Pseudometric generating property and autocontinuity of fuzzy measures

Several necessary and sufficient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any unif...

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Bibliographic Details
Published in:Fuzzy sets and systems 2000-06, Vol.112 (2), p.207-216
Main Authors: Jiang, Qingshan, Wang, Shengrui, Ziou, Djemel, Wang, Zhenyuan, Klir, George J.
Format: Article
Language:English
Subjects:
Absolute continuity
Applied sciences
Atom
Autocontinuity
Computer science
control theory
systems
Control theory. Systems
Exact sciences and technology
Exhaustivity
Fuzzy measure
Mathematical analysis
Mathematics
Measure and integration
Pseudometric-generating property
Sciences and techniques of general use
Subadditivity
System theory
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Summary:Several necessary and sufficient conditions for the pseudometric generating property of non-additive set functions are given. The relation among the pseudometric generating property and autocontinuity of fuzzy measures is depicted by using the absolute continuity and exhaustivity. Moreover, any uniformly autocontinuous finite fuzzy measure is equivalent to a subadditive finite fuzzy measure. A further research on purely atomic fuzzy measures is also made.
ISSN:0165-0114
1872-6801
DOI:10.1016/S0165-0114(97)00395-3