Relevant bibliographies by topics / Partial preorder

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Partial preorder'

Author: Grafiati
Published: 4 June 2021
Last updated: 6 February 2022

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Journal articles on the topic "Partial preorder"

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Miller, John Boris. "The natural ordering on a strictly real Banach algebra." Mathematical Proceedings of the Cambridge Philosophical Society 107, no. 3 (May 1990): 539–56. http://dx.doi.org/10.1017/s0305004100068808.

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AbstractA strictly real unital Banach algebra is one in which every element has real spectrum. An antilattice partial order and its associated open-interval topology are defined on by taking as positive cone the principal component of the maximal group of the algebra, and their properties are studied. The topology coincides with the semimetric topology of the spectral radius, which is a seminorm, making into a locally convex partially ordered topological algebra with continuous inversion and normal cone. Every positive element has a unique positive square root, and logarithm, and these functions and exp are continuous and monotone. The cone has the same closure in both open-interval and normal topologies, the closure being a wedge for an associated preorder on , this preorder coinciding with the preorder of Kelley and Vaught. The partial order and the associated preorder have the same dual cone. There is a modified Gelfand representation for (possibly non-commutative) , and a boundary integral representation for functionals in the order dual. The compact convex subset in the dual is metrizable if the cone of the partial order in is separable.
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Zoethout, Jetze. "On (co)products of partial combinatory algebras, with an application to pushouts of realizability toposes." Mathematical Structures in Computer Science 31, no. 2 (February 2021): 214–33. http://dx.doi.org/10.1017/s096012952100013x.

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AbstractWe consider two preorder-enriched categories of ordered partial combinatory algebras: OPCA, where the arrows are functional (i.e., projective) morphisms, and OPCA†, where the arrows are applicative morphisms. We show that OPCA has small products and finite biproducts, and that OPCA† has finite coproducts, all in a suitable 2-categorical sense. On the other hand, OPCA† lacks all nontrivial binary products. We deduce from this that the pushout, over Set, of two nontrivial realizability toposes is never a realizability topos. In contrast, we show that nontrivial subtoposes of realizability toposes are closed under pushouts over Set.
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French, Zack, and James B. Hart. "The predicate completion of a partial information system." Mathematica Slovaca 68, no. 2 (April 25, 2018): 253–70. http://dx.doi.org/10.1515/ms-2017-0098.

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Abstract Originally, partial information systems were introduced as a means of providing a representation of the Smyth powerdomain in terms of order convex substructures of an information-based structure. For every partial information system 𝕊, there is a new partial information system that is natrually induced by the principal lowersets of the consistency predicate for 𝕊. In this paper, we show that this new system serves as a completion of the parent system 𝕊 in two ways. First, we demonstrate that the induced system relates to the parent system 𝕊 in much the same way as the ideal completion of the consistency predicate for 𝕊 relates to the consistency predicate itself. Second, we explore the relationship between this induced system and the notion of D-completions for posets. In particular, we show that this induced system has a “semi-universal” property in the category of partial information systems coupled with the preorder analog of Scott-continuous maps that is induced by the universal property of the D-completion of the principal lowersets of the consistency predicate for the parent system 𝕊.
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Roldán, López, and Naseer Shahzad. "From graphical metric spaces to fixed point theory in binary related distance spaces." Filomat 31, no. 11 (2017): 3209–31. http://dx.doi.org/10.2298/fil1711209r.

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Very recently, many fixed point results have been introduced in the setting of graphical metric spaces. Due to their intimate links, such works also deal with metric spaces endowed with partial orders. As the reachability relationship in any directed graph (containing all cycles) is a reflexive transitive relation (that is, a preorder), but it is not necessarily a partial order, results on graphical metric spaces are independent from statements on ordered metric spaces. The main aim of this paper is to show that fixed point theorems in the setting of graphical metric spaces can be directly deduced from their corresponding results on measurable spaces endowed with a binary relation. Finally, we also describe the main advantages of involving this last class of spaces.
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Ali, Mabruka, Adem Kiliçman, and Azadeh Zahedi Khameneh. "Application of Induced Preorderings in Score Function-Based Method for Solving Decision-Making with Interval-Valued Fuzzy Soft Information." Mathematics 9, no. 13 (July 4, 2021): 1575. http://dx.doi.org/10.3390/math9131575.

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Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods.
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Burdick, Bruce S. "On the use of partial orders in uniform spaces." Applied General Topology 4, no. 1 (April 1, 2003): 99. http://dx.doi.org/10.4995/agt.2003.2013.

