On uniform belief revision

Rational belief-change policies are encoded in the so-called AGM revision functions, defined in the prominent work of Alchourrón, Gärdenfors and Makinson. The present article studies an interesting class of well-behaved AGM revision functions, called herein uniform-revision operators (or UR operators, for short). Each UR operator is uniquely defined by means of a single total preorder over all possible worlds, a fact that in turn entails a significantly lower representational cost, relative to an arbitrary AGM revision function, and an embedded solution to the iterated-revision problem, at no extra representational cost. Herein, we first demonstrate how weaker, more expressive—yet, more representationally expensive—types of uniform revision can be defined. Furthermore, we prove that UR operators, essentially, generalize a significant type of belief change, namely, parametrized-difference revision. Lastly, we show that they are (to some extent) relevance-sensitive, as well as that they respect the so-called principle of kinetic consistency.

A Unifying Framework for Probabilistic Belief Revision

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an "all purpose" method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis's imaging. Importantly, p-revision subsumes all three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis' imaging all obey the basic principles of AGM revision. As well our investigation sheds light on the corresponding operation of AGM expansion in the probabilistic setting.

On the Measures of Separation of a Fuzzy Clustering

This paper tested the measures of separation of a fuzzy clustering. Over the same labeled data, Fuzzy k-Means clustering algorithm generates the first fuzzy clustering, then the proposed revision function in (6) revises it several times to generate various fuzzy partitions with different pattern recognition rates computed by (5), finally the measures of separation measure the separation of each fuzzy clustering. Experimental results on real data show that the measures of separation in literatures fail to measure the separation of a fuzzy clustering in some cases, for they argue that the fuzzy clustering with higher pattern recognition rate is less separate between clusters and worse than that with lower pattern recognition rate.

On the Measure of Compactness of Fuzzy Clustering

This paper tested the measures of compactness of fuzzy partitions. Over the same labeled data, Fuzzy k-Means clustering algorithm generates the first partition, then the proposed revision function in (7) revises it several times to generate various fuzzy partitions with different pattern recognition rates computed by (6), finally the measures of compactness measure the compactness of each fuzzy partition. Experimental results on real data show that the measures of compactness in literatures fail to measure the compactness of a fuzzy clustering in some cases, for they argue that the fuzzy clustering with higher pattern recognition rate is less compact and worse than that with lower pattern recognition rate.