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A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System

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  • Muhammad Jabir Khan

    (KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Poom Kumam

    (KMUTTFixed Point Research Laboratory, SCL 802 Fixed Point Laboratory & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Peide Liu

    (School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, China)

  • Wiyada Kumam

    (Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, Thailand)

  • Shahzaib Ashraf

    (Department of Mathematics, Abdul wali Khan University, Mardan 23200, Pakistan)

Abstract

The basic idea underneath the generalized intuitionistic fuzzy soft set is very constructive in decision making, since it considers how to exploit an extra intuitionistic fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is redefined and clarified by F. Feng. In this paper, we introduced a method to solve decision making problems using an adjustable weighted soft discernibility matrix in a generalized intuitionistic fuzzy soft set. We define the threshold functions like mid-threshold, top-bottom-threshold, bottom-bottom-threshold, top-top-threshold, med-threshold function and their level soft sets of the generalized intuitionistic fuzzy soft set. After, we proposed two algorithms based on threshold functions, a weighted soft discernibility matrix and a generalized intuitionistic fuzzy soft set and also to show the supremacy of the given methods we illustrate a descriptive example using a weighted soft discernibility matrix in the generalized intuitionistic fuzzy soft set. Results indicate that the proposed method is more effective and generalized over all existing methods of the fuzzy soft set.

Suggested Citation

  • Muhammad Jabir Khan & Poom Kumam & Peide Liu & Wiyada Kumam & Shahzaib Ashraf, 2019. "A Novel Approach to Generalized Intuitionistic Fuzzy Soft Sets and Its Application in Decision Support System," Mathematics, MDPI, vol. 7(8), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:742-:d:257325
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    References listed on IDEAS

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    1. Fuqiang Wang & Xihua Li & Xiaohong Chen, 2014. "Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, July.
    2. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
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