Relevant bibliographies by topics / Ordinality

Academic literature on the topic 'Ordinality'

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Published: 10 December 2022
Last updated: 10 March 2023

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Journal articles on the topic "Ordinality"

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Ryder, John. "The Implications of Ordinality." Newsletter of the Society for the Advancement of American Philosophy 32, no. 98 (2004): 19–23. http://dx.doi.org/10.5840/saap200432986.

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Wallace, Kathleen. "Ontological Parity and/or Ordinality?" Metaphilosophy 30, no. 4 (October 1999): 302–18. http://dx.doi.org/10.1111/1467-9973.00140.

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Currie, Martin, and Ian Steedman. "The Ordinality of Effort Revisited." Metroeconomica 48, no. 3 (October 1997): 306–9. http://dx.doi.org/10.1111/1467-999x.00036.

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Mertens, Jean-Fran�ois. "Ordinality in non cooperative games." International Journal of Game Theory 32, no. 3 (June 1, 2004): 387–430. http://dx.doi.org/10.1007/s001820400166.

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Mandler, Michael. "Cardinality versus Ordinality: A Suggested Compromise." American Economic Review 96, no. 4 (August 1, 2006): 1114–36. http://dx.doi.org/10.1257/aer.96.4.1114.

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By taking sets of utility functions as primitive, we define an ordering over assumptions on utility functions that gauges their measurement requirements. Cardinal and ordinal assumptions constitute two levels of measurability, but other assumptions lie between these extremes. We apply the ordering to explanations of why preferences should be convex. The assumption that utility is concave qualifies as a compromise between cardinality and ordinality, while the Arrow-Koopmans explanation, supposedly an ordinal theory, relies on utilities in the cardinal measurement class. In social choice theory, a concavity compromise between ordinality and cardinality is also possible and rationalizes the core utilitarian policies.
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Mandler, Michael. "Cardinality versus Ordinality: A Suggested Compromise." American Economic Review 96, no. 4 (September 1, 2006): 1114–36. http://dx.doi.org/10.1257/000282806779468616.

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Vámos, Tas I. F., Maria C. Tello-Ramos, T. Andrew Hurly, and Susan D. Healy. "Numerical ordinality in a wild nectarivore." Proceedings of the Royal Society B: Biological Sciences 287, no. 1930 (July 8, 2020): 20201269. http://dx.doi.org/10.1098/rspb.2020.1269.

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Ordinality is a numerical property that nectarivores may use to remember the specific order in which to visit a sequence of flowers, a foraging strategy also known as traplining. In this experiment, we tested whether wild, free-living rufous hummingbirds ( Selasphorus rufus ) could use ordinality to visit a rewarded flower. Birds were presented with a series of linear arrays of 10 artificial flowers; only one flower in each array was rewarded with sucrose solution. During training, birds learned to locate the correct flower independent of absolute spatial location. The birds' accuracy was independent of the rewarded ordinal position (1st, 2nd, 3rd or 4th), which suggests that they used an object-indexing mechanism of numerical processing, rather than a magnitude-based system. When distance cues between flowers were made irrelevant during test trials, birds could still locate the correct flower. The distribution of errors during both training and testing indicates that the birds may have used a so-called working up strategy to locate the correct ordinal position. These results provide the first demonstration of numerical ordinal abilities in a wild vertebrate and suggest that such abilities could be used during foraging in the wild.
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Vermeulen, A. J., and M. J. M. Jansen. "Ordinality of solutions of noncooperative games." Journal of Mathematical Economics 33, no. 1 (February 2000): 13–34. http://dx.doi.org/10.1016/s0304-4068(99)00011-7.

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Harkleroad, Leon, and Harry Gonshor. "The ordinality of additively generated sets." Algebra Universalis 27, no. 4 (December 1990): 507–10. http://dx.doi.org/10.1007/bf01188996.

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Gauthier, Baptiste, Karin Pestke, and Virginie van Wassenhove. "Building the Arrow of Time… Over Time: A Sequence of Brain Activity Mapping Imagined Events in Time and Space." Cerebral Cortex 29, no. 10 (December 19, 2018): 4398–414. http://dx.doi.org/10.1093/cercor/bhy320.

