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Algebraic properties in hybrid Cosine-Jaccard measure for neutrosophic set

Authors

  • Madeleine Mei Lin Lim Sai Universiti Sains Malaysia, Malaysia.
  • Norazrizal Aswad Abdul Rahman Universiti Sains Malaysia, Malaysia.

Keywords

Hybrid cosine-Jaccard, Neutrosophic set, Similarity measures, Algebraic properties

Abstract

The recent hybrid cosine-Jaccard measure for neutrosophic sets proposed to handle uncertainty, indeterminacy, and inconsistency in the complex data more effectively. The three main properties: boundedness, symmetry, and reflexivity have been established; therefore, algebraic characteristics should be explored in depth for the establishment of advanced computational frameworks. This paper is the extension of the theoretical foundation by introducing monotonicity and a distributive-like property over weighted combinations. Mathematical proof is provided for each property, followed by numerical examples to demonstrate their validity and computational consistency. This research establishes a theoretical framework for a hybrid cosine-Jaccard measure for neutrosophic sets, facilitating its facilitating reliable implementation in intricate algebraic operations related to neutrosophic multi-criteria decision-making, clustering algorithms, and information retrieval systems. 

References

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Publication status

Accepted — production in progress