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A New Intuitionistic Fuzzy Entropy of Order-\(\alpha \) with Applications in Multiple Attribute Decision Making

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Proceedings of Sixth International Conference on Soft Computing for Problem Solving

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 546))

Abstract

In this paper, we have introduced a new intuitionistic fuzzy (IF) entropy called intuitionistic fuzzy entropy of order-\(\alpha \) in the settings of intuitionistic fuzzy set theory. It considers both the uncertainty and hesitancy degree of IF sets. Also, we have shown that the entropy suggested by Vlachos and Sergiadis is the particular case of the proposed entropy which does not satisfies the maximality property. Further we have proved the validity of the proposed intuitionistic fuzzy entropy. Some of the properties of the proposed entropy are also discussed and proved that the maximum and minimum values of the proposed entropy are independent of \(\alpha \). At last, application of the proposed entropy is given in multiple attribute decision making (MADM) problem. For this purpose, we have taken a case study on insurance companies.

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Authors and Affiliations

  1. Department of Mathematics, Maharishi Markandeshwar University, Mullana-Ambala, 133207, India

    Rajesh Joshi & Satish Kumar

Authors
  1. Rajesh Joshi
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  2. Satish Kumar
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Corresponding author

Correspondence to Rajesh Joshi .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India

    Kusum Deep

  2. Department of Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

  3. Department of Mathematics, National Institute of Technology, Silchar, Silchar, Assam, India

    Kedar Nath Das

  4. School of Mathematics, Thapar Institute of Engineering and Technology University, Patiala, Punjab, India

    Arvind Kumar Lal

  5. School of Mathematics, Thapar University Patiala, Patiala, Punjab, India

    Harish Garg

  6. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya K. Nagar

  7. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Roorkee, India

    Millie Pant

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Joshi, R., Kumar, S. (2017). A New Intuitionistic Fuzzy Entropy of Order-\(\alpha \) with Applications in Multiple Attribute Decision Making. In: Deep, K., et al. Proceedings of Sixth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 546. Springer, Singapore. https://doi.org/10.1007/978-981-10-3322-3_19

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  • DOI: https://doi.org/10.1007/978-981-10-3322-3_19

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3321-6

  • Online ISBN: 978-981-10-3322-3

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