### Abstract

A notion of a generated chain variation of a set function m with values in [- 1, 1] is proposed. The space BgV of set functions of bounded g-chain variation is introduced and properties of set functions from BgV are discussed. A general Choquet integral of bounded A-measurable function is defined with respect to a set function m ∈ BgV. A constructive method for obtaining this asymmetric integral is considered. A general fuzzy integral of bounded g-variation, comonotone ⊕-additiviteand positive ⊙-homogenous is represented by a general Choquet integral. The representation of a general Choquet integral in terms of a pseudo Lebesque-Stiltjes integral is obtained.

Original language | English |
---|---|

Pages (from-to) | 161-173 |

Number of pages | 13 |

Journal | Acta Polytechnica Hungarica |

Volume | 6 |

Issue number | 1 |

Publication status | Published - 2009 |

### Keywords

- Asymmetric choquet integral
- General fuzzy integral
- Non-monotonic set function
- Symmetric pseudo-operations

### ASJC Scopus subject areas

- General
- Engineering(all)

### Cite this

*Acta Polytechnica Hungarica*,

*6*(1), 161-173.

**Asymmetrie general choquet integrals.** / Mihailović, Biljana; Pap, E.

Research output: Contribution to journal › Article

*Acta Polytechnica Hungarica*, vol. 6, no. 1, pp. 161-173.

}

TY - JOUR

T1 - Asymmetrie general choquet integrals

AU - Mihailović, Biljana

AU - Pap, E.

PY - 2009

Y1 - 2009

N2 - A notion of a generated chain variation of a set function m with values in [- 1, 1] is proposed. The space BgV of set functions of bounded g-chain variation is introduced and properties of set functions from BgV are discussed. A general Choquet integral of bounded A-measurable function is defined with respect to a set function m ∈ BgV. A constructive method for obtaining this asymmetric integral is considered. A general fuzzy integral of bounded g-variation, comonotone ⊕-additiviteand positive ⊙-homogenous is represented by a general Choquet integral. The representation of a general Choquet integral in terms of a pseudo Lebesque-Stiltjes integral is obtained.

AB - A notion of a generated chain variation of a set function m with values in [- 1, 1] is proposed. The space BgV of set functions of bounded g-chain variation is introduced and properties of set functions from BgV are discussed. A general Choquet integral of bounded A-measurable function is defined with respect to a set function m ∈ BgV. A constructive method for obtaining this asymmetric integral is considered. A general fuzzy integral of bounded g-variation, comonotone ⊕-additiviteand positive ⊙-homogenous is represented by a general Choquet integral. The representation of a general Choquet integral in terms of a pseudo Lebesque-Stiltjes integral is obtained.

KW - Asymmetric choquet integral

KW - General fuzzy integral

KW - Non-monotonic set function

KW - Symmetric pseudo-operations

UR - http://www.scopus.com/inward/record.url?scp=74349115712&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74349115712&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:74349115712

VL - 6

SP - 161

EP - 173

JO - Acta Polytechnica Hungarica

JF - Acta Polytechnica Hungarica

SN - 1785-8860

IS - 1

ER -