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Interval Valued Spherical Fuzzy Aggregation Operators and Their Application in Decision Making Problem

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Decision Making with Spherical Fuzzy Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 392))

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Abstract

The collected data may be an interval number rather than the exact number in the process of information fusion for any real-world problem. By taking this into consideration interval numbers under interval spherical fuzzy environment have been used in this present work. To deal with vagueness, impreciseness, and uncertainty we have different environments namely fuzzy, intuitionistic fuzzy and Pythagorean fuzzy sets. All these environments are strictly following the restriction on the characteristic values and their sum. This gives the stress to the decision maker in giving preference values. Hence spherical fuzzy sets are used where the sum of the square of membership, non-membership and refusal degrees is less than or equal to 1. This condition helps the decision maker to give the preference values according to their knowledge without any limitations. Therefore, the interval valued spherical fuzzy sets, operational laws for interval valued spherical fuzzy numbers and aggregation operators with their properties are proposed. Also, the proposed aggregation operators are applied in a decision making problem to choose the best station which scrutinizes the quality of air. A further comparative study is done with the existing method to show the novelty and effectiveness of the proposed method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Hindustan Institute of Technology & Science, Chennai, 603103, India

    M. Lathamaheswari & D. Nagarajan

  2. School of Mathematics, Thapar University Patiala, Patiala, India

    Harish Garg

  3. Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn, Johor, Malaysia

    J. Kavikumar

Authors
  1. M. Lathamaheswari
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  2. D. Nagarajan
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  3. Harish Garg
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  4. J. Kavikumar
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Corresponding author

Correspondence to M. Lathamaheswari .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Faculty of Management, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Turkish Air Force Academy, National Defence University, Istanbul, Turkey

    Fatma Kutlu Gündoğdu

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Lathamaheswari, M., Nagarajan, D., Garg, H., Kavikumar, J. (2021). Interval Valued Spherical Fuzzy Aggregation Operators and Their Application in Decision Making Problem. In: Kahraman, C., Kutlu Gündoğdu, F. (eds) Decision Making with Spherical Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 392. Springer, Cham. https://doi.org/10.1007/978-3-030-45461-6_2

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