Abstract
In this work, the new VIKOR methods are established using the generalized Pythagorean fuzzy soft sets (GPFSSs). For GPFSSs, the distance measures such as Hamming, Euclidean, and generalized are given. Further, the basic characteristics of these distance measures are examined. Fuzzy and soft sets are strong instruments for uncertainty. This strongness has been demonstrated by the GPFSS combining Pythagorean fuzzy sets and soft sets and applied to imprecise and ambiguous information. In this context, new remoteness index-based methods have been proposed, which are dissimilar from available VIKOR methods. The displaced and fixed ideals positive and negative Pythagorean fuzzy values (PFV) were defined. Thus, based on this definition, displaced positive ideal remoteness indices, negative ideal remoteness indices, and fixed positive ideal, negative ideal remoteness indices were discussed. Two different weights are used here: weights based on OF preference information and precise weights calculated with the expectation score function. The VIKOR method given here provides a different way from canonical VIKOR methods: rank candidate alternatives and determining a compromise solution based on different preference structures. The processes principles of the newly defined GPFSSs VIKOR methods are given by four algorithms. An example of these algorithms is given with the behavioral development and cognitive development of the children of Early Childhood children in the COVID-19 quarantine.