Abstract Pythagorean fuzzy (PF) sets involving Pythagorean membership grades can befittingly manipulate inexact and equivocal information in real-life problems involving multiple criteria decision analysis (MCDA). The linear programming technique for multidimensional analysis of preference (LINMAP) is a prototypical compromising model, and it is widely used to carry on decision-making problems in many down-to-earth applications. In LINMAP, the employment of squares of Euclidean distances is a significant technique that is an effective approach to fit measurements. Taking the advantages of a newly developed Euclidean distance model on the grounds of PF sets, this paper initiates a beneficial concept of squared PF Euclidean distances and studies its valuable and desirable properties. This paper aims to establish a squared Euclidean distance (SED)-based outranking approach and develop a novel PF LINMAP methodology for handling an MCDA problem under PF uncertainty. In the SED-based outranking approach, a novel SED-based dominance index is proposed to reflect an overall balance of a PF evaluative rating between the connection and remotest connection with positive- and negative-ideal ratings, respectively. The properties of the proposed index are also analyzed to exhibit its efficaciousness in determining the dominance relations for intracriterion comparisons. Moreover, this paper derives the comprehensive dominance index to determine the overall dominance relation and defines measurements of rank consistency for goodness of fit and rank inconsistency for poorness of fit. The PF LINMAP model is formulated to seek to ascertain the optimal weight vector that maximizes the total comprehensive dominance index and minimizes the poorness of fit under consideration of the lowest acceptable level and specialized degenerate weighting issues. The practical application concerning bridge-superstructure construction methods is conducted to test the feasibility and practicability of the PF LINMAP model. Over and above that, a generalization of the proposed methodology, along with applications to green supplier selection and railway project investment, is investigated to deal with group decision-making issues. Several comparative studies are implemented to further validate its usefulness and advantages. The application and comparison results display the effectuality and flexibility of the developed PF LINMAP methodology. In the end, the directions for future research of this work are represented in the conclusion.