Integral representations and decision theory

Authors:
Yasuo Narukawa;Toshiaki Murofushi;Michio Sugeno
Affiliations:
Toho Gakuen, 3-1-10, Naka, Kunitachi, Tokyo, 186-0004, Japan;Comp. Intell. & Syst. Sci., Tokyo Inst. Tech. 4259 Nagatsuta, Midoriku, Yokohama, 226-8502, Japan;Laboratory for Language-Based Intelligent Systems Brain Science Institute, RIKEN 2-1, Hirosawa, Wako, Saitama, 351-0198, Japan
Venue:
Technologies for constructing intelligent systems
Year:
2002

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Abstract

A comonotonically additive and monotone functional (for short c.m.) on the class of continuous functions with compact support is represented by one Choquet integral if the universal set X is compact, while it is not represented by one Choquet integral but represented by the difference of two Choquet integral, if the universal set X is not compact but locally compact. This fact is expressed by the framework of decision making.