920 research outputs found
Strict Intuitionistic Fuzzy Distance/Similarity Measures Based on Jensen-Shannon Divergence
Being a pair of dual concepts, the normalized distance and similarity
measures are very important tools for decision-making and pattern recognition
under intuitionistic fuzzy sets framework. To be more effective for
decision-making and pattern recognition applications, a good normalized
distance measure should ensure that its dual similarity measure satisfies the
axiomatic definition. In this paper, we first construct some examples to
illustrate that the dual similarity measures of two nonlinear distance measures
introduced in [A distance measure for intuitionistic fuzzy sets and its
application to pattern classification problems, \emph{IEEE Trans. Syst., Man,
Cybern., Syst.}, vol.~51, no.~6, pp. 3980--3992, 2021] and [Intuitionistic
fuzzy sets: spherical representation and distances, \emph{Int. J. Intell.
Syst.}, vol.~24, no.~4, pp. 399--420, 2009] do not meet the axiomatic
definition of intuitionistic fuzzy similarity measure. We show that (1) they
cannot effectively distinguish some intuitionistic fuzzy values (IFVs) with
obvious size relationship; (2) except for the endpoints, there exist infinitely
many pairs of IFVs, where the maximum distance 1 can be achieved under these
two distances; leading to counter-intuitive results. To overcome these
drawbacks, we introduce the concepts of strict intuitionistic fuzzy distance
measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM),
and propose an improved intuitionistic fuzzy distance measure based on
Jensen-Shannon divergence. We prove that (1) it is a SIFDisM; (2) its dual
similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic
fuzzy entropy. Comparative analysis and numerical examples demonstrate that our
proposed distance measure is completely superior to the existing ones
Automatic leukocyte nucleus segmentation by intuitionistic fuzzy divergence based thresholding
The paper proposes a robust approach to automatic segmentation of leukocyte‟s nucleus from microscopic blood smear images under normal as well as noisy environment by employing a new exponential intuitionistic fuzzy divergence based thresholding technique. The algorithm minimizes the divergence between the actual image and the ideally thresholded image to search for the final threshold. A new divergence formula based on exponential intuitionistic fuzzy entropy has been proposed. Further, to increase its noise handling capacity, a neighborhood-based membership function for the image pixels has been designed. The proposed scheme has been applied on 110 normal and 54 leukemia (chronic myelogenous leukemia) affected blood samples. The nucleus segmentation results have been validated by three expert haematologists. The algorithm achieves an average segmentation accuracy of 98.52% in noise-free environment. It beats the competitor algorithms in terms of several other metrics. The proposed scheme with neighborhood based membership function outperforms the competitor algorithms in terms of segmentation accuracy under noisy environment. It achieves 93.90% and 94.93% accuracies for Speckle and Gaussian noises respectively. The average area under the ROC curves comes out to be 0.9514 in noisy conditions, which proves the robustness of the proposed algorithm
A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition
As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns
A New Feature Selection Method based on Intuitionistic Fuzzy Entropy to Categorize Text Documents
Selection of highly discriminative feature in text document plays a major challenging role in categorization. Feature selection is an important task that involves dimensionality reduction of feature matrix, which in turn enhances the performance of categorization. This article presents a new feature selection method based on Intuitionistic Fuzzy Entropy (IFE) for Text Categorization. Firstly, Intuitionistic Fuzzy C-Means (IFCM) clustering method is employed to compute the intuitionistic membership values. The computed intuitionistic membership values are used to estimate intuitionistic fuzzy entropy via Match degree. Further, features with lower entropy values are selected to categorize the text documents. To find the efficacy of the proposed method, experiments are conducted on three standard benchmark datasets using three classifiers. F-measure is used to assess the performance of the classifiers. The proposed method shows impressive results as compared to other well known feature selection methods. Moreover, Intuitionistic Fuzzy Set (IFS) property addresses the uncertainty limitations of traditional fuzzy set
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