A Way to Choquet Calculus

In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restri...
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Autor*in:	Sugeno, Michio [verfasserIn]

Format:	Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Generators Choquet calculus Fractional calculus Laplace equations Distortion measurement conditional distorted Lebesgue measure Integral equations distorted Lebesgue measure Differential equations Calculus

Übergeordnetes Werk:	Enthalten in: IEEE transactions on fuzzy systems - New York, NY : Inst., 1993, 23(2015), 5, Seite 1439-1457
Übergeordnetes Werk:	volume:23 ; year:2015 ; number:5 ; pages:1439-1457

Links:	Volltext Link aufrufen Link aufrufen

DOI / URN:	10.1109/TFUZZ.2014.2362148

Katalog-ID:	OLC1959562800

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allfields	10.1109/TFUZZ.2014.2362148 doi PQ20160617 (DE-627)OLC1959562800 (DE-599)GBVOLC1959562800 (PRQ)c1889-e2ccfc41a89bfc805b0c598160647ed0e5d1a3990359b39703800c0b0392ef940 (KEY)0226257620150000023000501439waytochoquetcalculus DE-627 ger DE-627 rakwb eng 004 DNB Sugeno, Michio verfasserin aut A Way to Choquet Calculus 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties. Generators Choquet calculus Fractional calculus Laplace equations Distortion measurement conditional distorted Lebesgue measure Integral equations distorted Lebesgue measure Differential equations Calculus Enthalten in IEEE transactions on fuzzy systems New York, NY : Inst., 1993 23(2015), 5, Seite 1439-1457 (DE-627)171085515 (DE-600)1149610-1 (DE-576)034198547 1063-6706 nnns volume:23 year:2015 number:5 pages:1439-1457 http://dx.doi.org/10.1109/TFUZZ.2014.2362148 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6918497 http://search.proquest.com/docview/1729225354 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_4318 AR 23 2015 5 1439-1457
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allfields_unstemmed	10.1109/TFUZZ.2014.2362148 doi PQ20160617 (DE-627)OLC1959562800 (DE-599)GBVOLC1959562800 (PRQ)c1889-e2ccfc41a89bfc805b0c598160647ed0e5d1a3990359b39703800c0b0392ef940 (KEY)0226257620150000023000501439waytochoquetcalculus DE-627 ger DE-627 rakwb eng 004 DNB Sugeno, Michio verfasserin aut A Way to Choquet Calculus 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties. Generators Choquet calculus Fractional calculus Laplace equations Distortion measurement conditional distorted Lebesgue measure Integral equations distorted Lebesgue measure Differential equations Calculus Enthalten in IEEE transactions on fuzzy systems New York, NY : Inst., 1993 23(2015), 5, Seite 1439-1457 (DE-627)171085515 (DE-600)1149610-1 (DE-576)034198547 1063-6706 nnns volume:23 year:2015 number:5 pages:1439-1457 http://dx.doi.org/10.1109/TFUZZ.2014.2362148 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6918497 http://search.proquest.com/docview/1729225354 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_4318 AR 23 2015 5 1439-1457
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allfieldsSound	10.1109/TFUZZ.2014.2362148 doi PQ20160617 (DE-627)OLC1959562800 (DE-599)GBVOLC1959562800 (PRQ)c1889-e2ccfc41a89bfc805b0c598160647ed0e5d1a3990359b39703800c0b0392ef940 (KEY)0226257620150000023000501439waytochoquetcalculus DE-627 ger DE-627 rakwb eng 004 DNB Sugeno, Michio verfasserin aut A Way to Choquet Calculus 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties. Generators Choquet calculus Fractional calculus Laplace equations Distortion measurement conditional distorted Lebesgue measure Integral equations distorted Lebesgue measure Differential equations Calculus Enthalten in IEEE transactions on fuzzy systems New York, NY : Inst., 1993 23(2015), 5, Seite 1439-1457 (DE-627)171085515 (DE-600)1149610-1 (DE-576)034198547 1063-6706 nnns volume:23 year:2015 number:5 pages:1439-1457 http://dx.doi.org/10.1109/TFUZZ.2014.2362148 Volltext http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6918497 http://search.proquest.com/docview/1729225354 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_30 GBV_ILN_70 GBV_ILN_4318 AR 23 2015 5 1439-1457
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author	Sugeno, Michio
spellingShingle	Sugeno, Michio ddc 004 misc Generators misc Choquet calculus misc Fractional calculus misc Laplace equations misc Distortion measurement misc conditional distorted Lebesgue measure misc Integral equations misc distorted Lebesgue measure misc Differential equations misc Calculus A Way to Choquet Calculus
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topic_title	004 DNB A Way to Choquet Calculus Generators Choquet calculus Fractional calculus Laplace equations Distortion measurement conditional distorted Lebesgue measure Integral equations distorted Lebesgue measure Differential equations Calculus
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title_auth	A Way to Choquet Calculus
abstract	In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties.
abstractGer	In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties.
abstract_unstemmed	In this paper, we deal with the Choquet integral and derivative with respect to fuzzy measures on the nonnegative real line and present a way to Choquet calculus as a new research paradigm. In Choquet calculus, a representation for calculating the continuous Choquet integral is first given by restricting the integrand to a class of nondecreasing and continuous functions and the fuzzy measure to a class of distorted Lebesgue measures. Next, the derivative of functions with respect to distorted Lebesgue measures is defined as the inverse operation of the Choquet integral. Then, elementary properties in Choquet calculus are explored. In addition, we clarify the relation of Choquet calculus with fractional calculus, where the fractional Choquet integral and derivative are newly defined. In addition, we consider differential equations with respect to distorted Lebesgue measures and give their solutions. Finally, we introduce conditional distorted Lebesgue measures and explore their properties.
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title_short	A Way to Choquet Calculus
url	http://dx.doi.org/10.1109/TFUZZ.2014.2362148 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6918497 http://search.proquest.com/docview/1729225354
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doi_str	10.1109/TFUZZ.2014.2362148
up_date	2024-07-03T17:52:50.530Z
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