A new dempster-shafer theory-based method with fuzzy targets for fuzzy sets ranking

In this paper, a new Fuzzy Set (FS) ranking method (for type-1 and interval type-2 FSs), which is based on the Dempster-Shafer Theory (DST) of evidence with fuzzy targets, is investigated. Fuzzy targets are adopted to reflect human viewpoints on fuzzy ranking. Two important measures in DST, i.e., the belief and plausibility measures, are used to rank FSs. The proposed approach is evaluated with several benchmark examples. The use of the belief and plausibility measures in fuzzy ranking are discussed and compared. We further analyze the capability of the proposed approach in fulfilling six reasonable fuzzy ordering properties as discussed in [9]-[11].

Recognition from appearance subspaces across image sets of variable scale

Linear subspace representations of appearance variation are pervasive in computer vision. In this paper we address the problem of robustly matching them (computing the similarity between them) when they correspond to sets of images of different (possibly greatly so) scales. We show that the naïve solution of projecting the low-scale subspace into the high-scale image space is inadequate, especially at large scale discrepancies. A successful approach is proposed instead. It consists of (i) an interpolated projection of the low-scale subspace into the high-scale space, which is followed by (ii) a rotation of this initial estimate within the bounds of the imposed “downsampling constraint”. The optimal rotation is found in the closed-form which best aligns the high-scale reconstruction of the low-scale subspace with the reference it is compared to. The proposed method is evaluated on the problem of matching sets of face appearances under varying illumination. In comparison to the naïve matching, our algorithm is shown to greatly increase the separation of between-class and within-class similarities, as well as produce far more meaningful modes of common appearance on which the match score is based.

Face recognition with image sets using manifold density divergence

In many automatic face recognition applications, a set of a person's face images is available rather than a single image. In this paper, we describe a novel method for face recognition using image sets. We propose a flexible, semi-parametric model for learning probability densities confined to highly non-linear but intrinsically low-dimensional manifolds. The model leads to a statistical formulation of the recognition problem in terms of minimizing the divergence between densities estimated on these manifolds. The proposed method is evaluated on a large data set, acquired in realistic imaging conditions with severe illumination variation. Our algorithm is shown to match the best and outperform other state-of-the-art algorithms in the literature, achieving 94% recognition rate on average.

Learning over sets using boosted manifold principal angles (BoMPA)

In this paper we address the problem of classifying vector sets. We motivate and introduce a novel method based on comparisons between corresponding vector subspaces. In particular, there are two main areas of novelty: (i) we extend the concept of principal angles between linear subspaces to manifolds with arbitrary nonlinearities; (ii) it is demonstrated how boosting can be used for application-optimal principal angle fusion. The strengths of the proposed method are empirically demonstrated on the task of automatic face recognition (AFR), in which it is shown to outperform state-of-the-art methods in the literature.

Learning aggregation weights from 3-tuple comparison sets

An important task in multiple-criteria decision making is how to learn the weights and parameters of an aggregation function from empirical data. We consider this in the context of quantifying ecological diversity, where such data is to be obtained as a set of pairwise comparisons specifying that one community should be considered more diverse than another. A problem that arises is how to collect a sufficient amount of data for reliable model determination without overloading individuals with the number of comparisons they need to make. After providing an algorithm for determining criteria weights and an overall ranking from such information, we then investigate the improvement in accuracy if ranked 3-tuples are supplied instead of pairs. We found that aggregation models could be determined accurately from significantly fewer 3-tuple comparisons than pairs. © 2013 IEEE.

Vector valued similarity measures for Atanassov's intuitionistic fuzzy sets

We present a new approach for defining similarity measures for Atanassov's intuitionistic fuzzy sets (AIFS), in which a similarity measure has two components indicating the similarity and hesitancy aspects. We justify that there are at least two facets of uncertainty of an AIFS, one of which is related to fuzziness while other is related to lack of knowledge or non-specificity. We propose a set of axioms and build families of similarity measures that avoid counterintuitive examples that are used to justify one similarity measure over another. We also investigate a relation to entropies of AIFS, and outline possible application of our method in decision making and image segmentation. © 2014 Elsevier Inc. All rights reserved.

Segmentation of gray scale image based on intuitionistic fuzzy sets constructed from several membership functions

Segmentation is the process of extraction of objects from an image. This paper proposes a new algorithm to construct intuitionistic fuzzy set (IFS) from multiple fuzzy sets as an application to image segmentation. Hesitation degree in IFS is formulated as the degree of ignorance (due to the lack of knowledge) to determine whether the chosen membership function is best for image segmentation. By minimizing entropy of IFS generated from various fuzzy sets, an image is thresholded. Experimental results are provided to show the effectiveness of the proposed method.