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Abstract When moving, the spatiotemporal unfolding of events is bound to our physical trajectory, and time and space become entangled in episodic memory. When imagining past or future events, or being in different geographical locations, the temporal and spatial dimensions of mental events can be independently accessed and manipulated. Using time-resolved neuroimaging, we characterized brain activity while participants ordered historical events from different mental perspectives in time (e.g., when imagining being 9 years in the future) or in space (e.g., when imagining being in Cayenne). We describe 2 neural signatures of temporal ordinality: an early brain response distinguishing whether participants were mentally in the past, the present or the future (self-projection in time), and a graded activity at event retrieval, indexing the mental distance between the representation of the self in time and the event. Neural signatures of ordinality and symbolic distances in time were distinct from those observed in the homologous spatial task: activity indicating spatial order and distances overlapped in latency in distinct brain regions. We interpret our findings as evidence that the conscious representation of time and space share algorithms (egocentric mapping, distance, and ordinality computations) but different implementations with a distinctive status for the psychological “time arrow.”
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Dissertations / Theses on the topic "Ordinality"

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PICOZZI, MARTA ANNA ELENA. "Ordinal knowledge and spatial coding of continuous and discrete quantities in infancy." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2010. http://hdl.handle.net/10281/7794.

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An important issue in human cognition concerns the origins and nature of the capacity to represent number. A great deal of research has focused on infants’ comprehension of the cardinal properties of number but another essential component of the concept of number is ordinality, which refers to the inherent “greater than” or “less than” relationships between numbers. Until recently, the development of this aspect of human numerical cognition in infancy had received little attention. while little is know. The aim of the current series of studies was to investigate whether the ability to appreciate ordinal relationships between numerical magnitudes is present in preverbal infants at an earlier age than previously reported. The current investigation thus includes a series of 6 experiments conducted with infants of 4 and 7 months of age and provides evidence for the debate about functional affordances of infants’ numerical representation, demonstrating that, under certain conditions, the ability to detect and grasp ordinal information embedded in non-numerical and numerical sequences of visual stimuli could be present early in infancy, at respectively 4 months and 7 months of age. Importantly, this study provided also evidence that account for the existence of a basic mapping of number to space the presence, showing that 7-month-old infants are able to link oriented spatial codes to representations of numerical magnitude.
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Rugani, Rosa. "At the root of number competence. Meta-analysis of literature on different animal species and an experimental contribution to the understanding of rudimental numerical abilities in an animal model, the young domestic chick (gallus gallus)." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3426394.

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Davis and Pérusse (1988) argued that, although animals can be trained to make numerical discriminations, they do so only as a last-resort strategy, when extensive training is provided and all other cues are eliminated. In spite of this criticism, in the last decade various types of numerical competences have been demonstrated in nonverbal creatures - namely pre-verbal infants and non-human species - that demonstrated the presence of number competence in the absence of language (reviews in Gallistel and Gelman, 1992; Dehaene, 1997; Hauser and Spelke, 2004). In the present study three separate sets of experiments were carried out to investigate respectively: Spontaneous numerical discrimination following imprinting, number discrimination using a conditioning procedure and ordinal numerical competence. In the first set of experiments, by employing a spontaneous choice paradigm, the ability to discriminate small sets of objects was confirmed in 3-day-old-chicks even when the continuous variables were controlled for. These data showed, for the first time, that spontaneous number discrimination can be based on numerical cues only. In the second set of experiment, chicks' ability to discriminate between small sets of object (up to 3) was confirmed by employing operant conditioning procedures. What is interesting is that although training was done with only one specific set of stimuli, in which number co-varied with several continuous physical variables, the chicks seemed to encode number rather than physical variables. These data also provided the first evidence of numerical discrimination of partly occluded objects. Furthermore, discrimination of small numerosities in young chicks seems to be carried out using an Object File System, with a set-size limit of around 4 elements. In the third set of experiments investigating ordinal abilities show that 5-day-old-chicks can successfully learn to identify a target on the exclusive basis of its serial position in a series of 10. A peculiar finding, in Experiment 4.3, was that whenever position had to be identified on a left/right oriented series, in the generalization test, chicks would more often find the correct position by starting from the left end of the series rather than from the right end. In the absence of environmental asymmetries a possible explanation would be that there is a right hemispheric dominance (left visual hemifield) for this sort of task. It would be interesting for future experiments to establish the limit of such ordinal ability, using a different apparatus with more positions as well as trying to understand the hemispheric asymmetry raised in this experiment. All these data demonstrated the presence of rudimentary numerical competence even in a species so distant and so different from humans. These results support the hypothesis that numerical competences are not only a prerogative of adult humans but that such abilities should have an evolutionary precursor in animals.
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Sibilano, Marialisa. "Numeri ordinali e cardinali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2010. http://amslaurea.unibo.it/1269/.

