Parametrized preference structures and some geometrical interpretation

J. Fodor, Marc Roubens

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Order structures such as linear orders, semiorders and interval orders are often used to model preferences in decision-making problems. In this paper we introduce a family of preference structures where the mutual indifference threshold belongs to a specific family parametrized by extended reals α. This family includes interval orders (α=1), tangent circle orders (α=0) and a new preference structure called ‘diamond order’ (α=-∞). All these preference relations present an asymmetric part which is shown to be always quasi-transitive and to be transitive for α > 1. Diamond orders present ‘forbidden configurations’ which can occur in the case of tangent circle orders.

Original languageEnglish
Pages (from-to)253-258
Number of pages6
JournalJournal of Multi-Criteria Decision Analysis
Volume6
Issue number5
DOIs
Publication statusPublished - Jan 1 1997

Fingerprint

Diamond
Preference structure
Interval order
Preference relation
Indifference
Semiorder
Decision making

Keywords

  • Co-comparability orders
  • Intransitive preferences
  • Ordering
  • Preference modelling
  • Tangent circle orders

ASJC Scopus subject areas

  • Decision Sciences(all)
  • Strategy and Management

Cite this

Parametrized preference structures and some geometrical interpretation. / Fodor, J.; Roubens, Marc.

In: Journal of Multi-Criteria Decision Analysis, Vol. 6, No. 5, 01.01.1997, p. 253-258.

Research output: Contribution to journalArticle

@article{4b10ee28d3484d3893f75cc70f7584ff,
title = "Parametrized preference structures and some geometrical interpretation",
abstract = "Order structures such as linear orders, semiorders and interval orders are often used to model preferences in decision-making problems. In this paper we introduce a family of preference structures where the mutual indifference threshold belongs to a specific family parametrized by extended reals α. This family includes interval orders (α=1), tangent circle orders (α=0) and a new preference structure called ‘diamond order’ (α=-∞). All these preference relations present an asymmetric part which is shown to be always quasi-transitive and to be transitive for α > 1. Diamond orders present ‘forbidden configurations’ which can occur in the case of tangent circle orders.",
keywords = "Co-comparability orders, Intransitive preferences, Ordering, Preference modelling, Tangent circle orders",
author = "J. Fodor and Marc Roubens",
year = "1997",
month = "1",
day = "1",
doi = "10.1002/(SICI)1099-1360(199709)6:5<253::AID-MCDA153>3.0.CO;2-S",
language = "English",
volume = "6",
pages = "253--258",
journal = "Journal of Multi-Criteria Decision Analysis",
issn = "1057-9214",
publisher = "John Wiley and Sons Ltd",
number = "5",

}

TY - JOUR

T1 - Parametrized preference structures and some geometrical interpretation

AU - Fodor, J.

AU - Roubens, Marc

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Order structures such as linear orders, semiorders and interval orders are often used to model preferences in decision-making problems. In this paper we introduce a family of preference structures where the mutual indifference threshold belongs to a specific family parametrized by extended reals α. This family includes interval orders (α=1), tangent circle orders (α=0) and a new preference structure called ‘diamond order’ (α=-∞). All these preference relations present an asymmetric part which is shown to be always quasi-transitive and to be transitive for α > 1. Diamond orders present ‘forbidden configurations’ which can occur in the case of tangent circle orders.

AB - Order structures such as linear orders, semiorders and interval orders are often used to model preferences in decision-making problems. In this paper we introduce a family of preference structures where the mutual indifference threshold belongs to a specific family parametrized by extended reals α. This family includes interval orders (α=1), tangent circle orders (α=0) and a new preference structure called ‘diamond order’ (α=-∞). All these preference relations present an asymmetric part which is shown to be always quasi-transitive and to be transitive for α > 1. Diamond orders present ‘forbidden configurations’ which can occur in the case of tangent circle orders.

KW - Co-comparability orders

KW - Intransitive preferences

KW - Ordering

KW - Preference modelling

KW - Tangent circle orders

UR - http://www.scopus.com/inward/record.url?scp=0009751523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009751523&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1099-1360(199709)6:5<253::AID-MCDA153>3.0.CO;2-S

DO - 10.1002/(SICI)1099-1360(199709)6:5<253::AID-MCDA153>3.0.CO;2-S

M3 - Article

AN - SCOPUS:0009751523

VL - 6

SP - 253

EP - 258

JO - Journal of Multi-Criteria Decision Analysis

JF - Journal of Multi-Criteria Decision Analysis

SN - 1057-9214

IS - 5

ER -