Linguistic quantifiers based on Choquet integrals

The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quanti...

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Bibliographic Details
Published in:International journal of approximate reasoning 2008-06, Vol.48 (2), p.559-582
Main Authors: Cui, Licong, Li, Yongming
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Choquet integral
Computer science
control theory
systems
Exact sciences and technology
Fuzzy logic
Fuzzy measure
Fuzzy quantification
Knowledge representation and reasoning
Learning and adaptive systems
Mathematical analysis
Mathematics
Measure and integration
Quantifier
Sciences and techniques of general use
Speech and sound recognition and synthesis. Linguistics
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Summary:The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno’s integral. Representing linguistic quantifiers by fuzzy measures, this paper evaluates linguistic quantified propositions by the Choquet integral. Some elegant logical properties of linguistic quantifiers are derived within this approach, including a prenex normal form theorem stronger than that in Ying’s model. In addition, our Choquet integral approach to the evaluation of quantified statements is compared with others, in particular with Ying’s Sugeno integral approach.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2007.11.001