We consider a multicriteria sorting procedure based on a majority rule, called MR-Sort. This procedure allows to sort each object of a set, evaluated on multiple criteria, in a category selected among a set of pre-defined and ordered categories. With MR-Sort, the ordered categories are separated by profiles which are vectors of performances on the different attributes. Using the MR-Sort rule, a...

In this paper, we study linear rewriting systems modulo a set of algebraic axioms. We introduce the structure (3,2)-polygraph as presentation category enriched in categories, (called (2,2)-category), by system symbolic computation method order to compute bases for vector spaces 2-cells these categories. particular, case pivotal 2-categories using isotopy relations given biadjunctions on 1-cells...

We discuss regression models for ordered responses, such as ratings of bonds, schooling attainment, or measures of subjective well-being. Commonly used models in this context are the ordered logit and ordered probit regression models. They are based on an underlying latent model with single index function and constant thresholds. We argue that these approaches are overly restrictive and preclud...

Modal logic is extended by partially ordering the modalities. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The partial order does not conflict with type of modality (K, S4, etc.) although this paper will concentrate on S4 since partially ordered S4 systems appear to be numerous. The partially-ordered norma...

Simulation methods were used to generate 1,000 experiments, each with 3 treatments and 10 experimental units/treatment, in completely randomized (CRD) and randomized complete block designs. Data were counts in 3 ordered or 4 nominal categories from multinomial distributions. For the 3-category analyses, category probabilities were 0.6, 0.3, and 0.1, respectively, for 2 of the treatments, and 0....

The question that serves as the title is to be understood in the context of Quillen model categories: having fixed the category of models and the subcategory of weak equivalences, how much ambiguity is there in finding suitable fibration and cofibration classes? Already for simplicial sets, infinitely many different subclasses of the monomorphisms can serve as cofibrations (with the usual weak ...

Given a category C and directed partially ordered set J, certain proJ-C on inverse systems in is constructed such that the ordinary pro-category pro-C most special case of singleton J ? {1}. Further, known pro*-category pro*-C becomes proN-C. Moreover, given pro-reflective pair (C, D), J-shape ShJ(C, D) corresponding functor SJ are which, mentioned cases, become well ones. Among several importa...

This article uses latent structure analysis to model ordered category ratings by multiple experts on the appropriateness of indications for the medical procedure carotid endarterectomy. The statistical method used is a form of located latent class analysis, which combines elements of latent class and latent trait analysis. It assumes that treatment indications fall into distinct latent classes,...

Directed Algebraic Topology is a recent field, deeply linked with ordinary and higher dimensional Category Theory. A 'directed space', e.g. an ordered topological space, has directed homotopies (generally non reversible) and fundamental n-categories (replacing the fundamental ngroupoids of the classical case). Finding a simple model of the latter is a non-trivial problem, whose solution gives r...

Given a poset P , the set Γ(P ) of all Scott closed sets ordered by inclusion forms a complete lattice. A subcategory C of Posd (the category of posets and Scott-continuous maps) is said to be Γ-faithful if for any posets P and Q in C, Γ(P ) ∼= Γ(Q) implies P ∼= Q. It is known that the category of all continuous dcpos and the category of bounded complete dcpos are Γ-faithful, while Posd is not....