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Candeal, Juan Carlos; Induráin, Esteban; Oloriz, Esteban

doi:10.1023/a:1018972116366

Annals of Operations Research

1998

DOI: 10.1023/a:1018972116366

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Juan Carlos Candeal

Esteban Induráin²,

Esteban Oloriz³

Abstract: This paper is concerned with the representability of totally ordered semigroups as subsets of the additive real line ‫,ޒ(‬ +, ≤). We prove in an elementary way the existence of an additive utility function.

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Cited by 3 publications

References 10 publications

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Preferences, risk neutrality and risk-sensitive MDPs

Alexander,

Sobel

2024

Ann Oper Res

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A binary preference relation on a real vector space satisfying four (natural) axioms is shown to induce a utility function composed of a linear function to the reals and a weakly monotonic function. The key axiom is decomposition, and the utility function can be taken to be linear if and only if this axiom’s converse is also satisfied. Important consequences follow for risk-sensitive discounted Markov decision processes, decision trees, and the discounted utility model in economics. Since the four axioms imply that preferences correspond to discounting, the four axioms without the converse imply that preferences are consistent with discounting without risk neutrality.

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Preferences, risk neutrality and risk-sensitive MDPs

Alexander,

Sobel

2024

Ann Oper Res

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Interval-Valued Representability of Qualitative Data: The Continuous Case

Bosi

Campión

Candeal

et al. 2007

Int. J. Unc. Fuzz. Knowl. Based Syst.

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In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.

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

Campión

Gómez‐Polo

Induráin

et al. 2018

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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.

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Untitled

Abstract: This paper is concerned with the representability of totally ordered semigroups as subsets of the additive real line ‫,ޒ(‬ +, ≤). We prove in an elementary way the existence of an additive utility function.

Cited by 3 publications

References 10 publications

Preferences, risk neutrality and risk-sensitive MDPs

Preferences, risk neutrality and risk-sensitive MDPs

Interval-Valued Representability of Qualitative Data: The Continuous Case

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

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