Transformation-Based Fuzzy Rule Interpolation With Mahalanobis Distance Measures Supported by Choquet Integral

Fuzzy rule interpolation (FRI) strongly supports approximate inference when a new observation matches no rules, through selecting and subsequently interpolating appropriate rules close to the observation from the given (sparse) rule base. Traditional ways of implementing the critical rule selection process are typically based on the exploitation of Euclidean distances between the observation and rules. It is conceptually straightforward for implementation but applying this distance metric may systematically lead to inferior results because it fails to reflect the variations of the relevance or significance levels amongst different domain features. To address this important issue, a novel transformation-based FRI approach is presented, on the basis of utilising the Mahalanobis distance metric. The new FRI method works by transforming a given sparse rule base into a coordinates system where the distance between instances of the same category becomes closer while that between different categories becomes further apart. In so doing, when an observation is present that matches no rules, the most relevant neighbouring rules to implement the required interpolation are more likely to be selected. Following this, the scale and move factors within the classical transformation-based FRI procedure are also modified by Choquet integral. Systematic experimental investigation over a range of classification problems demonstrates that the proposed approach remarkably outperforms the existing state-of-the-art FRI methods in both accuracy and efficiency

A Novel Scheme for Image Encryption Based on Piecewise Linear Chaotic Map

Abstract-Recently, the chaos based cryptographic algorithms have suggested some meaningful techniques to develop efficient image encryption schemes. In this paper, we propose a new digital image encryption scheme based on the piecewise linear chaotic map (PWLCM) in order to meet the requirements of the secure encryption. The proposed scheme is described in detail, along with the security analyses including key space analysis, sensitivity analysis, information entropy analysis and differential attack analysis. The results show that the suggested image encryption scheme has some properties desirable in a good security cryptosystem