Interval choice: classic and general cases

Agaev, Rafig; Aleskerov, Fuad

doi:10.1016/0165-4896(93)90022-b

Cited by 34 publications

(17 citation statements)

References 10 publications

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“…However, this interpretation is necessarily but not sufficiently applicable to the bounded real interval representations, since many numerical representational forms have been examined in which the size of a threshold may depend not only on target objects but also on objects under comparison (see, for example, Abbas & Vincke, 1993;Agoev & Aleskerov, 1993;Nakamura, 1990Nakamura, , 2000Rodriguez-Palmero, 1997; and many others).…”

Section: F(a) … G(x)mentioning

confidence: 97%

Real Interval Representations

Nakamura

2002

Journal of Mathematical Psychology

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Section: F(a) … G(x)mentioning

confidence: 97%

Real Interval Representations

Nakamura

2002

Journal of Mathematical Psychology

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“…(This numerical representation is a particular case of the general numerical representation due to Abbas and Vincke (1993) where the function Q is the mutual indifference threshold; the present representation was obtained independently by Agaev and Aleskerov (1993) and Abbas (1994). )…”

Section: Additional Interpretative Elementsmentioning

confidence: 97%

Preference Structures and Co-comparability Graphs

Abbas

Pirlot

Vincke

1996

J. Multi-Crit. Decis. Anal.

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Order structures such as linear orders, weak orders, semiorders and interval orders are often considered as models of a decision maker's preferences. In this paper we introduce and study new order structures characterized by their symmetric part belonging to certain classes of co-comparability graphs. We outline possible interpretations and suggest special representations of these structures and we point out their potential use for approximating relations obtained through a multicriteria aggregation procedure. We provide various characterizations of the new structures (as well as of older ones) in terms of minimal forbidden configurations and by algebraic conditions.

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“…That means that for the decreasing sequence (3 + 1 n ) n∈N that converges to 3 in R -but it converges to 2 in S 2 endowed with the order topology τ < -, the image sequence (g(3 + 1 n )) n∈N converges to g (2). Since g is also defined on S 1 and it is increasing, it implies that g(x) = g (2) for any x ∈ [2,3]. Therefore, for this example the function g can never be strictly increasing while removing the gap (2,3].…”

Section: Introductionmentioning

confidence: 96%

“…The reason is that, if the function g would remove the gaps of S 1 and S 2 , in particular it would remove the gap (2,3] of S 2 . That means that for the decreasing sequence (3 + 1 n ) n∈N that converges to 3 in R -but it converges to 2 in S 2 endowed with the order topology τ < -, the image sequence (g(3 + 1 n )) n∈N converges to g (2).…”

Section: Introductionmentioning

confidence: 97%

Generalized Debreu’s Open Gap Lemma and Continuous Representability of Biorders

Estevan

2015

Order

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We prove a generalization of Debreu's Open Gap Lemma. Given any subset of the real line, this lemma guarantees the existence of a strictly increasing real function such that all the gaps of the image of the subset are open. Now we extend it to the case of n subsets of the real line and study the existence of a strictly increasing real function such that all the gaps of the image of each set are open. This function does not exist in general so, we characterize the cases in which it exists. This generalization is not equivalent to Debreu's lemma working on the union of the n subsets, neither on the intersection. Then we use it in order to obtain new results on continuous representations of biorders. We also generalize the concept of biorder.

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Interval choice: classic and general cases

Cited by 34 publications

References 10 publications

Real Interval Representations

Real Interval Representations

Preference Structures and Co-comparability Graphs

Generalized Debreu’s Open Gap Lemma and Continuous Representability of Biorders

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