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Bulgarelli, Carlotta. "Numeri ordinali e cardinali nella teoria di Von Neumann-Bernays-Gödel." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2012. http://amslaurea.unibo.it/3801/.

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Zagagnin, Giulia <1995&gt. "Il modello CUB per comprendere i dati ordinali: il caso delle attrazioni turistiche a Venezia." Master's Degree Thesis, Università Ca' Foscari Venezia, 2020. http://hdl.handle.net/10579/16745.

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L’indagine sulle preferenze dei turisti in merito ad attrazioni e luoghi d’interesse è una pratica comune, utile sia a chi offre servizi, sia ai turisti. Il modo in cui le preferenze vengono espresse può essere condizionato da diversi fattori: di conseguenza, la valutazione espressa non dipende solamente dalla preferenza. Molti sono, nella letteratura, i modelli utilizzati per l’analisi dei dati ordinali derivanti da indagini sulle preferenze degli individui. Il modello CUB è tra questi e nasce con lo scopo di individuare, nelle valutazioni dei rispondenti, una componente di incertezza e una di effettiva preferenza. In particolare, l’obiettivo di questo elaborato è quello di analizzare le valutazioni espresse per i luoghi di interesse a Venezia, comprendendone le motivazioni alla base. I dati sono stati ricavati dal database del sito web TripAdvisor, piattaforma di riferimento per le recensioni online. All’interno di questo database, oltre alle valutazioni espresse dagli individui, sono presenti caratteristiche personali quali il genere e l’età. Risulta utile, questo, a effettuare una profilazione degli individui e a comprendere se esistono variabili che influiscono nella valutazione: il modello CUB permette, infatti, di introdurle nel modello e, così, analizzare la loro significatività.
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Ruaro, Lorenzo. "Cardinalità di insiemi e numeri cardinali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10081/.

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Carpani, Giacomo. "Cantor e l'aritmetica transfinita." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13445/.

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In quest’elaborato poniamo l’attenzione in particolare sul concetto di “numero transfinito” riferendoci direttamente alle intuizioni fondamentali di Georg Cantor. Punto di partenza sono quindi le idee e i risultati del matematico tedesco, che hanno aperto la strada alle teorie dei numeri ordinali e dei numeri cardinali, che noi esponiamo in chiave moderna assumendo la teoria degli insiemi Zermelo-Fraenkel. Nelle conclusioni, per illustrare gli sviluppi e l’importanza delle riflessioni di Cantor al giorno d’oggi, diamo alcuni accenni in merito all’ipotesi generalizzata del continuo e ai grandi cardinali.
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Baccelli, Jean. "Essais d'analyse de la théorie axiomatique de la décision." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE002.

