Abstract
This paper presents the information set which originates from a fuzzy set on applying the Hanman-Anirban entropy function to represent the uncertainty. Each element of the information set is called the information value which is a product of the information source value and its membership function value. The Hanman filter that modifies the information set is derived by using a filtering function. Adaptive Hanman-Anirban entropy is formulated and its properties are given. It paves the way for higher form of information sets called Hanman transforms that evaluate the information source based on the information obtained on it. Based on the information set six features, Effective Gaussian Information source value (EGI), Total Effective Gaussian Information (TEGI), Energy Feature (EF), Sigmoid Feature (SF), Hanman transform (HT) and Hanman Filter (HF) features are derived. The performance of the new features is evaluated on CASIA-IRIS-V3-Lamp database using both Inner Product Classifier (IPC) and Support Vector Machine (SVM). To tackle the problem of partially occluded eyes, majority voting method is applied on the iris strips and this enables better performance than that obtained when only a single iris strip is used.
Highlights
Representing the uncertainty in the fuzzy sets conceptualized by the pioneering work of Zadeh [1] is the main theme of this work
This transform derived from the adaptive Hanman-Anirban entropy function is called the Hanman transform (HT)
As the information need not be in the desirable form, this paper shows how to modify the information sets using a filter function resulting in Hanman Filter (HF) of zero-order and the first order
Summary
Representing the uncertainty in the fuzzy sets conceptualized by the pioneering work of Zadeh [1] is the main theme of this work. As we are aware any crisp set is deemed to have zero fuzziness, finding the difference between the uncertainty and the specificity [3] of a fuzzy subset containing one and only one element is one way of measuring the uncertainty. Representing the uncertainty in the fuzzy sets by the entropy functions is another way. Most of the entropy functions were defined in the probabilistic domain as an entropy measure gives the degree of uncertainty associated with a probability distribution. The Shannon entropy function [4] defined in the probabilistic domain has the logarithmic gain function which creates problems with zero probability; so it is replaced with the exponential gain in Pal and Pal entropy function [5]. The Hanman-Anirban entropy function [6] contains polynomial exponential gain with free parameters which enable it to become a membership function
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