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Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems

Author

Listed:
  • Aiyared Iampan
  • Gustavo Santos García
  • Muhammad Riaz
  • Hafiz Muhammad Athar Farid
  • Ronnason Chinram
  • Basil Papadopoulos

Abstract

The linear Diophantine fuzzy set (LDFS) has been proved to be an efficient tool in expressing decision maker (DM) evaluation values in multicriteria decision-making (MCDM) procedure. To more effectively represent DMs’ evaluation information in complicated MCDM process, this paper proposes a MCDM method based on proposed novel aggregation operators (AOs) under linear Diophantine fuzzy set (LDFS). A q-Rung orthopair fuzzy set (q-ROFS), Pythagorean fuzzy set (PFS), and intuitionistic fuzzy set (IFS) are rudimentary concepts in computational intelligence, which have diverse applications in modeling uncertainty and MCDM. Unfortunately, these theories have their own limitations related to the membership and nonmembership grades. The linear Diophantine fuzzy set (LDFS) is a new approach towards uncertainty which has the ability to relax the strict constraints of IFS, PFS, and q–ROFS by considering reference/control parameters. LDFS provides an appropriate way to the decision experts (DEs) in order to deal with vague and uncertain information in a comprehensive way. Under these environments, we introduce several AOs named as linear Diophantine fuzzy Einstein weighted averaging (LDFEWA) operator, linear Diophantine fuzzy Einstein ordered weighted averaging (LDFEOWA) operator, linear Diophantine fuzzy Einstein weighted geometric (LDFEWG) operator, and linear Diophantine fuzzy Einstein ordered weighted geometric (LDFEOWG) operator. We investigate certain characteristics and operational laws with some illustrations. Ultimately, an innovative approach for MCDM under the linear Diophantine fuzzy information is examined by implementing suggested aggregation operators. A useful example related to a country’s national health administration (NHA) to create a fully developed postacute care (PAC) model network for the health recovery of patients suffering from cerebrovascular diseases (CVDs) is exhibited to specify the practicability and efficacy of the intended approach.

Suggested Citation

  • Aiyared Iampan & Gustavo Santos García & Muhammad Riaz & Hafiz Muhammad Athar Farid & Ronnason Chinram & Basil Papadopoulos, 2021. "Linear Diophantine Fuzzy Einstein Aggregation Operators for Multi-Criteria Decision-Making Problems," Journal of Mathematics, Hindawi, vol. 2021, pages 1-31, July.
    • Handle: RePEc:hin:jjmath:5548033
    DOI: 10.1155/2021/5548033
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    Cited by:

    1. Z. K. Mohammed & A. A. Zaidan & H. B. Aris & Hassan A. Alsattar & Sarah Qahtan & Muhammet Deveci & Dursun Delen, 2024. "Bitcoin network-based anonymity and privacy model for metaverse implementation in Industry 5.0 using linear Diophantine fuzzy sets," Annals of Operations Research, Springer, vol. 342(2), pages 1193-1233, November.
    2. Muhammad Riaz & Hafiz Muhammad Athar Farid & Weiwei Wang & Dragan Pamucar, 2022. "Interval-Valued Linear Diophantine Fuzzy Frank Aggregation Operators with Multi-Criteria Decision-Making," Mathematics, MDPI, vol. 10(11), pages 1-36, May.
    3. Anam Habib & Zareen A. Khan & Muhammad Riaz & Dragan Marinkovic, 2023. "Performance Evaluation of Healthcare Supply Chain in Industry 4.0 with Linear Diophantine Fuzzy Sine-Trigonometric Aggregation Operations," Mathematics, MDPI, vol. 11(12), pages 1-29, June.
    4. Ibtesam Alshammari & Mani Parimala & Cenap Ozel & Muhammad Riaz & Rania Kammoun, 2022. "New MCDM Algorithms with Linear Diophantine Fuzzy Soft TOPSIS, VIKOR and Aggregation Operators," Mathematics, MDPI, vol. 10(17), pages 1-22, August.
    5. Muhammad Riaz & Hafiz Muhammad Athar Farid & Jurgita Antucheviciene & Gülay Demir, 2023. "Efficient Decision Making for Sustainable Energy Using Single-Valued Neutrosophic Prioritized Interactive Aggregation Operators," Mathematics, MDPI, vol. 11(9), pages 1-29, May.

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