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<p>We investigate the use of nets indexed by preorders in uniform spaces. Nine different Cauchy conditions and four different convergence conditions yield 36 completeness properties, each of which turns out to be equivalent to a known form of completeness. We also use these preordered nets to characterize the functors θ, λ, and v, which are associated with these completeness properties. In the case of λ we give an example to show that the analogous characterization with predirected nets does not work.</p>
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Babicová, Dušana. "Probability Integral as a Linearization." Tatra Mountains Mathematical Publications 72, no. 1 (December 1, 2018): 1–15. http://dx.doi.org/10.2478/tmmp-2018-0017.

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Abstract In fuzzified probability theory, a classical probability space (Ω, A, p) is replaced by a generalized probability space (Ω, ℳ(A), ∫(.) dp), where ℳ(A) is the set of all measurable functions into [0,1] and ∫(.)dp is the probability integral with respect to p. Our paper is devoted to the transition from p to ∫(.) dp. The transition is supported by the following categorical argument: there is a minimal category and its epireflective subcategory such that A and ℳ(A) are objects, probability measures and probability integrals are morphisms, ℳ(A) is the epireflection of A, ∫(.) dp is the corresponding unique extension of p, and ℳ(A) carries the initial structure with respect to probability integrals. We discuss reasons why the fuzzy random events are modeled by ℳ(A) equipped with pointwise partial order, pointwise Łukasiewicz operations (logic) and pointwise sequential convergence. Each probability measure induces on classical random events an additive linear preorder which helps making decisions. We show that probability integrals can be characterized as the additive linearizations on fuzzy random events, i.e., sequentially continuous maps, preserving order, top and bottom elements.
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Petrović, Marijana, Nataša Bojković, Mladen Stamenković, and Ivan Anić. "A Sensitivity Analysis of ELECTRE Based Stepwise Benchmarking for Policy: the Case of EU Digital Agenda." Management:Journal of Sustainable Business and Management Solutions in Emerging Economies 23, no. 2 (March 6, 2018): 57. http://dx.doi.org/10.7595/management.fon.2018.0003.

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Research question: This paper introduces a new parameter for evaluating the sensitivity of development paths in ELECTRE (ELimination Et Choix Traduisant la Realité) based stepwise benchmarking model. Motivation: The aim of the research was to devise a 'path sensitivity coefficient' which measures the sensitivity of a development path depending on parameters set by decision-maker (DM). The need for such measure comes from the fact that the hierarchical pre-order of benchmarking units are affected by the DM's subjective decisions on the threshold for declaring outranking relations among them. This consequently may disrupt the sequence of intermediate benchmarks - transitional targets to be followed on the route to the ultimate policy goals. The proposed approach is an extension of a stepwise benchmarking procedure devised by Petrovic et al. (2014) which evaluates development paths based on their gradualism. Idea: In this paper, we propose to characterize development paths by considering both gradualism and sensitivity to outranking thresholds. The standpoint of our research is that in order to make a reliable final choice the DM should be aware that the most gradual path is not necessary the most stable one. Tools: The proposed 'path sensitivity coefficient' combines four level of uncertainty coming from two threshold values set by DM. The coefficient has a relative nature, it points to the “distance” from the theoretically ideal solution - a path fully indifferent to threshold values. An approach to merge coefficients associated with gradualism and stability is also introduced. Data: To illustrate the proposed approach we applied it in the field of digital transformation of EU countries. We exploited indicators and data from Digital Agenda Scoreboard regarding specific policy goals to be achieved until 2020. Findings: The findings imply that the decision on the most gradual development path should be reconsidered in regards to the influence of model parameters. The final choice depends whether DM’s prefers the smoothness of the path or the overall stability in terms of underlying partial preorder. Contribution: This work contributes to the existing ELECTRE-based stepwise benchmarking by reducing the uncertainty coming from subjective parameterization and allows the DM to be more confident in the final path selection.
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Carosi, L., and A. Zaffaroni. "On the existence of maximal elements for partial preorders." Journal of Information and Optimization Sciences 20, no. 2 (May 1999): 271–86. http://dx.doi.org/10.1080/02522667.1999.10699417.

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Xu, Xiaozhan, Jean-Marc Martel, and Bernard F. Lamond. "A multiple criteria ranking procedure based on distance between partial preorders." European Journal of Operational Research 133, no. 1 (August 2001): 69–80. http://dx.doi.org/10.1016/s0377-2217(00)00184-3.

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Dissertations / Theses on the topic "Partial preorder"

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Serayet, Mariette. "Raisonnement à partir d'informations structurées et hiérarchisées : application à l'information archéologique." Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22032/document.