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Cette thèse rassemble trois essais sur la théorie axiomatique de la décision.Ils relèvent principalement de l’analyse épistémologique de cette théorie.Le premier essai, “Les limites de l’ordinalisme”, concerne la doctrine ordinaliste,qui a joué un rôle important dans la constitution de la théoriemicro-économique contemporaine. Dans un premier temps, nous définissonsabstraitement cette doctrine. Nous la caractérisons par la thèse suivant laquelledes données de choix ne peuvent pas rendre empiriquement signifiantesles propriétés non-ordinales de l’utilité. Dans un second temps, nous évaluonscette thèse, la confrontant à divers développements de la théorie de la décision,qui paraissent la remettre en cause. Nous montrons que, malgré lesapparences, cette thèse n’est pas remise en cause par les développementsthéoriques que nous étudions.Le deuxième essai, “L’analyse axiomatique et l’attitude par rapport aurisque”, porte sur le statut, en théorie de la décision, des concepts d’attitudepar rapport au risque. A première vue, l’analyse axiomatique n’exploite pasces idées-là. Ceci reflète une certaine neutralité des modèles de décision ausujet de l’attitude par rapport au risque. Mais un examen plus poussé permetde mettre en valeur ce que nous nommons la variation conditionnelle et lerenforcement de l’attitude par rapport au risque, établissant par là mêmel’importance axiomatique des concepts d’attitude par rapport au risque.Le troisième essai, “Les paris révèlent-ils les croyances ?”, examine la méthodeconsistant à identifier les croyances d’un agent à partir de ses préférences.Nous nous concentrons sur l’obstacle principal auquel cette méthodeest exposée, à savoir, le problème de l’utilité dépendante des états. En premierlieu, nous illustrons ce problème de manière détaillée, distinguant quatreformes de dépendance de l’utilité aux états. En second lieu, nous présentonset discutons une stratégie permettant, malgré la possibilité d’une telle dépendance,d’identifier les croyances. Cependant, pour résoudre ainsi le problème,il faut laisser la préférence s’étendre au-delà du choix. Nous défendons quetel doit être le cas dans toute solution complète au problème de l’utilitédépendante des états. Nous affirmons aussi que c’est là la principale leçonconceptuelle à tirer de ce problème, et montrons qu’elle intéresse tant leséconomistes que les philosophes
This thesis consists of three essays on axiomatic decision theory. Theybelong primarily to the epistemological analysis of decision theory.The first essay, “The limits of ordinalism”, focuses on ordinalism, a doctrinethat was instrumental in the constitution of contemporary microeconomictheory. First, I provide an abstract definition of this doctrine.I characterize it by the following claim: if the underlying data are choicedata, then no non-ordinal property of utility can be empirically meaningful.Second, I evaluate the above claim. I confront this claim with variousdecision-theoretic developments which seem to question its validity. I showthat, despite appearances, this claim is not challenged by the theoreticaldevelopments in question.The second essay, “Axiomatic analysis and risk attitudes”, examines thestatus of risk attitude concepts in decision theory. At first sight, axiomaticanalysis does not rely on these concepts. This indicates a certain neutrality ofdecision models regarding risk attitudes. Further analysis, however, leads oneto recognize the importance of what I call the conditional variation and thestrengthening of risk attitudes. This establishes the axiomatic significance ofrisk attitude concepts.The third essay, “Do bets reveal beliefs?”, examines the preference-basedapproach to the identification of beliefs. It focuses on the main problem towhich this approach is exposed, namely state-dependent utility. First, theproblem is illustrated in full detail. Four types of state-dependent utility issuesare distinguished. Second, a strategy for identifying beliefs under statedependentutility is presented and discussed. For the problem to be solvedfollowing this strategy, however, preferences need to extend beyond choices. Iargue that this is a necessary feature of any complete solution to the problemof state-dependent utility. I also claim that this is the main conceptuallesson to draw from this problem. I explain why this lesson is of interest toeconomists and philosophers alike
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Books on the topic "Ordinality"

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Kent, Alan M. Out of the ordinalia. St Austell: Lyonesse, 1995.

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Morton, Nance R., and Smith A. S. D, eds. The Cornish Ordinalia, first play: Origo Mundi. Redruth: Agan Tavas, 2001.

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M, Kent Alan, and Murdoch Brian 1944-, eds. Ordinalia: The Cornish mystery plays cycle : a verse translation. London: Francis Boutle Pub., 2005.

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Sandercock, Graham. Cornish Ordinalia. 2nd ed. Cornish Language Board, 1995.

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Longsworth, Robert. The Cornish Ordinalia. Harvard University Press, 2014.

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Longsworth, Robert. Cornish Ordinalia: Religion and Dramaturgy. Harvard University Press, 2013.

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The Ordinalia Trust: A vision for the future, an inspiration from the past. Truro (Nancemellyn, Perranwell Station, Truro, Cornwall): Ordinalia Trust, 1996.

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Clark, Andrew. SWB as a Measure of Individual Well-Being. Edited by Matthew D. Adler and Marc Fleurbaey. Oxford University Press, 2016. http://dx.doi.org/10.1093/oxfordhb/9780199325818.013.17.

