Independence concepts in evidence theory

We study three conditions of independence within evidence theory framework. The first condition refers to the selection of pairs of focal sets. The remaining two ones are related to the choice of a pair of elements, once a pair of focal sets has been selected. These three concepts allow us to formalize the ideas of lack of interaction among variables and among their (imprecise) observations. We illustrate the difference between both types of independence with simple examples about drawing balls from urns. We show that there are no implication relationships between both of them. We also study the relationships between the concepts of “independence in the selection” and “random set independence”, showing that they cannot be simultaneously satisfied, except in some very particular cases.     

A theorem in combinatorial matrix theory

Let Z be a matrix of order n, and suppose that the elements of Z consist of only two elements x and y, which are elements of a field F. We call Z an (x,y)-matrix over F. In this paper we study the matrix equation ZEZ^T = D+λJ, where Z is a nonsingular (x,y)-matrix over F, Z^T is the transpose of Z, D and E are nonsingular diagonal matrices, J is the matrix of 1's and λ is an element of F. Our main theorem shows that the column sums of Z are severely restricted. This result generalizes a number of earlier investigations that deal with symmetric block designs and related configurations. The problems that emerge are of interest from both a combinatorial and a matrix theoretic point of view.     

Reliability concepts under the theory of evidence

This paper presents an approach to reliability theory from the point of view of the theory of evidence. The basic assumption is that the time to failure (life) of an equipment is a variable characterized by means of an evidence on the real line, instead of a probability distribution (the classical model).Firstly some concepts of Dempster-Shafer's theory of evidence for a non-necessarily finite set are given. Then the fundamental concepts under the formulation of Dempster-Shafer's theory are introduced.     

Remarks on some basic concepts in the KKM theory

In the KKM theory, some authors adopt the concepts of the compact closure (ccl), compact interior (cint), transfer compactly closed-valued multimap, transfer compactly l.s.c. multimap, and transfer compactly local intersection property, respectively, instead of the closure, interior, closed-valued multimap, l.s.c. multimap, and possession of a finite open cover property. In this paper, we show that such adoption is inappropriate and artificial. In fact, any theorem with a term with “transfer” attached is equivalent to the corresponding one without “transfer”. Moreover, we can invalidate terms with “compactly” attached by giving a finer topology on the underlying space. In such ways, we obtain simpler formulations of KKM type theorems, Fan-Browder type fixed point theorems, and other results in the KKM theory on abstract convex spaces.     

Number theory of matrix semigroups

Unlike factorization theory of commutative semigroups which are well-studied, very little literature exists describing factorization properties in noncommutative semigroups. Perhaps the most ubiquitous noncommutative semigroups are semigroups of square matrices and this article investigates the factorization properties within certain subsemigroups of M_n(Z), the semigroup of n×n matrices with integer entries. Certain important invariants are calculated to give a sense of how unique or non-unique factorization is in each of these semigroups.     

Some applications of optimization in matrix theory

We apply a recent characterization of optimality for the abstract convex program with a cone constraint to three matrix theory problems: (1) a generalization of Farkas's lemma; (2) paired duality in linear programming over cones; (3) a constrained matrix best approximation problem. In particular, these results are not restricted to polyhedral or closed cones.     

The ultrametric correlation matrix for modelling hierarchical latent concepts

Advances in Data Analysis and Classification - Many relevant multidimensional phenomena are defined by nested latent concepts, which can be represented by a tree-structure supposing a hierarchical...     

New concepts in neutrosophic graphs with application

A neutrosophic set is a generalization of an intuitionistic fuzzy set. Neutrosophic models give more flexibility, precisions and compatibility to the system as compared to intuitionistic fuzzy models. In this research study, we apply the concept of neutrosophic sets to graphs and discuss certain concepts of single-valued neutrosophic graphs. We illustrate the concepts by several examples. We investigate some interesting properties. We describe an application of single-valued neutrosophic graph in decision making process. We also present the procedure of our proposed method as an algorithm.     

On weaker forms for concepts in theory of topological groupoids

In this paper, we investigate the topologically weak concepts of topological groupoids by giving the concepts of α-topological groupoid and α-topological subgroupoid. Furthermore, we show the role of the density condition to allow α-topological subgroupoid inherited properties from α-topological groupoid and the irresoluteness property for the structure maps in α-topological groupoid is studied. We also give some results about the fibers of α-topological groupoids.     

Averages of characteristic polynomials in random matrix theory

We compute averages of products and ratios of characteristic polynomials associated with orthogonal, unitary, and symplectic ensembles of random matrix theory. The Pfaffian/determinantal formulae for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and their bulk scaling limits are deduced from these formulae by a simple computation. We employ a discrete approximation method: the problem is solved for discrete analogues of random matrix ensembles originating from representation theory, and then a limit transition is performed. Exact Pfaffian/determinantal formulae for the discrete averages are proven using standard tools of linear algebra; no application of orthogonal or skew‐orthogonal polynomials is needed. © 2005 Wiley Periodicals, Inc.     

A new look at some basic concepts in arbitrage pricing theory

The notion of No Free Lunch with Vanishing Risk (or NFLVR in short) w.r.t. admissible strategies depends on the choice of numeraire. Yan introduced the notion of allowable strategy and showed that condition of NFLVR w.r.t. allowable strategies is independent of the choice of numeraire and is equivalent to the existence of an equivalent martingale measure for the deflated price process. In this paper we establish a version of the Kramkov's optional decomposition theorem in the setting of equivalent martingale measures. Based on this theorem, we have a new look at some basic concepts in arbitrage pricing theory: superhedging, fair price, attainable contingent claims, complete markets and etc.