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La thèse s'inscrit dans le cadre du projet européen VENUS. Dans ce contexte, la photogrammétrie est utilisée pour produire des relevés 3D sur les objets. La connaissance sur ces objets provient à la fois de l'archéologie sous-marine et de la photogrammétrie. Les informations étant structurées, hiérarchisées et parfois incomparables, nous nous sommes intéressés aux bases de croyance partiellement préordonnées. Par ailleurs, l'acquisition des données peut conduire à l'apparition d'incohérence. Nous avons étendu l'approche des R-ensembles à la restauration de la cohérence. Nous avons également proposé un cadre de travail pour la révision de bases de croyance partiellement préordonnées et deux relations d'inférence lexicograhique. nous avons fourni pour ces approches une mise en oeuvre en utilisant la programmation logique avec ASP. Finalement, nous avons implanté notre méthode de restauration de la cohérence dans le contexte de VENUS et nous l'avons testé sur les relevés issus du projet
This PHD has been performed within the European VENUS project. In this context, photogrammetry is used to produced 3D survey on objects and the knowledge on studied artefacts comes from both underwater archaeology and photogrammetry. This information being structured, hierachized and sometimes incomparable, we focused on partially preordered belief bases. Data acquisition possibly leads to inconsistency. We extended the Removed Set approach to inconsistency handling. To compare subsets of formulae to remove in order to restore consistency, we introduced the lexicographic comparator. Moreover, we proposed a new framework for the revision of partially preordered belief bases and two lexicographic inference relations. We proposed an implementation stemming from ASP. Finally, we implemented our inconsistency handling method in the VENUS context and we provided an experimental study on 3D surveys of the project
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Trần, Thế Quang. "Unfolding based verification of concurrent infinite-state systems." Thesis, Bordeaux 1, 2009. http://www.theses.fr/2009BOR13832/document.

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Nous proposons une technique de dépliage pour vérifier les systèmes concurrents infinis bien structurés. Certaines propriétés d'intérêt comme la bornitude, la couverture et la terminaison sont décidables grâce à la bonne structure de ces systèmes. D'autre part, le dépliage réduit efficacement l'explosion combinatoire en exploitant l'ordre partiel entre les événements des systèmes concurrents. Nous proposons une modélisation par structure d'événements pour des systèmes bien structurés élémentaires, tels les compteurs et les files de communication. Le dépliage d'un réseau de structures d'événements étant une structure d'événements, nous proposons ensuite une approche hiérarchique à la modélisation et à la vérification des systèmes, qui préserve la bonne structure. Enfin, nous proposons une technique d'élimination des événements redondants. La mise en œuvre de notre approche dans l'outil ESU nous permet de conclure à son efficacité
We propose an unfolding technique for verifying concurrent infinite-state systems that are well-structured. Some properties of interest such as boundedness, coverability and termination are decidable thanks to the well-structure of these systems. Moreover, the unfolding effectively reduces the combinatorial explosion by exploiting the partial order between events of concurrent systems. We propose a modelization using event structures for basic well-structured systems, such as counters and communication channels. As the unfolding of a synchronized product of event structures is an event structure, we obtain a hierarchical approach to modeling as well as to verifying systems, which preserves the well-structure. Finally, we propose a technique for eliminating redundant events. The implementation of our approach in the ESU tool allows us to conclude on its efficiency
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Nguyen, Thi Van Anh. "On Partial Regularities and Monomial Preorders." Doctoral thesis, 2018. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2018062823.

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My PhD-project has two main research directions. The first direction is on partial regularities which we define as refinements of the Castelnuovo-Mumford regularity. Main results are: relationship of partial regularities and related invariants, like the a-invariants or the Castelnuovo-Mumford regularity of the syzygy modules; algebraic properties of partial regularities via a filter-regular sequence or a short exact sequence; generalizing a well-known result for the Castelnuovo-Mumford regularity to the case of partial regularities of stable and squarefree stable monomial ideals; finally extending an upper bound proven by Caviglia-Sbarra to partial regularities. The second direction of my project is to develop a theory on monomial preorders. Many interesting statements from the classical theory of monomial orders generalize to monomial preorders. Main results are: a characterization of monomial preorders by real matrices, which extends a result of Robbiano on monomial orders; secondly, leading term ideals with respect to monomial preorders can be studied via flat deformations of the given ideal; finally, comparing invariants of the given ideal and the leading term ideal with respect to a monomial preorder.
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Book chapters on the topic "Partial preorder"

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Manjunatha Prasad, K., K. S. Mohana, and Y. Santhi Sheela. "Matrix Partial Orders Associated with Space Preorder." In Combinatorial Matrix Theory and Generalized Inverses of Matrices, 195–226. India: Springer India, 2013. http://dx.doi.org/10.1007/978-81-322-1053-5_17.

