论文信息 - Some Characterizations of the Systems Represented by Choquet and Multi-Linear Functionals through the use of Möbius Inversion

Some Characterizations of the Systems Represented by Choquet and Multi-Linear Functionals through the use of Möbius Inversion

The systems represented by the Choquet or the multi-linear fuzzy integral with respect to fuzzy measure is equivalently decomposable into hierarchically sub-systems through the use of Inclusion-Exclusion Covering (IEC) (Theorem 4.1,4.2). Hence, IEC is one of very useful concepts/indexes for structural analysis of the fuzzy integral systems (short for: the systems represented by the Choquet or the multi-linear fuzzy integral) However, it is quite difficult to identify all IEC's. This paper shows a method for identifying it easily, through the use of Mobius inversion (Theorem 5.1).

Toshiaki Murofushi | Katsushige Fujimoto

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