Jonathan Lawry

A framework for linguistic modelling

A new framework for linguistic reasoning is proposed based on a random set model of the degree of appropriateness of a label. Labels are assumed to be chosen from a finite predefined set of labels and the set of appropriate labels for a value is defined as a random set-valued function from a population of individuals into the set of subsets of labels. Appropriateness degrees are then evaluated relative to the distribution on this random set where the appropriateness degree of a label corresponds to the probability that it is contained in the set of appropriate labels. This interpretation is referred to as label semantics. A natural calculus for appropriateness degrees is described which is weakly functional while taking into account the logical structure of expressions. Given this framework it is shown that a bayesian approach can be adopted in order to infer probability distributions on the underlying variable given constraints both in the form of linguistic expressions and mass assignments. In addition, two conditional measures are introduced for evaluating the appropriateness of a linguistic expression given other linguistic information.

A methodology for computing with words

Abstract An alternative interpretation of linguistic variable is introduced together with the notion of a linguistic description of a value or set of values. The latter is taken to be a fuzzy set on words where the membership values quantify the suitability of a particular word as a label for the value or values being considered. This concept is then applied to reasoning with linguistic quantifiers these being defined as linguistic descriptions of probability values. From this viewpoint linguistic quantifiers are constraints on probability values and hence using the voting model and Bayesian methods infer second order densities. In this respect such quantifiers can be view as an alternative form of imprecise probability. These ideas are then used in our proposed methodology for converting probabilistic inference rules into linguistic inference rules and a computationally cheap approximation algorithm for such rules is then introduced. The approach is illustrated in a number of worked examples using various types of rules including linguistic syllogisms and a linguistic version of Jeffreys rule. Finally a number of methods for information fusion with linguistically quantified statements are discussed.

A mass assignment theory of the probability of fuzzy events

Abstract Mass assignment theory techniques for processing uncertainty in Fril are reviewed. The notion of the probability of a fuzzy event is introduced together with the t-norm definition of conditional probabilities. The latter is then shown to be probability/possibility inconsistent. An alternative theory of conditional probabilities based on mass assignments is presented together with a number of results illustrating some intuitive properties. In particular, the mass assignment theory of conditional probabilities is shown to be probability/possibility consistent.

Generation, combination and extension of random set approximations to coherent lower and upper probabilities

Abstract Random set theory provides a convenient mechanism for representing uncertain knowledge including probabilistic and set-based information, and extending it through a function. This paper focuses upon the situation when the available information is in terms of coherent lower and upper probabilities, which are encountered, for example, when a probability distribution is specified by interval parameters. We propose an Iterative Rescaling Method (IRM) for constructing a random set with corresponding belief and plausibility measures that are a close outer approximation to the lower and upper probabilities. The approach is compared with the discrete approximation method of Williamson and Downs (sometimes referred to as the p-box), which generates a closer approximation to lower and upper cumulative probability distributions but in most cases a less accurate approximation to the lower and upper probabilities on the remainder of the power set. Four combination methods are compared by application to example random sets generated using the IRM.

An alternative approach to computing with words

An alternative theory of linguistic variables is introduced based on voting model semantics. This theory is then applied to computing with words whereby a calculus is introduced for inference from linguistic facts and rules.

Appropriateness measures : an uncertainty model for vague concepts

We argue that in the decision making process required for selecting assertible vague descriptions of an object, it is practical that communicating agents adopt an epistemic stance. This corresponds to the assumption that there exists a set of conventions governing the appropriate use of labels, and about which an agent has only partial knowledge and hence significant uncertainty. It is then proposed that this uncertainty is quantified by a measure corresponding to an agent’s subjective belief that a vague concept label can be appropriately used to describe a particular object. We then apply Bayesian networks to investigate, in the case when knowledge of labelling conventions is represented by an ordering or ranking of the labels according to their appropriateness, how measure values allocated to basic labels can be used to directly infer the appropriateness measure of compound expressions.

Uncertainty modelling for vague concepts: A prototype theory approach

An epistemic model of the uncertainty associated with vague concepts is introduced. Label semantics theory is proposed as a framework for quantifying an agents uncertainty concerning what labels are appropriate to describe a given example. An interpretation of label semantics is then proposed which incorporates prototype theory by introducing uncertain thresholds on the distance between elements and prototypes for description labels. This interpretation naturally generates a functional calculus for appropriateness measures. A more general model with distinct threshold variables for different labels is discussed and we show how different kinds of semantic dependence can be captured in this model.

A study of death by anoikis in cultured epithelial cells

Background: Epithelial cells are critically dependent upon cell‐matrix and cell‐cell adhesion for growth and survival. Anoikis is programmed cell death caused by disruption of cell‐substrate adhesion in normal epithelial cells.

A Probability-Based Approach to Comparison of Fuzzy Numbers and Applications to Target-Oriented Decision Making

In this paper, we introduce a new comparison relation on fuzzy numbers based on their alpha-cut representation and comparison probabilities of interval values. Basically, this comparison process combines a widely accepted interpretation of fuzzy sets together with the uncertain characteristics inherent in the representation of fuzzy numbers. The proposed comparison relation is then applied to the issue of ranking fuzzy numbers using fuzzy targets in terms of target-based evaluations. Some numerical examples are used to illuminate the proposed ranking technique as well as to compare with previous methods. More interestingly, according to the interpretation of the new comparison relation on fuzzy numbers, we provide a fuzzy target-based decision model as a solution to the problem of decision making under uncertainty, with which an interesting link between the decision makers different attitudes about target and different risk attitudes in terms of utility functions can be established. Moreover, an application of the proposed comparison relation to the fuzzy target-based decision model for the problem of fuzzy decision making with uncertainty is provided. Numerical examples are also given for illustration.

Longitudinal study of chemokine receptor expression on peripheral lymphocytes in multiple sclerosis: CXCR3 upregulation is associated with relapse

The interaction between chemokines and their recepto rs leads to selective recruitment of cells to foci of inflammation. C ross-sectional studies have reported significantly different expression of chemokine recepto rs C XC R3, C C R5 and C C R2 on peripheral blood lymphocytes in multiple sclerosis (MS) compared with controls. C ells expressing these receptors are likely to play a pathogenic role as suggested by studies of experimental autoimmune encephalo myelitis. A lso, immunogenetic studies of nonfunctional C C R5 recepto rs in MS patients, due to 32d deletion, demonstrated a delay in time to next relapse. The aims of this study were to detect any changes in the serial expression of chemokine recepto rs C C R2, C C R3, C C R5 and C XCR3 on peripheral blood C D4 lymphocytes from patients with MS and to correlate the changes with relapses. Upregulation of C XCR3 expression on peripheral blood C D4 lymphocytes was associated with all relapses and C C R5 expression was significantly affected with all relapses. C linical recovery, with or without intravenous methylprednisolone treatment, coincided with the return of C XC R3 towards baseline in all but one case. Fluctuation in the expression of C XC R3 and C C R5 was also significantly greater in clinically stable patients with MS compared with controls, which may be due to subclinical disease activity. These findings provide further support for the view that C XC R3 and C C R5 antagonists could have a therapeutic value in MS.