Generalizations of semiorders: a review note

Real interval representations

A NaP-preference (necessary and possible preference) on a set A is a pair ${\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}$
 of binary relations on A such that its necessary component ${\succsim^{^{_N}} \!\!}$
 is a partial preorder, its possible component ${\succsim^{^{_P}} \!\!}$
 is a completion of ${\succsim^{^{_N}} \!\!}$
 , and the two components jointly satisfy natural forms of mixed completeness and mixed transitivity. We study additional mixed transitivity properties of a NaP-preference ${\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}$
 , which culminate in the full transitivity of its possible component ${\succsim^{^{_P}} \!\!}$
 . Interval orders and semiorders are strictly related to these properties, since they are the possible components of suitably transitive NaP-preferences. Further, we introduce strong versions of interval orders and semiorders, which are characterized by enhanced forms of mixed transitivity, and use a geometric approach to compare them to other well known preference relations.

A Genesis of Interval Orders and Semiorders: Transitive NaP-preferences

This article focuses on the monitoring of a supply chain dedicated to a mass production of strongly diversified products and more particularly in the part of this chain which contributes to the production of a set of alternate modules assembled on a work station of the assembly line. The approach of the MRP is adopted in the monitoring of that chain but the distance of the production units leads to a mixing between production to stock and production to order. The literature available on safety stock does not help in decision making. The relation that exists between frozen horizon and Order Penetration Point in MRP will be examine and the analytical relations which links planned orders of a reference to the requirements of the MPS which uses them, is established. Then we set the relations which make it possible to define, in the steady state, the quantities to produce to cope with requirements that are partially or completely random, taking into account or not the problem of quality, in order to limit the stockout risk to a predetermined level.

Laboratoire d'Analyse et Modélisation de Systèmes pour l'Aide à la Décision

This paper studies an extension of biorders that has a “frontier” between the relation and the absence of relation. This extension is motivated by a conjoint measurement problem consisting in the additive representation of ordered coverings defined on product sets of two components. We also investigate interval orders and semiorders with frontier.

/pdf/biorders-with-frontier-4xx0w06mlg.pdf

Biorders with Frontier

On the separation of in vivo relations by a biorder or a semiorder

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On the separation of in vivo relations by a biorder or a semiorder