Affiliations: [a] Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan
| [b] KERMIT, Department of Mathematical Modeling, Statistics and Bioinformatics, Coupure links 653, Ghent University, Ghent, Belgium
| [c] Department of Operations Research and Statistics, Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia
Correspondence:
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Corresponding author. Tahir Mahmood, Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan. E-mail: tahirbakhat@iiu.edu.pk.
Abstract: To manage ambiguity and uncertainty information in real life problems, certain intellectuals have initiated numerous modifications of fuzzy sets. But, in certain situations, the decision-makers have been neglected to take a feasible decision. For instance, when an intellectual provides information in the form of a two-dimension or type-1 fuzzy set, then the prevailing theories have been neglected. For this, in this study, we elaborated the new idea of type-2 picture fuzzy sets (T2-PFS) and their algebraic laws have been given. Moreover, by using the T2-PFS, Hamacher aggregation operators are proposed and discussed their important properties. The Minkowski sorts of measures under the T2-PFS are also initiated. In the current study, we aim to utilize the matrix game in a type-2 picture fuzzy environment. By using the proposed operators and measures based on the Hausdorff metric. The elaborated idea has been defined with the biogas-plant implementation dilemma to verify the pertinence and authenticity. Lastly, to discuss the sensitivity analysis and geometrical shown of the initiated works, certain examples are illustrated to determine the supremacy and consistency of the proposed approaches.
