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A Novel ( R , S )-Norm Entropy Measure of Intuitionistic Fuzzy Sets and Its Applications in Multi-Attribute Decision-Making

Author

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  • Harish Garg

    (School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India)

  • Jaspreet Kaur

    (School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, Punjab, India)

Abstract

The objective of this manuscript is to present a novel information measure for measuring the degree of fuzziness in intuitionistic fuzzy sets (IFSs). To achieve it, we define an ( R , S ) -norm-based information measure called the entropy to measure the degree of fuzziness of the set. Then, we prove that the proposed entropy measure is a valid measure and satisfies certain properties. An illustrative example related to a linguistic variable is given to demonstrate it. Then, we utilized it to propose two decision-making approaches to solve the multi-attribute decision-making (MADM) problem in the IFS environment by considering the attribute weights as either partially known or completely unknown. Finally, a practical example is provided to illustrate the decision-making process. The results corresponding to different pairs of ( R , S ) give different choices to the decision-maker to assess their results.

Suggested Citation

  • Harish Garg & Jaspreet Kaur, 2018. "A Novel ( R , S )-Norm Entropy Measure of Intuitionistic Fuzzy Sets and Its Applications in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 6(6), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:6:p:92-:d:149790
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    References listed on IDEAS

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    1. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
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    Cited by:

    1. Li Li & Hegong Lei & Jun Wang, 2020. "Q -Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making," Mathematics, MDPI, vol. 8(9), pages 1-34, September.

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