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Mathematical topics on representations of ordered structures and utility theory. Essays in honor of Professor Ghanshyam B. Mehta. (English) Zbl 1446.91009
Studies in Systems, Decision and Control 263. Cham: Springer (ISBN 978-3-030-34225-8/hbk; 978-3-030-34226-5/ebook). xxii, 368 p. (2020).

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Publisher’s description: This book offers an essential review of central theories, current research and applications in the field of numerical representations of ordered structures. It is intended as a tribute to Professor Ghanshyam B. Mehta, one of the leading specialists on the numerical representability of ordered structures, and covers related applications to utility theory, mathematical economics, social choice theory and decision-making. Taken together, the carefully selected contributions provide readers with an authoritative review of this research field, as well as the knowledge they need to apply the theories and methods in their own work.
The articles of this volume will be reviewed individually.
Indexed articles:
Beardon, A. F., Topology and preference relations, 3-21 [Zbl 1452.91110]
Candeal, Juan C., The existence and the non-existence of utility functions in order-theoretic, algebraic and topological environments, 23-45 [Zbl 1452.91143]
Campión, María J.; Indurain, Esteban, Open questions in utility theory, 47-81 [Zbl 1452.91142]
Rébillé, Yann, Representations of interval orders on connected separable topological spaces, 85-108 [Zbl 1452.91120]
Estevan, Asier, Searching for a Debreu’s open gap lemma for semiorders, 109-128 [Zbl 1452.91113]
Bouyssou, Denis; Pirlot, Marc, A note on candeal and Induráin’s semiorder separability condition, 129-141 [Zbl 1452.91141]
Bouyssou, Denis; Doignon, Jean-Paul, Chain representations of nested families of biorders, 143-169 [Zbl 07273624]
Chis, C.; Künzi, H.-P. A.; Sanchis, M., A note on representable group topologies, 171-186 [Zbl 07273625]
Cardin, Marta, Preferences in abstract convex structures, 187-195 [Zbl 1452.91112]
Hervés-Beloso, Carlos; Monteiro, Paulo K., Strictly monotonic preferences, 197-209 [Zbl 1452.91115]
Bosi, Gianni; Zuanon, Magalì, Continuity and continuous multi-utility representations of nontotal preorders: some considerations concerning restrictiveness, 213-236 [Zbl 1452.91140]
Caterino, Alessandro; Ceppitelli, Rita; Holá, Lubica, Jointly continuous multi-utility representations of non-total preorders, 237-254 [Zbl 1452.91144]
Kochov, Asen, Subjective states without the completeness axiom, 255-266 [Zbl 1452.91116]
Evren, Özgür, Preference for flexibility: a continuous representation in an ordinal setup, 267-280 [Zbl 1452.91114]
Bridges, Douglas S., The Arrow-Hahn construction in a locally compact metric space, 281-299 [Zbl 1452.91111]
Knoblauch, Vicki, Continuous utility representation of fuzzy preferences, 301-309 [Zbl 1452.91146]
Vázquez, Carmen, Ranking opportunity sets taking into account similarity relations induced by money-metric utility functions, 313-324 [Zbl 1452.91147]
Alcantud, José Carlos R.; Giarlotta, Alfio, The interplay between intergenerational justice and mathematical utility theory, 325-351 [Zbl 1452.91137]
Quiggin, John; Chambers, Robert G., Comparative risk aversion for state-dependent preferences, 353-368 [Zbl 1448.91108]

MSC:
91-06 Proceedings, conferences, collections, etc. pertaining to game theory, economics, and finance
91B16 Utility theory
91B08 Individual preferences
91B06 Decision theory
00B15 Collections of articles of miscellaneous specific interest
Biographic References:
Mehta, Ghanshyam B.
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