Sugeno integral based on absolutely monotone real set functions

The class of all absolutely monotone and sign stable set functions with m ( ∅ ) = 0 , denoted by AMSS, is introduced. Necessary and sufficient conditions are obtained for a set function m, m ( ∅ ) = 0 , to be a member of AMSS. A Sugeno type integral of an A - measurable real-valued function is defin...

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Veröffentlicht in:	Fuzzy sets and systems 2010-11, Vol.161 (22), p.2857-2869
Hauptverfasser:	Mihailović, Biljana, Pap, Endre
Format:	Artikel
Sprache:	eng
Schlagworte:	Absolutely monotone set function Applied sciences Circuit properties Computer science control theory systems Digital circuits Electric, optical and optoelectronic circuits Electronic circuits Electronics Exact sciences and technology Fuzzy set theory Information, signal and communications theory Integrals Mathematical analysis Mathematical methods Mathematics Miscellaneous Real functions Representations Sciences and techniques of general use Sign stable set function Sugeno integral Symmetric Sugeno integral Telecommunications and information theory Theoretical computing
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Beschreibung
Zusammenfassung:	The class of all absolutely monotone and sign stable set functions with m ( ∅ ) = 0 , denoted by AMSS, is introduced. Necessary and sufficient conditions are obtained for a set function m, m ( ∅ ) = 0 , to be a member of AMSS. A Sugeno type integral of an A - measurable real-valued function is defined with respect to an absolutely monotone and sign stable set function and some of its properties are shown. A representation of a comonotone–cosigned ▪ -additive functional by Sugeno integral based on m ∈ AMSS is obtained.
ISSN:	0165-0114 1872-6801
DOI:	10.1016/j.fss.2010.03.004