We propose a new data mining approach in ranking documents based on the concept of cone-based generalized inequalities between vectors. A partial ordering between two vectors is made with respect to a proper cone and thus learning the preferences is formulated as learning proper cones. A pairwise learning-to-rank algorithm (ConeRank) is proposed to learn a non-negative subspace, formulated as a...

In this paper, we propose a new distributed heap-based data structure called Cone. Cone maintains an ordering of key values in a distributed fashion, and can support queries of the form, “Find resources of size .” Cone can be built on any routing substrate as long as the substrate supports longest prefix match-based lookups. We describe the Cone data structure, the operations it supports, and i...

Scalarization of the multiobjective programming problems with fuzzy coefficients using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Since the set of all fuzzy numbers can be embedded into a normed space, this motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to evaluate the multiobjective pr...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...

Recently Kazama and Yokoi (arXiv:0801.1561 [hep-th]) have used a phase-space method to study the Virasoro algebra of type IIB superstring theory in the maximally supersymmetric R-R plane wave background in a semi-light-cone gauge. Two types of normal ordering have been considered, namely “phase space normal ordering” (PNO) and “massless normal ordering” (MNO). The second one, which is the right...

Abstract In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) preordered by a not necessarily solid (and pointed) convex cone. It well-known that there are many examples ordering cone has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim consider Pareto-type solu...

We establish that for every computably enumerable (c.e.) Turing degree b, the upper cone of c.e. Turing degrees determined by b is the degree spectrum of the successor relation of some computable linear ordering. This follows from our main result, that for a large class of linear orderings, the degree spectrum of the successor relation is closed upward in the c.e. Turing degrees.

Let A be a uniformly complete almost f -algebra and a natural number p ∈ {3, 4, . . . }. Then Πp(A) = {a1 . . . ap; ak ∈ A, k = 1, . . . , p} is a uniformly complete semiprime f -algebra under the ordering and multiplication inherited from A with Σp(A) = {a; 0 ≤ a ∈ A} as positive cone.