可能性措施诱导$σ$ -有限$σ$ -可加性措施，模糊集和系统126（2002）265-268]。证明了在$σ$ -主测度的附加条件下，二值$σ$ -极大测度可以由$σ$ -可加测度导出.
英文摘要：
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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