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There is much discussion about using subjective well-being measures as inputs into a social welfare function, which will tell us how well societies are doing. But we have (many) more than one measure of subjective well-being. This chapter considers examples of three of the main types (life satisfaction, affect, and eudaimonia) in three European surveys. These are quite strongly correlated with each other, and are correlated with explanatory variables in pretty much the same manner. The chapter provides an overview of a recent literature that has compared how well different subjective well-being measures predict future behavior, and addresses the issue of the temporality of well-being measures, and whether they should be analyzed ordinally or cardinally.
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Ray, Edwards. Notes on the meaning and use of words based on examination of the Charter Fragment, the Passion Poem, the Ordinalia, Bywnans Meryasek, Creation of the World and Tregear. Kesva an Taves Kernewek (Cornish Language Board), 1997.

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Book chapters on the topic "Ordinality"

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Scarf, Damian. "Ordinality." In Encyclopedia of Animal Cognition and Behavior, 1–4. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-47829-6_766-1.

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Scarf, Damian. "Ordinality." In Encyclopedia of Animal Cognition and Behavior, 4840–43. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-319-55065-7_766.

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von Auer, Ludwig. "Conditions for Stability, Ordinality, and Contractibility." In Lecture Notes in Economics and Mathematical Systems, 151–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-642-58879-2_10.

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Sinclair, Nathalie, and Alf Coles. "Returning to Ordinality in Early Number Sense: Neurological, Technological and Pedagogical Considerations." In Mathematics Education in the Digital Era, 39–58. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61488-5_3.

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Ahmad, Amir, and Gavin Brown. "Random Ordinality Ensembles $\colon$ A Novel Ensemble Method for Multi-valued Categorical Data." In Multiple Classifier Systems, 222–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02326-2_23.

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Bloklander, Lucien, and Albert Bock. "Ordinalia." In Kindlers Literatur Lexikon (KLL), 1–2. Stuttgart: J.B. Metzler, 2020. http://dx.doi.org/10.1007/978-3-476-05728-0_14928-1.

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Abrusci, Vito Michele, and Lorenzo Tortora de Falco. "Gli ordinali." In UNITEXT, 265–346. Milano: Springer Milan, 2018. http://dx.doi.org/10.1007/978-88-470-3968-1_6.

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Ng, Yew-Kwang. "What is Happiness? Why is Happiness Important?" In Happiness—Concept, Measurement and Promotion, 1–14. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4972-8_1.

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AbstractThe (net) happiness (or welfare) of an individual is the excess of her positive affective feelings over negative ones. This subjective definition of happiness is more consistent with common usage and analytically more useful. Over the past century or so, both psychology and economics has gone through the anti-subjectivism revolution (behaviorism in psychology and ordinalism in economics) but has come back to largely accept subjectivism (cognitive psychology and recent interest of economists on happiness issues).
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Hagen, Ole. "Expected Utility Theory and Ordinalism. A Political Marriage." In Risk, Decision and Rationality, 209–20. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-4019-2_14.

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Tangian, Andranik. "A Unified Model for Cardinally and Ordinally Constructing Quadratic Objective Functions." In Lecture Notes in Economics and Mathematical Systems, 117–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-56038-5_8.

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Conference papers on the topic "Ordinality"

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Mogi, Wataru, and Masaaki Shinohara. "Ordinality Consistency Test About Items and Notation Of a Pairwise Comparison Matrix In AHP." In The International Symposium on the Analytic Hierarchy Process. Creative Decisions Foundation, 2009. http://dx.doi.org/10.13033/isahp.y2009.067.

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"BIO-INFORMATICS IN THE LIGHT OF THE MAXIMUM ORDINALITY PRINCIPLE - The Case of Duchenne Muscular Dystrophy." In International Conference on Bioinformatics Models, Methods and Algorithms. SciTePress - Science and and Technology Publications, 2011. http://dx.doi.org/10.5220/0003273002440250.

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Paul, Rohan, Jacob Arkin, Nicholas Roy, and Thomas M. Howard. "Grounding Abstract Spatial Concepts for Language Interaction with Robots." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/696.

