### Abstract

In this chapter, we justify theoretically the original axiomatic approach to Pareto set reduction based on a finite collection of information quanta. Here the exposition seems most difficult in mathematical terms, but the readers with an insufficient background may skip it without losing the comprehension of further material. The whole essence of the results derived below can be expressed as follows. Information in the form of quanta is complete: for any multicriteria choice problem from a definite (rather wide) class, it is possible to find the unknown set of nondominated vectors (nondominated alternatives) with an arbitrary accuracy only based on such information. Moreover, if the number of feasible vectors is finite, then the set of nondominated vectors can be constructed precisely.

Original language | English |
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Title of host publication | Studies in Systems, Decision and Control |

Publisher | Springer |

Pages | 139-149 |

Number of pages | 11 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Publication series

Name | Studies in Systems, Decision and Control |
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Volume | 126 |

ISSN (Print) | 2198-4182 |

ISSN (Electronic) | 2198-4190 |

### Fingerprint

### Scopus subject areas

- Computer Science (miscellaneous)
- Decision Sciences (miscellaneous)
- Economics, Econometrics and Finance (miscellaneous)
- Automotive Engineering
- Control and Systems Engineering
- Control and Optimization
- Social Sciences (miscellaneous)

### Cite this

*Studies in Systems, Decision and Control*(pp. 139-149). (Studies in Systems, Decision and Control; Vol. 126). Springer. https://doi.org/10.1007/978-3-319-67873-3_6

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*Studies in Systems, Decision and Control.*Studies in Systems, Decision and Control, vol. 126, Springer, pp. 139-149. https://doi.org/10.1007/978-3-319-67873-3_6

**Completeness property of information quanta.** / Noghin, Vladimir D.

Research output › › peer-review

TY - CHAP

T1 - Completeness property of information quanta

AU - Noghin, Vladimir D.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this chapter, we justify theoretically the original axiomatic approach to Pareto set reduction based on a finite collection of information quanta. Here the exposition seems most difficult in mathematical terms, but the readers with an insufficient background may skip it without losing the comprehension of further material. The whole essence of the results derived below can be expressed as follows. Information in the form of quanta is complete: for any multicriteria choice problem from a definite (rather wide) class, it is possible to find the unknown set of nondominated vectors (nondominated alternatives) with an arbitrary accuracy only based on such information. Moreover, if the number of feasible vectors is finite, then the set of nondominated vectors can be constructed precisely.

AB - In this chapter, we justify theoretically the original axiomatic approach to Pareto set reduction based on a finite collection of information quanta. Here the exposition seems most difficult in mathematical terms, but the readers with an insufficient background may skip it without losing the comprehension of further material. The whole essence of the results derived below can be expressed as follows. Information in the form of quanta is complete: for any multicriteria choice problem from a definite (rather wide) class, it is possible to find the unknown set of nondominated vectors (nondominated alternatives) with an arbitrary accuracy only based on such information. Moreover, if the number of feasible vectors is finite, then the set of nondominated vectors can be constructed precisely.

UR - http://www.scopus.com/inward/record.url?scp=85030765574&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-67873-3_6

DO - 10.1007/978-3-319-67873-3_6

M3 - Chapter

AN - SCOPUS:85030765574

T3 - Studies in Systems, Decision and Control

SP - 139

EP - 149

BT - Studies in Systems, Decision and Control

PB - Springer

ER -