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 |
|---|---|
| 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 |
|---|---|
| Volume | 126 |
| ISSN (Print) | 2198-4182 |
| ISSN (Electronic) | 2198-4190 |
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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
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Completeness property of information quanta. / Noghin, Vladimir D.
Studies in Systems, Decision and Control. Springer, 2018. p. 139-149 (Studies in Systems, Decision and Control; Vol. 126).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 -