The Evolution of the Concept of Fuzzy Measure

@inproceedings{Garmendia2005TheEO,
  title={The Evolution of the Concept of Fuzzy Measure},
  author={Luis Garmendia},
  booktitle={Intelligent Data Mining},
  year={2005}
}
  • L. Garmendia
  • Published in Intelligent Data Mining 2005
  • Computer Science
Most information discovery processes need to understand the reasons of the success of the inference methods or the usability of the new information, which can sometimes be somehow explained with a few useful measures on the premises or on the chosen relations, logics and implications. This chapter presents a state of art on the latest concepts of measure, from the additive measures, to monotone fuzzy measures and the latest monotone measures in relation to a preorder that gives an ordering for… 
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References

SHOWING 1-10 OF 86 REFERENCES
A class of fuzzy measures based on triangular norms
TLDR
An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short), which encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures.
Fuzzy sets and applications : selected papers
TLDR
This book discusses the role of Fuzzy Logic in the Management of Uncertainty in Expert Systems, and the concept of a Linguistic Variable and its application to Approximate Reasoning.
Fuzzy Measures Defined by Fuzzy Integral and their Absolute Continuity
TLDR
This paper generalizes in several different ways the concept of absolute continuity of set functions, as defined in classical measure theory, and investigates the relationship among these generalizations by using the structural characteristics of set function functions such as null-additivity and autocontinuity.
Fuzzy Measures and Integrals: Theory and Applications
TLDR
This work presents a Hierarchical Subjective Evaluation Model Using Non-monotonic Fuzzy Measures and the Choquet Integral, and an Algorithm for Calculating Natural Extensions with Respect to Lower Probabilities.
MEASURES OF UNCERTAINTY AND INFORMATION BASED ON POSSIBILITY DISTRIBUTIONS
TLDR
The proposed measures of U-uncertainty and conditional U-UNcertainty provide a foundation for developing an alternative theory of information, one based on possibility theory rather than probability, as well as avoiding a current controversy in possibility theory.
Similarity relations and fuzzy orderings
...
...