Multicriteria decision-making method under the complex Pythagorean fuzzy environment

Madad Khan (), Inam Ul Haq (), Muhammad Zeeshan (), Saima Anis () and Muhammad Bilal ()
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Madad Khan: COMSATS University Islamabad, Abbottabad Campus
Inam Ul Haq: COMSATS University Islamabad, Abbottabad Campus
Muhammad Zeeshan: COMSATS University Islamabad, Islamabad Campus
Saima Anis: COMSATS University Islamabad, Abbottabad Campus
Muhammad Bilal: COMSATS University Islamabad, Abbottabad Campus

DECISION: Official Journal of the Indian Institute of Management Calcutta, 2022, vol. 49, issue 4, No 5, 415-434

Abstract: 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.

Keywords: Complex Pythagorean fuzzy set; Operations on complex Pythagorean fuzzy set; Decision-making matrices; Decision-making method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s40622-023-00332-5

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