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Nishizawa, Koki, Koji Yasuda, and Hitoshi Furusawa. "Preorders, Partial Semigroups, and Quantales." In Relational and Algebraic Methods in Computer Science, 237–52. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43520-2_15.

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Schwartz, Niels, and James J. Madden. "Preordered and partially ordered rings." In Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings, 21–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0093970.

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Schwartz, Niels, and James J. Madden. "Real spectra of preordered rings." In Semi-algebraic Function Rings and Reflectors of Partially Ordered Rings, 45–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0093973.

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Belabbes, Sihem, and Salem Benferhat. "Inconsistency Handling for Partially Preordered Ontologies: Going Beyond Elect." In Knowledge Science, Engineering and Management, 15–23. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-29551-6_2.

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Belabbes, Sihem, Salem Benferhat, and Jan Chomicki. "Elect: An Inconsistency Handling Approach for Partially Preordered Lightweight Ontologies." In Logic Programming and Nonmonotonic Reasoning, 210–23. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20528-7_16.

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Sérayet, Mariette, Pierre Drap, and Odile Papini. "Encoding the Revision of Partially Preordered Information in Answer Set Programming." In Lecture Notes in Computer Science, 421–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02906-6_37.

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Benferhat, Salem, and Safa Yahi. "Complexity and Cautiousness Results for Reasoning from Partially Preordered Belief Bases." In Lecture Notes in Computer Science, 817–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02906-6_70.

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"Preorders and Partial Orders." In Discrete Structures and Their Interactions, 83–106. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b15067-10.

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Conference papers on the topic "Partial preorder"

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Nguyen, Vu-Linh, Sébastien Destercke, Marie-Hélène Masson, and Eyke Hüllermeier. "Reliable Multi-class Classification based on Pairwise Epistemic and Aleatoric Uncertainty." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/706.

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We propose a method for reliable prediction in multi-class classification, where reliability refers to the possibility of partial abstention in cases of uncertainty. More specifically, we allow for predictions in the form of preorder relations on the set of classes, thereby generalizing the idea of set-valued predictions. Our approach relies on combining learning by pairwise comparison with a recent proposal for modeling uncertainty in classification, in which a distinction is made between reducible (a.k.a. epistemic) uncertainty caused by a lack of information and irreducible (a.k.a. aleatoric) uncertainty due to intrinsic randomness. The problem of combining uncertain pairwise predictions into a most plausible preorder is then formalized as an integer programming problem. Experimentally, we show that our method is able to appropriately balance reliability and precision of predictions.
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Delgrande, James. "A Preference-Based Approach to Defeasible Deontic Inference." In 17th International Conference on Principles of Knowledge Representation and Reasoning {KR-2020}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/kr.2020/33.

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In this paper we present an approach to defeasible deontic inference. Given a set of rules R expressing conditional obligations and a formula A giving contingent information, the goal is to determine the most desirable outcome with respect to this information. Semantically, the rules R induce a partial preorder on the set of models, giving the relative desirability of each model. Then the set of minimal A models characterises the best that can be attained given that A holds. A syntactic approach is also given, in terms of maximal subsets of material counterparts of rules in R, and that yields a formula that expresses the best outcome possible given that A holds. These approaches are shown to coincide, providing an analogue to a soundness and completeness result. Complexity is not unreasonable, being at the second level of the polynomial hierarchy when the underlying logic is propositional logic. The approach yields desirable and intuitive results, including for the various “paradoxes” of deontic reasoning. The approach also highlights an interesting difference in how specificity is dealt with in nonmonotonic and deontic reasoning.
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Creignou, Nadia, Adrian Haret, Odile Papini, and Stefan Woltran. "Belief Update in the Horn Fragment." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/246.

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In line with recent work on belief change in fragments of propositional logic, we study belief update in the Horn fragment. We start from the standard KM postulates used to axiomatize belief update operators; these postulates lend themselves to semantic characterizations in terms of partial (resp. total) preorders on possible worlds. Since the Horn fragment is not closed under disjunction, the standard postulates have to be adapted for the Horn fragment. Moreover, a restriction on the preorders (i.e., Horn compliance) and additional postulates are needed to obtain sensible characterizations for the Horn fragment, and this leads to our main contribution: a representation result which shows that the class of update operators captured by Horn compliant partial (resp. total) preorders over possible worlds is precisely that given by the adapted and augmented Horn update postulates. With these results at hand, we provide concrete Horn update operators and are able to shed light on Horn revision operators based on partial preorders.
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