This manuscript provides an advanced mathematical model for the censuses process to reduce the drawbacks of the existing methods. From the living ideas of m-polar fuzzy set (MPFS) and Pythagorean fuzzy set (PFS), we establish a novel concept of Pythagorean m-polar fuzzy set (PMPFS). We introduce some fundamental operations on Pythagorean m-polar fuzzy sets and explain these concepts with the help of illustrations. With this novel perspective, we build up modified forms of Dombi’s aggregation operators named as Pythagorean m-polar fuzzy Dombi weighted arithmetic average (PMPFDWAA) operator and Pythagorean m-polar fuzzy Dombi weighted geometric average (PMPFDWGA) operator. We discuss certain properties of the proposed operators based on Pythagorean m-polar fuzzy numbers (PMPFNs). Mathematical modeling on real world problems often implicate multi-factors, multi-attributes and multi-polar information. We discuss a case study for the censuses process to elaborate the proposed algorithm for multi-criteria decision-making (MCDM). We also discuss how the drawbacks of existing methods can be handled by applying this novel perspective. Lastly, we present a comparative analysis, validity of proposed algorithm, influence of operational parameter, convergence and sensitivity analysis to indicate the flexibility and advantages of the proposed method.
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