### Abstract

Based on a minimal set of axioms we introduce a general integral which can be defined on arbitrary measurable spaces. It acts on measures which are only (finite) monotone set functions and on measurable functions whose range is contained in the unit interval. We introduce the notion of integral equivalence of pairs of measures and functions which leads us to a special important general integrals called universal integral. Several special types of such functionals, including extremal ones, are characterized.

Original language | English |
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Title of host publication | New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference |

Pages | 253-256 |

Number of pages | 4 |

Volume | 1 |

Publication status | Published - 2007 |

Event | 5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007 - Ostrava, Czech Republic Duration: Sep 11 2007 → Sep 14 2007 |

### Other

Other | 5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007 |
---|---|

Country | Czech Republic |

City | Ostrava |

Period | 9/11/07 → 9/14/07 |

### Keywords

- Choquet integral
- General integral
- Integral equivalence
- Monotone set function
- Semicopula
- Universal integral

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Information Systems

### Cite this

*New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference*(Vol. 1, pp. 253-256)

**A universal integral.** / Klement, Erich Peter; Mesiar, Radko; Pap, E.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference.*vol. 1, pp. 253-256, 5th Conference of the European Society for Fuzzy Logic and Technology, EUSFLAT 2007, Ostrava, Czech Republic, 9/11/07.

}

TY - GEN

T1 - A universal integral

AU - Klement, Erich Peter

AU - Mesiar, Radko

AU - Pap, E.

PY - 2007

Y1 - 2007

N2 - Based on a minimal set of axioms we introduce a general integral which can be defined on arbitrary measurable spaces. It acts on measures which are only (finite) monotone set functions and on measurable functions whose range is contained in the unit interval. We introduce the notion of integral equivalence of pairs of measures and functions which leads us to a special important general integrals called universal integral. Several special types of such functionals, including extremal ones, are characterized.

AB - Based on a minimal set of axioms we introduce a general integral which can be defined on arbitrary measurable spaces. It acts on measures which are only (finite) monotone set functions and on measurable functions whose range is contained in the unit interval. We introduce the notion of integral equivalence of pairs of measures and functions which leads us to a special important general integrals called universal integral. Several special types of such functionals, including extremal ones, are characterized.

KW - Choquet integral

KW - General integral

KW - Integral equivalence

KW - Monotone set function

KW - Semicopula

KW - Universal integral

UR - http://www.scopus.com/inward/record.url?scp=58049220934&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58049220934&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:58049220934

SN - 9788073683863

VL - 1

SP - 253

EP - 256

BT - New Dimensions in Fuzzy Logic and Related Technologies - Proceedings of the 5th EUSFLAT 2005 Conference

ER -