An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.

México and the United States; a study of subjects affecting their polítical, commercial and social relations, made with a view to their promotion

UANL

México, and the United States; their mutual relations and common interests 7

UANL

Upper Semicontinuous Extensions of Binary Relations.

Suzumura shows that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semi-continuous binary relation to an upper semicontinuous weak order. Jaffray proves that any asymmetric (or reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (or weak) order extension. We provide sufficient conditions for existence of upper semicontinuous extensions of consistence rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove one theorem using a further consistency property and another with an additional continuity requirement.

Consistent Relations

Consistency, a natural weakening of transitivity introduced in a seminal contribution by Suzumura (1976b), has turned out to be an interesting and promising concept in a variety of areas within economic theory. This paper summarizes its recent applications and provides some new observations in welfarist social choice and in population ethics. In particular, it is shown that the conclusion of the welfarism theorem remains true if transitivity is replaced by consistency and that an impossibility result in variable-population social-choice theory turns into a possibility if transitivity is weakened to consistency.

Les relations verticales gerees par des contrats, etude theorique et application au contrat d'electricite entre Norsk-Hydro Canada Inc. et Hydro Quebec..

Rapport de recherche

Annales de Domingo Francisco de San Anton Chimalpahin Cuauhtlehuanitzin, sixieme et septieme relations (1258-1612)

UANL

La dimension juridique des relations entre Samuel de Champlain et les Autochtones de la Nouvelle-France

Contrairement à ce qui s’est produit dans les colonies espagnoles, en Nouvelle-Fance, les Français ont privilégié le maintien de relations pacifiques avec les peuples autochtones. Même si les représentants de la couronne sont autorisés à les assujettir par la force, très rapidement, le roi exige le respect des traités conclus avec eux. Ces alliances constituent d’ailleurs la première étape d’un processus de sédentarisation et de conversion qui doit, dans l’esprit des autorités, culminer par l’assujettissement des Autochtones à la couronne. Pour l’heure, au début du XVIIe siècle, ils sont considérés comme des alliés vivant selon leurs propres coutumes. C’est pourquoi Champlain doit renoncer à appliquer le droit français dans les cas où un Français a été tué par un Autochtone, alors qu’il n’envisage même pas d’imposer ces règles quand les protagonistes sont tous autochtones.