# Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

• Zeeshan Ali Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
• Tahir Mahmood Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
• Kifayat Ullah Department of Mathematics, Riphah International University, Lahore Campus, Pakistan
• Qaisar Khan Department of Mathematics, University of Huripur, Pakistan
Keywords: Complex interval-valued Pythagorean fuzzy sets; Generalized Geometric aggregation operators; Einstein t-norm and t-conorm; Multicriteria decision-making method

### Abstract

The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. The principle of CIVPFS is a mixture of the two separated theories such as complex fuzzy set and interval-valued Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real and unreal parts are the sub-interval of the unit interval. The superiority of the CIVPFS is that the sum of the square of the upper grade of the real part (also for an unreal part) of the duplet is restricted to the unit interval. The goal of this article is to explore the new principle of CIVPFS and its algebraic operational laws. By using the CIVPFSs, certain Einstein operational laws by using the t-norm and t-conorm are also developed. Additionally, we explore the complex interval-valued Pythagorean fuzzy Einstein weighted geometric (CIVPFEWG), complex interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (CIVPFEOWG) operators and utilized their special cases. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated operators by using the complex interval-valued Pythagorean fuzzy (CIVPF) information. To determine the consistency and reliability of the elaborated operators, we illustrated certain examples by using the explored principles. Finally, to determine the supremacy and dominance of the explored theories, the comparative analysis and graphical expressions of the developed principles are also discussed.

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Published
2021-06-09
How to Cite
Ali, Z., Mahmood, T., Ullah, K., & Khan, Q. (2021). Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management. Reports in Mechanical Engineering, 2(1), 105-134. https://doi.org/10.31181/rme2001020105t
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Articles