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Weighted Intuitionistic Fuzzy C-Means Clustering Algorithms

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Abstract

Atanassov intuitionistic fuzzy set (AIFS)-based C-means algorithms are successful in clustering uncertain or vague real-world datasets. The AIFS-based clustering algorithms are classified into adaptive class and non-adaptive class. An algorithm from the adaptive class computes its feature weight distribution with the help of the given dataset. On the other side, the algorithm belonging to the non-adaptive class mostly computes the feature weight distribution by employing an equally likely approach. The guarantee to reach up to the mark clustering performance is missing within this approach. Simultaneously, the performance gets deteriorated if the datasets showcase noises/irrelevant features. The irrelevant features in the datasets add to the computational cost. So, a feature reduction-equipped clustering algorithm called uni-weighted intuitionistic fuzzy C-means (uW-IFCM) is introduced in the paper. Moreover, the probabilistic weights-based adaptive clustering algorithm, namely bi-weighted probabilistic intuitionistic fuzzy C-means (bW-PIFCM) is proposed under the AIFS environment. The parametric analysis for uW-IFCM is provided to comprehend and compare its performance with bW-PIFCM, PIFCM, IFCM, and FCM algorithms. Here, an intuitionistic data fuzzification technique transforms the real-valued dataset into AIFS dataset, therefore bW-PIFCM and uW-IFCM algorithms cluster the real-valued datasets. The research proposal of Yang and Nataliani in [IEEE Transactions on Fuzzy Systems, 26(2), 817–835] motivates us to introduce a feature reduction-equipped uW-IFCM algorithm. We have considered synthetic datasets and some UCI machine learning datasets for the experimental study of uW-IFCM and bW-PIFCM. The efficacy and the precision of proposed algorithms are tested in terms of some popular benchmark indexes as well.

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Funding

The research work of the first author is funded by University Grants Commission (UGC), New Delhi, India under the grant number 19/06/2016(i)EU-V.

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  1. O. Castillo have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, South Asian University, Chanakyapuri, New Delhi, 110021, India

    Meenakshi Kaushal & Q. M. Danish Lohani

  2. Division of Graduate Studies and Research, Tijuana Institute of Technology, Mexico, Tijuana, Mexico

    Oscar Castillo

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  1. Meenakshi Kaushal
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  2. Q. M. Danish Lohani
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  3. Oscar Castillo
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Kaushal, M., Danish Lohani, Q.M. & Castillo, O. Weighted Intuitionistic Fuzzy C-Means Clustering Algorithms. Int. J. Fuzzy Syst. 26, 943–977 (2024). https://doi.org/10.1007/s40815-023-01644-5

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