Semiorders and thresholds of utility discrimination: Solving the Scott–Suppes representability problem

Candeal, Juan Carlos; Induráin, Esteban

doi:10.1016/j.jmp.2010.06.003

Cited by 30 publications

(40 citation statements)

References 22 publications

(42 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Let ≺ denote a semiorder defined on a nonempty set X. We say that ≺ is representable in the sense of Scott and Suppes (see [40,117]) when there is a real-valued function u : X → R and a strictly positive constant k > 0 such that a ≺ b ⇔ u(a) + k < u(b) holds true for every a, b ∈ X. The pair (u, k) is then said a Scott-Suppes pair representing ≺.…”

Section: Remark 23mentioning

confidence: 99%

See 1 more Smart Citation

A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings

Campión

Gómez‐Polo

Induráin

et al. 2018

Axioms

Self Cite

View full text Add to dashboard Cite

Different abstract versions of entropy, encountered in science, are interpreted in the light of numerical representations of several ordered structures, as total-preorders, interval-orders and semiorders. Intransitivities, other aspects of entropy as competitive systems, additivity, etc., are also viewed in terms of representability of algebraic structures endowed with some compatible ordering. A particular attention is paid to the problem of the construction of an entropy function or their mathematical equivalents. Multidisciplinary comparisons to other similar frameworks are also discussed, pointing out the mathematical foundations.

show abstract

Section: Remark 23mentioning

confidence: 99%

“…The Scott-Suppes representability of semiorders is finally characterized as follows (see, e.g., [117][118][119][120]…”

Section: Remark 23mentioning

confidence: 99%

A Survey on the Mathematical Foundations of Axiomatic Entropy: Representability and Orderings

Campión

Gómez‐Polo

Induráin

et al. 2018

Axioms

Self Cite

View full text Add to dashboard Cite

show abstract

“…Notice that "one mile" acts here as, so-to-say, a threshold of discrimination. A semiorder ≺ on a set X is said to be representable in the sense of Scott and Suppes (see [48,60]) if there exists a real-valued map f : X → R and a strictly positive constant k > 0 such that given x, y ∈ X it holds true that x ≺ y ⇔ f (x) + k < f (y). Notice again that k > 0 acts here as a "quantum" or threshold of discrimination.…”

Section: Suggestions For Further Researchmentioning

confidence: 99%

Entropy of chemical processes versus numerical representability of orderings

et al. 2015

View full text Add to dashboard Cite

Leaning on the mathematical concept of an interval order, we show that intransitivities that appear in several chemical processes, mainly related to mixing and competition, can actually be located and handled within a thermodynamical setting whose basis is the classical axiomatics due to Carathéodory, now using two intertwined entropy functions. Interdisciplinary comparisons to other similar theories (e.g., Utility Theory) are also made, pointing out the common mathematical background based on the numerical representability of total preorders and interval orders.

show abstract

“…Extending them to possibly countably infinite sets and to possibly uncountable sets is an important open problem. The recent breakthrough on the constant threshold representation of semiorders on general sets (Candeal and Induráin, 2010) gives some hope to obtain interpretable results. This will require a proof strategy that is different from the one used here.…”

Section: Theoremmentioning

confidence: 99%