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Our goal is to develop models that allow a robot to understand or ``ground" natural language instructionsin the context of its world model. Contemporary approaches estimate correspondences between an instruction and possible candidate groundings such as objects, regions and goals for a robot's action. However, these approaches are unable to reason about abstract or hierarchical concepts such as rows, columns and groups that are relevant in a manipulation domain. We introduce a probabilistic model that incorporates an expressive space of abstract spatial concepts as well as notions of cardinality and ordinality. Abstract concepts are introduced as explicit hierarchical symbols correlated with concrete groundings. Crucially, the abstract groundings form a Markov boundary over concrete groundings, effectively de-correlating them from the remaining variables in the graph which reduces the complexity of training and inference in the model. Empirical evaluation demonstrates accurate grounding of abstract concepts embedded in complex natural language instructions commanding a robot manipulator. The proposed inference method leads to significant efficiency gains compared to the baseline, with minimal trade-off in accuracy.
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Sanu, Joseph, Mingbin Xu, Hui Jiang, and Quan Liu. "Word Embeddings based on Fixed-Size Ordinally Forgetting Encoding." In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2017. http://dx.doi.org/10.18653/v1/d17-1031.

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Doignon, Jean-Paul, Stefano Moretti, and Meltem Ozturk. "On the Ordinal Invariance of Power Indices on Coalitional Games." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/37.

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In a coalitional game, the coalitions are weakly ordered according to their worths in the game. When moreover a power index is given, the players are ranked according to the real numbers they are assigned by the power index. If any game inducing the same ordering of the coalitions generates the same ranking of the players then, by definition, the game is (ordinally) stable for the power index, which in turn is ordinally invariant for the game. If one is interested in ranking players of a game which is stable, re-computing the power indices when the coalitional worths slightly fluctuate or are uncertain becomes useless. Bivalued games are easy examples of games stable for any power index which is linear. Among general games, we characterize those that are stable for a given linear index. Note that the Shapley and Banzhaf scores, frequently used in AI, are particular semivalues, and all semivalues are linear indices. To check whether a game is stable for a specific semivalue, it suffices to inspect the ordering of the coalitions and to perform some direct computation based on the semivalue parameters.
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Watcharawittayakul, Sedtawut, Mingbin Xu, and Hui Jiang. "Dual Fixed-Size Ordinally Forgetting Encoding (FOFE) for Competitive Neural Language Models." In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing. Stroudsburg, PA, USA: Association for Computational Linguistics, 2018. http://dx.doi.org/10.18653/v1/d18-1502.

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Zhang, ShiLiang, Hui Jiang, MingBin Xu, JunFeng Hou, and LiRong Dai. "The Fixed-Size Ordinally-Forgetting Encoding Method for Neural Network Language Models." In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 2: Short Papers). Stroudsburg, PA, USA: Association for Computational Linguistics, 2015. http://dx.doi.org/10.3115/v1/p15-2081.

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Kamikawa, Kyohei, Keisuke Maeda, Takahiro Ogawa, and Miki Haseyama. "Feature Integration via Semi-Supervised Ordinally Multi-Modal Gaussian Process Latent Variable Model." In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2021. http://dx.doi.org/10.1109/icassp39728.2021.9414109.

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9

Maeda, Keisuke, Sho Takahashi, Takahiro Ogawa, and Miki Haseyama. "Neural Network Maximizing Ordinally Supervised Multi-View Canonical Correlation for Deterioration Level Estimation." In 2019 IEEE International Conference on Image Processing (ICIP). IEEE, 2019. http://dx.doi.org/10.1109/icip.2019.8803038.

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10

Chen, Jiehua, Sanjukta Roy, and Manuel Sorge. "Fractional Matchings under Preferences: Stability and Optimality." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/13.

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Abstract:
We study generalizations of stable matching in which agents may be matched fractionally; this models time-sharing assignments. We focus on the so-called ordinal stability and cardinal stability, and investigate the computational complexity of finding an ordinally stable or cardinally stable fractional matching which either maximizes the social welfare (i.e., the overall utilities of the agents) or the number of fully matched agents (i.e., agents whose matching values sum up to one). We complete the complexity classification of both optimization problems for both ordinal stability and cardinal stability, distinguishing between the marriage (bipartite) and roommates (non-bipartite) cases and the presence or absence of ties in the preferences. In particular, we prove a surprising result that finding a cardinally stable fractional matching with maximum social welfare is NP-hard even for the marriage case without ties. This answers an open question and exemplifies a rare variant of stable marriage that remains hard for preferences without ties. We also complete the picture of the relations of the stability notions and derive structural properties.
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