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ON AUTOCONTINUITY AND PSEUDO-AUTOCONTINUITY OF FUZZY COMPLEX MEASURES

Jiqing Qiu, Ting Sun, Yan Shi

Abstract

In this paper, we investigate the extension of classical complex measure and fuzzy measure - fuzzy complex measure, and show the concepts of autocontinuity and pseudo-autocontinuity on fuzzy complex measure. We give the equivalent relation of autocontinuity from above and autocontinuity from below and illuminate it by an exam- ple. We verify the equivalent relation of pseudo-autocontinuity from above and pseudo- autocontinuity from below of fuzzy complex measure and give a set of equivalent defi- nitions of pseudo-autocontinuity. It will build the certain foundation for the intensive research of fuzzy complex analysis. Keywords: Fuzzy complex measure, Null additivity, Pseudo-null additivity, Autocon- tinuity, Pseudo-autocontinuity

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Key concepts: Measure (data warehouse), Fuzzy logic, Mathematics, Fuzzy measure theory, Fuzzy set, Extension (predicate logic), Null (SQL), Fuzzy classification