Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

Multiplication and comultiplication of beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the analytical product and coproduct of beta probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions. (C) 2004 Elsevier Inc. All rights reserved.

The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

Detecting and sorting targeting peptides wtih neural networks and support vector machines

This paper presents a composite multi-layer classifier system for predicting the subcellular localization of proteins based on their amino acid sequence. The work is an extension of our previous predictor PProwler v1.1 which is itself built upon the series of predictors SignalP and TargetP. In this study we outline experiments conducted to improve the classifier design. The major improvement came from using Support Vector machines as a "smart gate" sorting the outputs of several different targeting peptide detection networks. Our final model (PProwler v1.2) gives MCC values of 0.873 for non-plant and 0.849 for plant proteins. The model improves upon the accuracy of our previous subcellular localization predictor (PProwler v1.1) by 2% for plant data (which represents 7.5% improvement upon TargetP).