In this chapter, we examine several issues for ordering or partially ordering elements of hyper-power sets involved in the DSmT. We will show the benefit of some of these issues to obtain a nice and interesting structure of matrix representation of belief functions. 3.

Peskun ordering is a partial ordering defined on the space of transition matrices of discrete time Markov chains. If the Markov chains are reversible with respect to a common stationary distribution π, Peskun ordering implies an ordering on the asymptotic variances of the resulting Markov chain Monte Carlo estimators of integrals with respect to π. Peskun ordering is also relevant in the framew...

Most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. For making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. In line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

A well-partial-ordering is a well-founded ordering with no infinite antichain. In other words, every ordering extending Θ is still well founded. So Higman’s lemma provides a syntactic criterion for the definition of well-founded orderings on strings. Let us mention the Knuth–Bendix ordering, the recursive path ordering, and the polynomial orderings. What concerns us is the expressiveness of str...

One of the central issues in Arti cial Intelligence (AI) in general|and in the area of knowledge representation and reasoning in particular|is common sense reasoning. This includes logics of knowledge and belief, non-monotonic reasoning, truth-maintenance and belief revision. Within these elds the notion of a consistent belief state is the crucial one. Additionally, there is a growing interest ...

A partial ordering P is chain-Ramsey if, for every natural number n and every coloring of the n-element chains from P in finitely many colors, there is a monochromatic subordering Q isomorphic to P. Chain-Ramsey partial orderings stratify naturally into levels. We show that a countably infinite partial ordering with finite levels is chain-Ramsey if and only if it is biembeddable with one of a c...

In this paper, we reconsider the problem of deciding whether one probability distribution is more informative (in the sense of representing a less indeterminate situation) than another one. Instead of using well-established information measures such as the Shannon entropy, however, we take up the idea of comparing probability distributions in a qualitative way. More specifically, we focus on a ...

In many practical applications, multiple interrelated tasks must be accomplished in sequential order through user interactions with multiple retrieval, classification and recommendation systems. The ordering of the tasks may have a significant impact on the overall utility (or performance); hence optimal ordering of tasks is desirable. However, manual specification of near-optimal ordering is o...

The problem of allocating maxmin rates with minimum rate constraints for connection-oriented networks is considered. This paper proves that the convergence of maxmin rate allocation satisfies a partial ordering in the bottleneck links. This partial ordering leads to a tighter lower bound for the convergence time for any maxmin protocol. An optimally fast maxmin rate allocation protocol called t...

The notion of “similarity” as defined in this paper is essentially a generalization of the notion of equivalence. In the same vein, a fuzzy ordering is a generalization of the concept of ordering. For example, the relation x *y (x is much larger than y) is a fuzzy linear ordering in the set of real numbers. More concretely, a similarity relation, S, is a fuzzy relation which is reflexive, symme...