### Abstract

The problem of reliable processing of heteroscedastic interval data occupies an important niche among urgent topics of measurement science. The paper is devoted to a combinatorial characterization of so called 'inrankings' which are weak orders induced by input intervals of the interval fusion with preference aggregation (IF&PA) procedure. The procedure transforms the given m initial real line intervals into inrankings, which are a specific case of weak order relations (or rankings) over a set of n discrete values belonging to these intervals. The new notation of inranking appears as a result of restrictions imposed on the ordinary rankings by interval character of the initial data. In the paper, the inranking spaces properties are investigated from the combinatorial theory point of view. It is shown that the inranking space is a subset of the set of all weak orders with a single symbol of strict order. The cardinality of inranking space is defined by the triangle number for the given number n of the discrete elements. Cardinalities of other adjacent spaces are considered.

Original language | English |
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Article number | 012052 |

Journal | Journal of Physics: Conference Series |

Volume | 1379 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Nov 2019 |

Event | Joint IMEKO TC1-TC7-TC13-TC18 Symposium 2019 - St. Petersburg, Russian Federation Duration: 2 Jul 2019 → 5 Jul 2019 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of Physics: Conference Series*,

*1379*(1), [012052]. https://doi.org/10.1088/1742-6596/1379/1/012052