Real-valued Choquet integrals with fuzzy-valued integrand

Authors:
Zhenyuan Wang;Rong Yang;Pheng-Ann Heng;Kwong-Sak Leung
Affiliations:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182, USA;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong;Department of Computer Science and Engineering, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
Venue:
Fuzzy Sets and Systems
Year:
2006

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Abstract

The Choquet integral of a real-valued function defined on a set of attributes with respect to a signed fuzzy measure is generalized for allowing a fuzzy-valued function to be its integrand while keeping its value to be a crisp real number. Thus, the Choquet integral can be used as a defuzzifying aggregation tool to deal with data set involving categorical attributes, linguistic variables, and/or fuzzy numbers. A numerical method with the relevant algorithm is developed to estimate the value of the Choquet integral for any given fuzzy-valued function.