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Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures

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Abstract

In this paper, we extend the basic distance measure in picture fuzzy sets to the new measures called generalized picture distance measures and picture association measures. Some properties of these measures are examined. An application to clustering problem is given to illustrate applicability of the proposed works.

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Acknowledgments

The authors wish to thank the Editor-in-chief and anonymous reviewers for their valuable comments and suggestions. We acknowledge the Center for High Performance Computing, VNU University of Science for executing the program on the IBM 1350 cluster server.

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. VNU University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam

    Le Hoang Son

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  1. Le Hoang Son
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Correspondence to Le Hoang Son.

Additional information

This work is dedicated to Prof. Bui Cong Cuong (Institute of Mathematics, VAST) for 3-year presence of the picture fuzzy set.

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Son, L.H. Measuring analogousness in picture fuzzy sets: from picture distance measures to picture association measures. Fuzzy Optim Decis Making 16, 359–378 (2017). https://doi.org/10.1007/s10700-016-9249-5

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  • DOI: https://doi.org/10.1007/s10700-016-9249-5

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