Information Volume of Fuzzy Membership Function

Fuzzy membership function plays an important role in fuzzy set theory. However, how to measure the information volume of fuzzy membership function is still an open issue. The existing methods to determine the uncertainty of fuzzy membership function only measure the first-order information volume, but do not take higher-order information volume into consideration. To address this issue, a new information volume of fuzzy membership function is presented in this paper, which includes the first-order and the higher-order information volume. By continuously separating the hesitancy degree until convergence, the information volume of the fuzzy membership function can be calculated. In addition, when the hesitancy degree of a fuzzy membership function equals to zero, the information volume of this special fuzzy membership function is identical to Shannon entropy. Two typical fuzzy sets, namely classic fuzzy sets and intuitiontistic fuzzy sets, are studied. Several examples are illustrated to show the efficiency of the proposed information volume of fuzzy membership function

On Relations between Some Types of (α,β)-Intuitionistic Fuzzy Ideals of Ternary Semigroups

In this article, the notion of (α,β)-intuitionistic fuzzy ideals (briefly, (α,β)-IF ideals) of ternary semigroups is described using ”belong to” relation (ϵ) and “quasi-coincidence with” relation (q) connecting two objects, i.e., an intuitionistic fuzzy point (IFP, for short) and an intuitionistic fuzzy set (briefly, IFS). Throughout this paper, α∈{ϵ,q,ϵ∨q} and β∈{ϵ,q,ϵ∨q,ϵ∧q}.  The main purposes of this research are to construct the definition of (α,β)-intuitionistic fuzzy ideals of ternary semigroups and to investigate the relations between some types of these ideals. To achieve these goals, we use literature review method to study previous researches regarding (α,β)-fuzzy ideals of ternary semigroups and (α,β)-IF ideals of semigroups. As a result, we find the conditions for an IFS and an ideal of a ternary semigroup to be classified as an (α,ϵ∨q)-IF ideal of ternary semigroup. Relations between some types of (α,β)-IF ideals of a ternary semigroup are also discussed here

Leveraging the Bhattacharyya coefficient for uncertainty quantification in deep neural networks

Modern deep learning models achieve state-of-the-art results for many tasks in computer vision, such as image classification and segmentation. However, its adoption into high-risk applications, e.g. automated medical diagnosis systems, happens at a slow pace. One of the main reasons for this is that regular neural networks do not capture uncertainty. To assess uncertainty in classification, several techniques have been proposed casting neural network approaches in a Bayesian setting. Amongst these techniques, Monte Carlo dropout is by far the most popular. This particular technique estimates the moments of the output distribution through sampling with different dropout masks. The output uncertainty of a neural network is then approximated as the sample variance. In this paper, we highlight the limitations of such a variance-based uncertainty metric and propose an novel approach. Our approach is based on the overlap between output distributions of different classes. We show that our technique leads to a better approximation of the inter-class output confusion. We illustrate the advantages of our method using benchmark datasets. In addition, we apply our metric to skin lesion classification-a real-world use case-and show that this yields promising results