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Multicriteria decision-making method under the complex Pythagorean fuzzy environment

Author

Listed:
  • Madad Khan

    (COMSATS University Islamabad, Abbottabad Campus)

  • Inam Ul Haq

    (COMSATS University Islamabad, Abbottabad Campus)

  • Muhammad Zeeshan

    (COMSATS University Islamabad, Islamabad Campus
    The University of Agriculture)

  • Saima Anis

    (COMSATS University Islamabad, Abbottabad Campus)

  • Muhammad Bilal

    (COMSATS University Islamabad, Abbottabad Campus)

Abstract

The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from the unit circle in the plane, i.e., in the form of a complex number instead of [0,1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the further development of the theory of complex Pythagorean fuzzy sets (CPFSs) has been discussed. Some new operations on CPFSs, such as bounded difference, disjoint sum, disjunctive sum, probabilistic sum, bold sum, bold intersection, s-norm and t-norm have been proposed. The distance of two CPFSs has been proposed. This distance measure is then used to define $$\eta $$ η -equalities of CPFSs. Moreover, we define some new notions for the multicriteria decision-making (MCDM) problems such as the CPF decision-making matrix, CPF $$\max $$ max and $$\min $$ min decision-making matrix, and the distance measure between CPF $$\max $$ max and $$\min $$ min decision-making matrices. An MCDM method has been developed on the proposed novel notions. A real-life example demonstrates that the MCDM method developed in the paper can be utilized to deal with problems of uncertainty. Further, the comparative study of CPFSs with complex intuitionistic fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, complex fuzzy sets, and fuzzy sets is established.

Suggested Citation

  • Madad Khan & Inam Ul Haq & Muhammad Zeeshan & Saima Anis & Muhammad Bilal, 2022. "Multicriteria decision-making method under the complex Pythagorean fuzzy environment," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 49(4), pages 415-434, December.
    • Handle: RePEc:spr:decisn:v:49:y:2022:i:4:d:10.1007_s40622-023-00332-5
    DOI: 10.1007/s40622-023-00332-5
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    References listed on IDEAS

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    1. Sahadeb Sarkar & Anirban Banerjee, 2016. "Measuring batting consistency and comparing batting greats in test cricket: innovative applications of statistical tools," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 43(4), pages 365-400, December.
    2. Shankha Shubhra Goswami & Dhiren Kumar Behera, 2021. "Evaluation of the best smartphone model in the market by integrating fuzzy-AHP and PROMETHEE decision-making approach," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 48(1), pages 71-96, March.
    3. Monika Dhochak & Anil Kumar Sharma, 2016. "Using interpretive structural modeling in venture capitalists’ decision-making process," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 43(1), pages 53-65, March.
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