摘要
基于完备格值模糊积分在信息融合、不确定决策等方面的应用,本文讨论了取值于完备格值的模糊积分.考虑到Lebesgue积分可用实值简单可测函数来逼近,完备格值模糊积分亦有类似的性质,利用完备格值简单映射的模糊积分刻画了完备格值模糊积分,给出了刻画定理,并且运用单调的完备格值简单映射的模糊积分逼近一般的完备格值模糊积分.这些结论丰富了模糊积分理论的内容.
In this paper, the complete lattices fuzzy integral is discussed due to its application in the information fusion, the uncertain decision-making, etc. Since the Lebesgue integral can be approximated by the real simple measurable function, the complete lattices fuzzy integral also have similar properties. We obtain that complete lattices fuzzy integral can be characterized with the fuzzy integral of complete lattices simple mapping, and present the characterization theorems. Furthermore, we verify that the general complete lattices fuzzy integral can be approximated by the fuzzy integral of monotonous complete lattices simple mapping. These conclusions enrich the theories of fuzzy integral.
出处
《工程数学学报》
CSCD
北大核心
2013年第2期169-174,共6页
Chinese Journal of Engineering Mathematics
基金
国家自然科学基金(71061013
61262022)~~
