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Picture Fuzzy Maclaurin Symmetric Mean Operators and Their Applications in Solving Multiattribute Decision-Making Problems

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  • Kifayat Ullah

Abstract

To evaluate objects under uncertainty, many fuzzy frameworks have been designed and investigated so far. Among them, the frame of picture fuzzy set (PFS) is of considerable significance which can describe the four possible aspects of expert’s opinion using a degree of membership (DM), degree of nonmembership (DNM), degree of abstinence (DA), and degree of refusal (DR) in a certain range. Aggregation of information is always challenging especially when the input arguments are interrelated. To deal with such cases, the goal of this study is to develop the notion of the Maclaurin symmetric mean (MSM) operator as it aggregates information under uncertain environments and considers the relationship of the input arguments, which make it unique. In this paper, we studied the theory of MSM operators in the layout of PFSs and discussed their applications in the selection of the most suitable enterprise resource management (ERP) scheme for engineering purposes. We developed picture fuzzy MSM (PFMSM) operators and investigated their validity. We developed the multiattribute decision-making (MADM) algorithm based on the PFMSM operators to examine the performance of the ERP systems using picture fuzzy information. A numerical example to evaluate the performance of ERP systems is studied, and the effects of the associated parameters are discussed. The proposed aggregated results using PFMSM operators are found to be reliable as it takes into account the interrelationship of the input information, unlike traditional aggregation operators. A comparative study of the proposed PFMSM operators is also studied.

Suggested Citation

  • Kifayat Ullah, 2021. "Picture Fuzzy Maclaurin Symmetric Mean Operators and Their Applications in Solving Multiattribute Decision-Making Problems," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-13, October.
    • Handle: RePEc:hin:jnlmpe:1098631
    DOI: 10.1155/2021/1098631
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    Cited by:

    1. Hari Darshan Arora & Anjali Naithani, 2022. "Logarithmic similarity measures on Pythagorean fuzzy sets in admission process," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 5-24.
    2. Majed Albaity & Tahir Mahmood, 2022. "Medical Diagnosis and Pattern Recognition Based on Generalized Dice Similarity Measures for Managing Intuitionistic Hesitant Fuzzy Information," Mathematics, MDPI, vol. 10(15), pages 1-15, August.
    3. Areeba Naseem & Kifayat Ullah & Maria Akram & Darko Božanić & Goran Ćirović, 2022. "Assessment of Smart Grid Systems for Electricity Using Power Maclaurin Symmetric Mean Operators Based on T-Spherical Fuzzy Information," Energies, MDPI, vol. 15(21), pages 1-25, October.
    4. Mujab Waqar & Kifayat Ullah & Dragan Pamucar & Goran Jovanov & Ðordje Vranješ, 2022. "An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators," Energies, MDPI, vol. 15(11), pages 1-23, May.
    5. Tahir Mahmood & Ubaid ur Rehman & Zeeshan Ali & Muhammad Aslam & Ronnason Chinram, 2022. "Identification and Classification of Aggregation Operators Using Bipolar Complex Fuzzy Settings and Their Application in Decision Support Systems," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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